🏠 No Place Like ~

      • Algos when inputs are biased
      • Allocation Problem
      • Fair Division via Quantile Share
      • Fairly Allocating Goods, Chores and Mixed
      • FSTTCS Talks - Fairness
      • Matching with Fairness Constraints
      • Welfare Maximisation
      • Welfare Maximization - Provisioning Public Projects
        • Drawing 2025-01-07 12.06.37.excalidraw
      • A class of rational trace relation closed under composition
      • A generalized quantum braching program
      • Acyclic Petri and Workflow Nets with Resets
      • Algorithms in the presence of Biased Inputs
      • bandwidth of Timed Automata
      • Causal Ingerence
      • Fitting Manifolds to data in presence of noise
      • From Concept Learning to SAT-Based Invariant Inference
      • Languages given by Finite Automata over the Unary Alphabet
      • Measuring Complexity
      • Random Path
      • Reachability Games and Friends
      • Regular Separators for VASS Coverability Languages
        • 0-Atlas
        • Algebraic Automata Theory
        • Category Theory
        • Complexity Theory
        • Concurrent Programming
        • Conformance Checking
        • Data Structures
        • Descriptive Complexity Theory
        • Finite Model Theory
        • Games on Graphs
        • Homotopy Type Theory
        • IFPL Note Order
        • Independence of CH - Dana Scott
        • Infinite State Verification
        • Intro to Martingales
        • Logic
        • Logic, Automata and Games
        • Measure Theoretic Probability
        • Model Repair and Conformance Checking of Time Aware Models (MOC)
        • Module Theory
        • Revisiting Complexity of First-Order and Monadic-Second-Order Logic
        • Ring Theory
        • Set Theory
        • Software Verification and Analysis
        • Static Analysis
        • Topics in Algorithms
        • Topology via Logic
        • Undecidability in Algebra and Topology
        • Weighted Automata and Transducers
        • (Weighted) Vertex Cover using LP
        • + is epxressible in FO(BIT, <)
        • 1-Forms
        • 2-Categories
        • 2-Way DFA
        • 2DFAs are equivalent to DFAs
        • 17th Jan LAG lecture
        • 21st Nov Class Dump AAT
        • 22 Oct AAT
        • 24th October Classwork
        • 25th October stuff
        • 29th LP Notes
        • 2023-04-11
        • 2023-04-13
        • A better Axiom of Choice for Type Theory
        • A Categorical notion of Equivalence Relation
        • A complete, locally small category with a jointly weakly initial set of objects has an initial object
        • A Fiberwise Transformation is an Equivalence if its Total is an Equivalence
        • A functor admits a left adjoint iff all its comma categories have an initial object
        • A Language if Regular iff its Characteristic Function is regular
        • A locally small, complete category with a small coseparator and intersections of all collections of subobjects has an initial object
        • A More Efficient Method for Petri Net Coverability
        • A natural isomorphism between diagrams induces an isomorphism between limits and colimits
        • A Poset is a complete and cocomplete category iff it is a complete lattice
        • A Proof System for FOL
        • A Simple Example - cat theory 1
        • Abelian Groups
        • Absoluteness of Formulas
        • AC0
        • Acyclicity of Graphs is Definable in LFP
        • Adal week 3
        • Addition is Associative (Type Theory)
        • Adjacency Algebra of a Graph
        • Adjoint Functor Theorem for locally presentable categories
        • Adjoints of Inclusion functor from Ring to Rng
        • Adjunction of Bifunctors
        • Adjunctions
        • Adjunctions in Functor Categories
        • Adjunctions in Posets
        • Affirmative and Refutative Assertions
        • Alg3 class
        • Algebraic Classification of Recognizable functions
        • Algebraic Closure
        • Algebraic Extension
        • Algebraic Integers
        • Algorithm for Arborescence
        • Algorithm for Finding the Weight of a Word
        • Algorithmic Coding Theory Lec 1
        • Almost All Automorphism Groups are Trivial
        • Almost certain model checking
        • Alt
        • Alternating Finite Automaton
        • Alternating Timed Automata
        • Alternating Turing Machine
        • Amdahl's Law
        • Analytic Function
        • Anderson's Lock
        • Another way to Complement a Büchi Autromata
        • Any Category with Coproducts and Coequalizers is Cocomplete, with Products and Equalizers is Complete
        • Any category with Pullback and a terminal object has all finite limits, with pushouts and an initial object has all finite colimits
        • Any Equivalence can be promoted to an Adjunction
        • Aperiodic Languages are Star Free Regular
        • Aperiodic Monoids recognize all FO Definable Languages
        • Application in Error Correcting Codes
        • Application of Static Analysis
        • Applications of Error Correcting Codes
        • Approximation Algorithms
        • APX (Complexity Class)
        • Arborescence
        • Arc-Transitivity and diameter
        • Arc-Transitivity and Girth Relation
        • Arc-Transitivity of a Graph
        • Arden's Lemma
        • Arenas for Games on Graphs
        • Arithmetic Operators are Definable in LFP
        • Arrow Type
        • Ascending Chain Condition
        • Associates in Rings
        • Asymmetric Graphs
        • Atomic Types
        • Atomization of Programs
        • Automorphism Group of a Graph
        • Autonomous System
        • Axiom of Choice and its Variants
        • Axiom of Constructibility
        • Axioms for Higher Order Theory of Reals
        • Axioms of ZFC
        • Axioms Satisfied in M[G]
        • Backoff Lock
        • Banach-Mazur Games
        • Based Path Induction
        • Bases for a topology
        • Basic Feasible Solution
        • Basic ways to prove things using coq
        • Bi-invertible Maps
        • Big Software Fails
        • Bijective Ehrenfeucht-Fraïssé Game
        • Binary Heaps
        • Binomial Heaps
        • Bipartite Expander Graphs
        • Bipartite Graph Perfect Matching
        • BIT is expressible in FO(+, *)
        • Block-Graph Theory
        • Boolean Algebra
        • Boolean Circuits
        • Boolean Type
        • Borel Sigma Field
        • Borel's Law of Large Numbers
        • Borsuk Ulam Theorem
        • Boruvka's Algorithm
        • Both Directions of Half Adjoints are Logically Equivalent
        • Bounded Number of Degrees Property
        • Bounded Wait-freeness
        • BPP Complexity Class
        • Britton's Lemma
        • Brouwer's Fixed Point Theorem
        • Büchi Automata
        • Büchi Automata for Linear Temporal Logic
        • Büchi Automata for Monadic Second Order Logic
        • Building of Assignment Tester
        • Burnside's Lemma
        • Calc - Problem Session - 7 Oct
        • Calculus Assignment
        • Caley Graphs
        • Can there be sparse sets that are NP-hard?
        • Cana Assignment 4
        • CANA-HW-4
        • CANA-HW-5
        • Cannonical Decomposition of Module Homomorphisms
        • Cannonical Decomposition of Ring Homomorphisms
        • Cardinal Arithmetic
        • Cardinality of a small category
        • Cardinals
        • Cardinals Pre-reqs
        • Cartesian Closed Category
        • Cat and CAT are complete and Cocomplete
        • Categorization of Equivalent Categories
        • Category
        • Category of Abelian Groups is closed
        • Category of Compactly Generated Hausdorff Spaces is CCC
        • Category of Modules
        • Category Theory Introduction Page
        • Cauchy-Reimann Equation
        • Cayley-Graph-Examples
        • Cesaro Summability
        • Chain Complex
        • Channel Systems
        • Characterisic of a field
        • Checking if a word is related to Sigma*
        • Choosing Limits of diagrams in Functorial
        • Church Booleans
        • Church Numerals
        • Church-Style typing
        • Circle (HoTT)
        • Circuit Value Problem
        • Circulant Graphs
        • CLH queue Lock
        • Closed Category
        • Closed sets
        • Closure and Atoms for Büchi construction of LTL formulas
        • Closure and Interior and Limit Points
        • Closure of a set under a set of functions
        • Closure Properties of Büchi Automata and Omega-regular languages
        • Closure Properties of Rational Relations
        • Closure Properties of Recognizable functions
        • Co-NP (Complexity Class)
        • Cofinality
        • Coherence Spaces
        • Coherence Types for Equivalences
        • Coin Example
        • Colimit of Limits gives Limit fo Colimit of a Bifunctor
        • Combinatorial Proofs
        • Combinatorial Optimisation
        • Combinatory Logic
        • Combined Complexity of a Logic
        • Communication Free Petri-Net
        • Commutative Ring
        • Commuting of Rectangles and Squares
        • Compactness
        • Complete and Cocomplete Categories
        • Complete Lattice
        • Complete or Cocomplete k-small categories are pre-order
        • Complete problem for NL
        • Completion of a Measure Space
        • Complex Analysis Assignment 3
        • Complex Convergence Results
        • Complex Numbers
        • Complex Numbers as quotients of polynomial ring over Reals
        • Complex Polynomials
        • Complex Rational Functions
        • Complexity Assignment 1
        • Complexity Assignment 2
        • Complexity Assignment 3
        • Complexity Classes
        • Complexity of FO
        • Complexity of FO(Cnt)All
        • Complexity of KKT Algorithm
        • Complexity of Model Checking in Monadic Second Order Logic
        • Complexity of MSO
        • Complexity of MSO over Bounded Tree-Width Structures
        • Composite Field
        • Composition of Adjunctions
        • Composition of Sequential Transducers
        • Computable and Uncomputable Functions
        • Computation Tree Logic
        • Computational History
        • Computing m_q
        • Concrete Categories
        • Concurrent Registers
        • Conditional Expectation
        • Cones and Cocones
        • Cones and Suspensions (Topology)
        • Conformality Transformation on let(rec) expressions
        • Conjugation Problem on a Free group
        • Connectedness
        • Connectivity is not EMSO definable but is AMSO
        • Connectivity is not FO Definable
        • Connectivity is not FO definable for Finite Graphs
        • Consensus
        • Consensus Number for Compare and Set - Omega
        • Consensus Number of Atomic Read Write Registers - 1
        • Consensus Number of Atomic Read Write Registers and Atomic Queue - 2
        • Constant Pattern to Lambda Calculus
        • Constructable Sets
        • Constructible Numbers
        • Constructing the Free Group
        • Constructing the Left Adjoint of Inclusion Functor from Ring to Rng
        • Construction of Syntactic Monoid of an Automata
        • Constructor Rule for Match Function
        • Continuous and Cocontinuous Functor
        • Continuous Functions
        • Continuum Hypothesis
        • Contractible Fibers
        • Contractible Types
        • Convergence of a Sequence of Martingles
        • Convergence of Fourier Series
        • Converting Case Expressions to Ordinary Lambda Calculus
        • Converting Enriched Lambda Calculus to Ordinary Lambda Calculus
        • Convolutions
        • Cook-Levin Theorem
        • Coproducts in Category Theory
        • Coq Basics
        • Corollaries of RAPL
        • Correspondence of Topological and Probabilistic Semantics for LTL
        • Countably Compact
        • Counter Automata
        • Counting and Locality
        • Coverability in Petri Nets is Decidable
        • Covering Spaces
        • CTL*
        • Curry Howard Isomorphism
        • Curry-Style typing
        • Cyclically Reduced Term
        • Cyclotomic Fields
        • D-Timed Automata to Timed Automata Construction
        • Data Complexity of a Logic
        • Deadlock-freeness
        • Decidability (HoTT)
        • Decidability of Finitely Satisfiability and Validity
        • Decidability of Presburger Arithmetic
        • Dedekind Domains
        • Definable Formulas
        • Definable Formulas are Countable
        • Definable Power Set
        • Definablity of Even Atoms
        • Deformation Retracts
        • Degree of a Structure (FMT)
        • Delta0 Formulas
        • Denotational Semantics for lambda Calculus
        • Dependency analysis for letrec expressions
        • Dependent Function Type
        • Dependent Pair Types
        • Dependent Types
        • Determinants
        • Deterministic Rabin Automata accept omega-regular languages
        • Deterministic Timed Automata
        • Diagonal Constraints Offer Exponential Succinctness.
        • Diagram
        • Dice Example
        • Diff Eq - Nice Info
        • Dimension of a Path
        • Dinic's algo for max-flow
        • Dinur's Theorem
        • Direct sum of Modules
        • Dirichlet Kernels
        • Discriminant of an n-tuple
        • Distance Functions for Timed Traces on Petri Nets
        • Distance of a Code
        • Distances in Graphs
        • Division Ring
        • Doob Decomposition Theorem
        • Doob's Martingale Convergence Theorem
        • Doob's Maximal Inequality
        • Doob's Upcrossings Inequality
        • Double Negation Does Not Cancel
        • Double on Natural Numbers using W-Types
        • DTIME(f) Complexity Class
        • Dual Vector Space Example
        • Duality
        • Duality Theorems for LP
        • Dualling Both Categories in an Adjunctions
        • Eckmann-Hilton
        • Edge-Transitive, Non Transitive is Bipartite
        • Edmond's algorithm for general Matching
        • Edmonds-Karp algo for max flow
        • Ehrenfeucht-Fraïssé Game
        • Ehrenfeucht-Fraïssé Game for MSO
        • Ehrenfeucht-Fraïssé Games Proof
        • Ehrenfeucht-Fraïssé Theorem
        • Element Category
        • Element Category is Isomorphic to Comma Category
        • Elementary Functions
        • Ellipsoid Algorithm
        • Emptiness for Updatable Timed Automata
        • Emptiness Of Support
        • Empty Rule for Match Function
        • Emulating a Multi-tape Turing machine on a Single Tape Turing Machine Effeciently
        • Encoding and Decoding Functions
        • Encoding Finite Model
        • Encoding for Proposition Formulas
        • Encoding of Tuples
        • Endsem ACT
        • Enriched Lambda Calculus
        • Enumeration Machine
        • Epimorphisms and Monomorphisms of Exact Sequences
        • Equality in Tropical Weighted Automata
        • Equality of Semigroups
        • Equalizers and Coequalizers
        • Equational form of LP
        • Equations over Finite Fields
        • Equivalence between Machines
        • Equivalence Induction
        • Equivalence of Categories
        • Equivalence of Definitions of Universal Property
        • Equivalence of more complicated structures - Semi-groups
        • Equivalence of Rational Relations is Undecidable
        • Equivalences Reflect, Preserve and Create Colimits
        • Equivalent Definitions of Adjuctions
        • Equivalent Definitions of Well-preorder
        • Error Correcting Codes
        • Error Reduction for RP algorithms
        • Evaluating Pattern Matching in Lambda Calculus
        • Even Atoms in Boolean Algebras
        • Even is (MSO + <)-expressible
        • Even is not FO-definable for Linear Orders
        • Even is not MSO-expressible
        • Event Clock Automata
        • Event Predicting Automata
        • Event Recording Automata
        • Every Finite Semi Group has an idempotent element
        • Exact Sequences
        • Example for Proof System in FOL
        • Examples for W-Types
        • Examples of Adjunctions
        • Examples of Categories
        • Examples of Coequalizers
        • Examples of Element Categories
        • Examples of Equalizers
        • Examples of Equivalence of Categories
        • Examples of FO(Cnt)
        • Examples of Free-Forgetful Adjoint Pairs
        • Examples of Functors
        • Examples of Matroids
        • Examples of Modules
        • Examples of Mutual left and right adjoints
        • Examples of Natural Transformation
        • Examples of Natural Transformation with Representable Functor as Domain
        • Examples of Pullbacks
        • Examples of Pushouts
        • Examples of Reflective Subcategories
        • Examples of Representable Functors
        • Examples of Representable Universal Property of Colimits
        • Examples of Rings
        • Examples of Sets in Type Theory
        • Existence and uniqueness for linear systems
        • Existence of Gomory-Hu trees
        • EXP (Complexity Class)
        • Expander Graphs
        • Expander Graphs and Applications
        • Expander Mixing Lemma
        • Exponential Generating Functions
        • Exponential of a Matrix
        • Expressability of One-Clock Alternating Timed Automata
        • Expressing Transitive Closure with Fixed Points
        • Expression Complexity of a Logic
        • Expressive Power Of Event Clock Automata
        • Expressive Power of Gödel's system T
        • Extending FO
        • Extension Field
        • Extension of Proper Filter to Prime Filter in Heyting Algebras
        • Exterior Algebra
        • Exterior Differentiation
        • Extrapolation for Zone Automata
        • Factorization Forest Theorem
        • Fagin's Theorem
        • Failure of CH in a suitable Model
        • False Assumptions easy to make about Patterns
        • Farkas' Lemma
        • Fejer Kernel
        • Fiber of first projection of Sigma Types
        • Fibers (HoTT)
        • Fibers of Half Adjoint Equivalences are Contractible
        • Fibonacci Heap
        • Field (Measure Theory)
        • Fields
        • Filter Lock
        • Filtered Category
        • Filtered Colimits commute with finite limits in Set
        • Filtered Probability Space
        • Filters
        • Filters in Heyting Algebras
        • Filtrations (Measure Theory)
        • Finding the Downward Closure of Some Languages
        • Finite Essentially Uninterpreted (FEU) fragment
        • Finite Fields
        • Finite Integral Domains are Fields
        • Finite Intersection Property
        • Finite Monoids and idempotent elements in big words
        • Finite Sat for FOL
        • Finite Sat for FOL Motivation
        • Finite Type Algebra
        • Finite Variable Logics
        • Finitely Satisfiable and Valid Sentences
        • First Countable space
        • First Order Logic
        • Fixed Parameter Tractibility
        • Fixed Point Logics
        • Fixed Point Logics are subsumed by Finite Variable Logics
        • Fixed Points
        • FO for Verifying CNF Encoding
        • FO on Finite Words accepts Star Free Languages
        • FO Queries are Hanf Local
        • FO with Infinitary Connectives
        • FO(+, *)
        • FO(All)
        • FO(All) is in AC0
        • FO(Cnt)
        • FOL Inexpressibility
        • FOL-Examples for Definability
        • Forbidden Ideal of an element in a Monoid
        • Forgetful functor from comma category strictly creates limits
        • Forgetful Functors that do not have an adjoint
        • Formal Description of a 2-DFA
        • Formalising Precision and Fitness for Time Petri Nets
        • Forward Reachability Tree
        • Fourier Series
        • Fourier series is the best approximation
        • Fractional Tree Packing
        • Fragments of Second Order Logic
        • Frames(Algebra)
        • Frechet Property
        • Fredmen and Tarjan's Algorithm
        • Free Abelian Group
        • Free Algebra
        • Free Category on a Directed graph
        • Free Group
        • Free Module
        • Free Monoid
        • Freyd's Representability Theorem
        • Fully Faithful Functors and Adjunctions
        • Fully Faithful Functors Reflect Limits and Colimits
        • Function Type
        • Functions as Equivalences
        • Functions as Functors
        • Functions as Functors of 2 Category
        • Functions Computable in Lambda Calculus
        • Functions types to isomorphic types are isomorphic
        • Functor Categories inherit Limits and Colimits object-wise
        • Functors
        • Fundamental Group
        • Fundamental Groupoid
        • Gaifman Graph
        • Gaifman Theorem
        • Gaifman-Locality
        • Gaifman-Locality implies BNDP
        • Galois Correspondence
        • Galois Extensions
        • Game for Counting Logic
        • Gameplay for Games on Graphs
        • Games of Graphs with Fixed Points
        • Gauss sums
        • General Adjoint Functor Theorem
        • Generalized Steiner Tree-Forest Problem
        • Generating Effects
        • Generating Functions
        • Generic Extensions of Set Theory Models
        • Generously Transitive
        • Geometric Propositional Logic
        • Gödel's system T
        • Good Kernels
        • Good Samaritan vs the Minimally Decent Samaritan
        • Graph Connectivity is not Hanf-Local
        • Greedy Cost Bounded Model Repair for Sequential Time Petri Nets with Delay Only Distance
        • Green's Lemma
        • Green's Relations
        • Green's Theorem
        • Group Testing problem
        • Group-Free Semi-group
        • Groupoids
        • Groups In First Order Logic
        • Gurevich-Shelah's Theorem
        • Guruswami-Sudan's list decoding of RS codes
        • Half Adjoint Equivalences
        • Half Adjoint Equivalences are Mere Propositions
        • Hamming Bound
        • Hamming Codes
        • Hamming Distance
        • Hanf-local Queries are Gaifman-local
        • Hanf-Locality
        • Hardness of LTL Model Checking using Timed Automata
        • hat V- Deterministic Büchi Automata
        • Hausdorff Property
        • Hereditarily Finite Sets
        • Heyting Algebra
        • Higher Groupoid Structure of Cartesian Product
        • Higher Groupoid Structure of Identity Types
        • Higher Groupoid Structure of Natural Numbers
        • Higher Groupoid Structure of Pi Type
        • Higher Groupoid Structure of Sigma Type
        • Higher Groupoid Structure of Unit Type
        • Higher Groupoids Structure of Coproducts
        • Higher Inductive Types
        • Higman's Lemma
        • Hilbert's Basis Theorem
        • Hilbert's cube
        • History(Concurrent Programming)
        • HNN - Extensions
        • Hoare Logic
        • Homeomorphisms
        • Homework 1
        • Homework 2
        • Homogenous Linear Systems
        • Homology
        • Homology as generalization of Kernel and Cokernel
        • Homology Theory
        • Homotopy Equivalence
        • Homotopy Group
        • Homotopy Induction
        • Homotopy Inductive Types
        • Homotopy of paths
        • Homotopy(HoTT)
        • Hover Operator (Verifiction of MST)
        • How to count
        • IC3 Algrorithm
        • Ideals
        • Ideals in a Monoid
        • Ideals in Quotients
        • Identity Functor admits a limit iff there is an initial object
        • Identity is an Equivalence
        • Identity System
        • Identity System at a point
        • Identity Type
        • Identity Types form an Inductive Family
        • If C is Complete and Cocomplete, so are the slice and coslice categories over C
        • If R is a PID then submodules of free module over R are free
        • If R is noetherian and M is finitely generated then M is noetherian
        • IFPL Lec 2
        • Image of a Regular Language under a Sequential Transducer is Regular
        • Immerman–Szelepcsényi Theorem
        • Immerman–Vardi's Theorem
        • Implementation of Sets and Set Operations
        • Inapproximability of Max Independent Set
        • Incidence Matrix
        • Increasing Upward-Closed sets in Preorders
        • Independence of meaning from changing the order on the left hand side implies uniform definition
        • Inductive Types
        • Inductive Types are Initial Algebras
        • Infinte product and coproduct of modules do not coincide
        • Inhomogenous Linear Systems
        • Initial, Terminal and Zero Objects
        • Integers in Simply Typed Lambda Calculus
        • Integral Curves
        • Integral Domain
        • Integrality Gap
        • Integration (Measure Theory)
        • Intermediate Value Theorem
        • Interval (HoTT)
        • Interval implies Function Extensionality
        • Interval is Contractible
        • Intuitionistic Logic
        • Invariant Queries
        • Inverse Limits and Direct Limts
        • INW generator for Space Bounded Computation
        • Irrefutable let(rec)
        • Irrefutable let(rec)s to Simple let(rec)s
        • Isolating Cut Heuristic for Multicut Problem
        • Isomorphism Between First Order Interpretations
        • Isomorphism Types of Models
        • Isomorphisms (Category Theory)
        • ISV lec 3
        • Jacobi Sums
        • Job Scheduling Problem
        • Johnson Graphs
        • Joint Distribution Measure and Product of Probability
        • Karger, Klein and Tarjan's Algorithm
        • Karger's min-cut algorithm
        • Karp-Lipton Theorem
        • Kernel and Cokernels in R-Mod
        • Kernels and Cokernels
        • Kleene Shutzenberger Theorem
        • Knaster-Tarski Theorem
        • Kneser Graph
        • Kolmogorov Property
        • Kolmogorov Translation
        • Kolmogorov's Law of Large Numbers
        • Kolmogorov's One Series Theorem
        • Kripke Models
        • Kripke Models are Equivalent to Heyting Algebra
        • Krull Dimension
        • Kruskal's Algorithm
        • L is a model of ZF
        • L is a Model of ZFC
        • L is a Model of ZFC + GCH
        • L Rank of a constructible set
        • L_infty,omega star
        • l,k Ajtai-Fagin Game for EMSO
        • L* example
        • L* Learning Algorithm
        • Ladner's Theorem
        • LAG 4 May
        • Lambda Calculus Evaluation Rules
        • Lambda Calculus Introduction
        • Lambda Calculus Syntax
        • Lambda Mu Calculus
        • Lambda Term In Combinatory Logic
        • Lamport's Bakery Lock
        • Language of Infinite words
        • Language Operations on Monoids
        • Largest common independent set of a matroid
        • Last Appearance Record
        • Lattice
        • Lattice Graphs
        • Lebesgue Number Lemma
        • LECTURE
        • Lecture local fields
        • Left and Right Adjoints are Unique
        • Left and Right Inverses
        • Left and Right Inverses of Ring Homomorphisms
        • Legendre Symbol
        • Lemma 1 for Complementation of omega-Regular Languages
        • Lemma 1 for Quasi-inverse is not a Mere Proposition
        • Lemma 2 for Complementation of omega-Regular Languages
        • Lemma 2 for Quasi-inverse is not a Mere Proposition
        • Lemma 3 for Complementation of omega-Regular Languages
        • Lemma for BEF Games
        • Lemma for H-smooth Words
        • Lemma for J-smooth words
        • Lemma for Minimax Theorem
        • Lemma for Natural Number Encoding
        • Lemma for R-smooth Words
        • Lemma for Threshold Equivalence
        • Lemma-Number of isomorphism classes on graphs
        • let-expressions in Enriched Lambda Calculus
        • letrec-expressions in Enriched lambda Calculus
        • letrec-expressions to Irrefurtable let-expressions
        • LFPsimult = LFP
        • Lifted Reed Solomon Codes
        • Lifting Correspondence
        • Lifts
        • Limits and Colimits
        • Limits and Colimits as Adjunctions
        • Limits and Colimits in multiple variables can be taken in any order
        • Limits in the Category of Sets
        • Lindelof Space
        • Lindenbaum-Tarski Algebra
        • Line Graph
        • Line Integral
        • Linear Algorithm for Special case of TPMP
        • Linear Programming
        • Linear systems with constant coefficients
        • Linear Temporal Logic
        • List decoding Folded RS
        • List decoding RS codes up to the Johnson radius
        • Local Compactness
        • Local Connectedness
        • Local Correcting and Decoding of RM codes
        • Local Decoding
        • Local Equivalence
        • Local Equivalence Lemma
        • Local Path Connectedness
        • Local problems on codes
        • Local Self-correction of Bivariate Multiplicity Codes
        • Locality (Finite Model Theory)
        • Locally Finite and Summable Series
        • locally presentable categories
        • Locally Small and Complete Categories with a small coseparating set where all collections of subobjects of a fixed object have an intersection then it is cocomplete
        • Locally Small, Complete category with a small coseparator where all collections of subobjects of an object have an intersection has all continuous functors form it be representable
        • Location Lemma
        • Logic L capturing the complexity class K
        • Logic, Regular Languages and Languages Recognized by Monoids
        • Loop is not refl
        • Loop Space
        • Los-Vaught Test
        • Lovasz Local Lemma
        • Löwenheim-Skolem and its Variants
        • Lower Bound on Shared Process
        • LP algorithm for Bipartite Matching
        • LP algorithm for general Perfect Matching
        • LP Solution examples
        • LTL vs CTL
        • M is noetherian if for every sub-module N, N and MN are noetherian
        • Machinery for Probabilistic Semantics for Timed Automata
        • Machines Realising Rational Functions
        • Martingale Transform
        • Martingales
        • Match Function for Enriched Lambda Calculus
        • Matching Problem
        • Matroid Intersection
        • Matroids
        • Max wt base of a matroid
        • Maximal Traces for Linear Time Petri Nets for Delay Only Distance
        • Mealy Machines and Moore Machines
        • Measurable Functions
        • Measure Space
        • Measurement of Redundancy in a code
        • Mere Propositions
        • Mere Propositions are Sets
        • Metric Topology
        • Metrizable Spaces
        • Miller-Rabin Algorithm for Primality
        • Minimax Theorem for Zero-Sum Games
        • Minimizing a Weighted Automata
        • Minimum k-cut Problem
        • Minimum Spanning Trees
        • Mixed Nash Equilibrium
        • Mixed Strategies
        • Mixture Rule for Match Expression
        • Model Checking of CTL formulas
        • Model Repair and Conformance Checking of Time Aware Models
        • Modular Machines
        • Modular Machines are Turing Complete
        • Modules
        • Monadic Second Order Logic
        • Monoid Homomorphisms
        • Monoid Ring
        • Monoidal Category
        • Monoidal Closed Category
        • Monoids
        • Monoids as Idempotent Commutative Langauges
        • Monoids as Languages
        • Monoids as Regular Languages
        • Monolithic Timed Automaton for a Network of Timed Automata
        • Monomials, Polynomials and Series
        • Monomorphisms and Epimorphisms
        • Monomorphisms and Epimorphisms in Rings
        • Monotone Domination Order
        • Monotone, Inflationary and Inductive Functions
        • Monotonicity is Undecidable
        • Motivation for Concurrency Theory
        • Motivation for Games
        • MSO has Problems in each PH level
        • MSO on Finite Words accept Regular Languages
        • MSOL(lt) equivalent to MSOL(succ)
        • MTP 17-09-24
        • Mu-Recursion
        • Multi-choose
        • Multi-way Cuts
        • Multiplicative Characters
        • Multiplicity Automata
        • Multiplicity Codes
        • Multiset
        • Multivariate Polynomial Interpolation on Lines
        • Mutual Exclusion
        • Mutual Left and Right Adjunctions
        • Myhill Nerode Theorem
        • N is the initial object in the category of N-Algebras
        • N_L admits Quantifier Elimination
        • Naive Algorithm for Reachability in Zone Automata
        • Natural Deduction
        • Natural Numbers in Type Theory
        • Natural Numbers with Successor
        • Natural Numbers with Successor and Ordering
        • Natural Numbers with Successor Function is Complete
        • Natural Transformation
        • Neighborhood (Finite Model Theory)
        • Network Flows
        • Network Reliability
        • Networks of Timed Automata
        • Newman's Lemma
        • Nivat's Theorem
        • Noetherian Modules
        • Noetherian Ring and PIDs
        • Non deterministic Space Hierarchy Theorem
        • Non deterministic Time Hierarchy Theorem
        • Normal Extensions
        • Normal Spaces
        • Normalization Theorem for Gödel's system T
        • Normalizing a Transducer
        • Not Unification Algorithm For Type Inference
        • Notes
        • NP (Complexity Class)
        • NP Complete
        • NTIME(f) Complexity Class
        • Number Field
        • Number Of Roots and Poles of a Rational Function
        • Number Rings
        • Object Classifiers
        • ODE
        • Olog
        • omega-Automata
        • Omega-Regular Languages
        • One Parameter Group Of Diffeomorphisms
        • One Point Compactification
        • Open and Closed Functions
        • Operations on Integrals
        • Opposite Category
        • Optimal Reachability in Weighted Timed Games
        • Optimality of Basic Feasible Solution
        • Optimisations for Expressions containing FAIL and Fatbar
        • Optimisations for Overlapping Patterns
        • Orbits in X x X being strongly connected under transitive automorphism
        • Orbits on X and X x X
        • Order Invariant FO
        • Order Invariant FO(Cnt) is not Gaifman Local
        • Order Topology
        • Ordered Fields
        • Ordered Fields and Archimedean Axiom
        • Ordering between Axiomatic Theories
        • Ordering Equations in Uniform Definitions
        • Ordinal Definable Sets
        • Ordinary Generating Functions
        • Owing to a Person vs Them having a Right against you
        • P (Complexity Class)
        • P implies not-not P - Intuitionistic Logic
        • P-adic Solenoid
        • P-Generic classes
        • P-name
        • Pairs in Lambda Calculus
        • Partial Functions
        • Partial Isomorphism
        • Path Connected Component Functor
        • Path Connectedness
        • Path Induction
        • Paths on Graphs and Finite Variable Logics
        • Pattern Matching to Ordinary Lambda Calculus
        • Patterns
        • PCP'
        • Peano Axioms and Type Theory
        • Pebble Games
        • Perfect Fields
        • Permutation Matrix Theorem
        • Phase Flow
        • Phase Space
        • PLC Assignment 3
        • Pointed Predicates and maps
        • Pointed Type
        • Polynomial and matrices over semi rings form semi rings
        • Polynomial Rings
        • Polynomial Rings over a Noetherian Ring are Noetherian
        • Polynomial-Time Hierarchy
        • Polytime Approx Algo for Steiner Trees
        • Positive Formulas
        • Post Correspondence Problem
        • Power Series
        • Pre-Image of a Regular Language under a Sequential Transducer is Regular
        • Predicable Process
        • Prefix Preserving
        • Preorder
        • Presentation of a Group
        • Preservation, Reflection and Creation of Limits
        • Prim's Algorithm
        • Primal - Dual LP
        • Primal-Dual Algorithm for Bipartite Min-cost Perfect Matching
        • Primal-Dual Algorithm for general Min-cost Perfect Matching
        • Prime and Irreducible elements
        • Prime elements are irreducible
        • Prime Ideals and Maximal Ideals
        • Prime Ideals are Maximal in PIDs
        • Primitive Element Theorem
        • Primitive Recursion
        • Primitive Transitive Permutation Group
        • Principle Ideals
        • Probabilistic Automata
        • Probabilistic Semantics for LTL
        • Probabilistically Checkable Proof
        • Probability
        • Probability Measure over Finite Paths in a Timed Automata
        • Probability Theory and Gambling
        • Product Constructor Pattern Matching to Lambda Calculus
        • Product in Category Theory
        • Product Measures
        • Product of Well-Preorders
        • Product topology
        • Product Type
        • Product Type(HoTT)
        • Products and Coporducts
        • Products in Rings
        • Products in Topology from Products in Category Theory
        • Products respect Universal Properties
        • Program for RAM
        • Proof by Induction in Coq
        • Proof for Lower Bound on Shared Processes
        • Proof for Reflection Theorem
        • Proof for the Undecidability of the Word Problem
        • Proof that L2 cannot be accepted by a 1 Clock Timed Automata
        • Properties of Karp-Miller Trees
        • Properties of Minimum Spanning Trees
        • Properties of the Attractor function and Traps
        • Propositional Resizing
        • Propositional Truncation
        • Pseudocode for CLH queue Lock
        • PSPACE
        • PSPACE-Hardness of LTL Model Checking
        • PTAS (Complexity Class)
        • Pullbacks and Pushouts
        • Pullbacks in CAT
        • Pure Sequential Transducers
        • Purely Timed Alignment Problem for Linear Time Petri Nets for Delay Only Distance
        • Push Down Automata
        • Pushouts in CAT
        • Quadratic Reciprocity
        • Quanitifier Elimination for Natural Numbers With Successor
        • Quantified Boolean Formulas
        • Quantifier Rank
        • Quantifier rank
        • Quasi-inverse is not a Mere Proposition
        • Queue Based Locks
        • Quotient Rings
        • Quotient Topology
        • Quotienting by monic polynomial is an abelian group isomorphism with direct sum
        • Quotients in Monoids
        • Quotients of Polynomial Rings
        • Quotients of Syntactic Monoid of a language
        • R with Lower Limit topology
        • R_K
        • R-Mod is a CCC
        • R^w
        • Radon-Nikodym Theorem for Countably Generated Sigma Field
        • Ramsay's Theorem
        • Random Access Machines
        • Randomised or Probabilistic Computation
        • Randomized Algorithms
        • Rank of a module
        • Rank-k m,l Types MSO
        • Rank-k Types (FO)
        • Ranked Tree Automata
        • Ranked Trees in Logic
        • RAPL
        • Rational Functions (Weighted Automata)
        • Rational Relations as Weighted Automata
        • Rational Series
        • Rational, Automatic and Recognizable relations
        • Reachability Algorithm for Zone Automata
        • Reachability in Finite Pushdown VASS
        • Reachability in Lossy Channel Systems
        • Reachable Vectors
        • README
        • Recursive and Recursively Eumberable Sets
        • Reducibility
        • Reducibility Theorems
        • Reducing a Weighted Automata
        • Reduction
        • Reflection Theorems
        • Reflective subcategories create limits and contain colimits
        • Reflective Subcategory
        • Region Automata Alternate Definition
        • Regular Permutation Groups
        • Regular Spaces
        • Regular Tree Languages
        • Relative Strength of ZF- and ZF
        • Removable Singularities in Analytic Functions
        • Repeated Events
        • Representable Functors
        • Representable Functors Define Representing Objects
        • Representable Matroids
        • Representable Universal Property of Colimits
        • Representable Universal Property of Limits
        • Representation of Limits and Colimits as Limits in category of sets
        • Residuals using Longest Common Prefixes
        • Result of Expressive Power of Gödel's system T
        • Retract of an Equivalence is an Equivalence
        • Retractions
        • Retracts (HoTT)
        • Right Congruent Equivalence Relation
        • Ring
        • Ring Homomorphisms
        • Rules for Higher Inductive Types
        • Runtime
        • S^1
        • Sankalp Talk - Ax Grothediek Raw
        • Satisfiability in First Order Logic
        • Savitch's Theorem
        • Scientific Data Science
        • Search vs Decision for NP complete problems
        • Second Countability
        • Second Order Logic
        • Semantics for CTL
        • Semantics for LTL
        • Semantics of First Order Logic
        • Semaphores
        • Semi Groups in Types Theory
        • Semi Ring
        • Semi-Groups
        • Semi-Modules
        • Semifield
        • Separable Extensions
        • Separable Polynomials
        • Separable Spaces
        • Separating and Coseparating sets
        • Separation Axioms
        • Separation Oracle for perfect matching LP
        • Sequent Calculus
        • Sequential Transducers
        • Sequentially Compact
        • Set Cover Problem
        • Set is Complete
        • Set is Complete and Cocomplete
        • Set of Languages accepted by Büchi Automata are exactly Omega-Regular
        • Sets in Type Theory
        • Short Exact Sequences
        • Shortest Path using Primal-Dual
        • Showing a Point is Isolated is Undecidable
        • Sigma Field
        • Sigma Types respect Universal Properties
        • sigma-paradise
        • Similar description of inductive types lead to equal types
        • similar tunes
        • Simple let expressions to Ordinary Lambda Calculus
        • Simple Regular Expressions
        • Simplex Method
        • Simplicial Complexes
        • Simply Connected
        • Simply Typed Lambda Calculus Syntax
        • Simulation for Zone Automata
        • Simultaneous Fixed Points
        • Simultaneous Unboundedness Problem
        • Size of subsets of Reals
        • Slice Category Strictly Creates Limits
        • Slide Plan
        • Small Progress Measures
        • Small Categories
        • Small Limits in Set are Equalizers
        • Small Tree Decomposition
        • Small Tree Decompositions are Small
        • Smallest Filter Heyting Algebras
        • Snake Lemma
        • Solution of a differential equation
        • Solution of an LP
        • Solving a First Order ODE
        • Solving a linear differential equations
        • Solving SAT using MSO
        • Some Algorithms for finding the Minimum Spanning Trees
        • Some Applications of Kripke Structures
        • Some Contractible Types
        • Some Generalization of Inductive Datatypes
        • Some Problems in Computational Algebra
        • Some Type Formers respect Mere Propositions
        • Some Useful Inequalities
        • Some ways to Characterize Homotopy W types
        • Sparse recovery-compressed sensing
        • Special Adjunct Functor Theorem
        • Special Case of Tree Path Maxima Problem
        • Special Types of Measures
        • Specifying a Type
        • Spectrum of a Cube Graph
        • Spectrum of a Ring
        • Spectrum of The adjacency Matrix
        • Spectrum of the complement of a graph
        • Spectrums in PIDs
        • Sphere (HoTT)
        • Spin Locks
        • Split Exact Sequences
        • Splitting Fields
        • Splitting of Primes in extensions
        • Spooky Day Logic stuff
        • Stable Subsemodule of Series
        • Stage Comparisons
        • Stages(Finite Model Theory)
        • Star Free Regular Languages are Aperiodic
        • Star Free Regular Languages can be accepted by FO on words
        • Starvation-freeness
        • Steiner Trees
        • Steiner Trees are NP Complete
        • Steinhaus Random sign problem
        • Stochastic Languages
        • Stochastic Languages are Regular if Threshold Point is Isolated
        • Stochastic Languages are Undecidable in General
        • Stoke's Theorem
        • Stone Cech Compactification from Special Adjunct Functor Theorem
        • Stone's Representation Theorem
        • Stopping Time
        • Strategy for Games on Graphs
        • Streams as Frames
        • Streams as Frames Alt
        • Strictly Creating Limits
        • Strings in Logic
        • Strong Normalization Theorem
        • Strongly Regular Graphs
        • Structure Preserving Maps
        • Sub-basis
        • Sub-Games
        • Sub-Types
        • Submodule and quotients
        • Subobjects
        • Subset Relation between Timed Regular Languages
        • Subset Sum Problem
        • Subspace Topology
        • Successor invariant FOL on finite structures
        • Succinct Encoding of Natural Numbers Using Strings
        • Sum Constructor Pattern Matching to Lambda Calculus
        • Sum of all Fibers of a Function is the Domain
        • Sum off all Functions from all types are equivalent to a type family
        • Sum Types
        • Support of an Automorphism on a Graph
        • Surjection and Embedding are equivalent to Equivalences
        • Surjections and Embeddings
        • Suspensions (HoTT)
        • SVA Assignment 0
        • SVA Assignment 0 part 4
        • SVA Staggered Problems
        • Syntax of First Order Logic
        • System of First Order Differential Equations
        • T-Transitiviy of Graphs
        • TAS Lock
        • Temporal Logic
        • Tensor Products as Universal Properties
        • Tensors
        • Textbook review 8 math
        • The Category Ring
        • The fundamental theorem of Galois Theory
        • The matching polytope has exponential extension complexity
        • The Principle of Unique Choice
        • The Riemann Sphere
        • Theorem- Bipartite Graph Eigen Value Pairs
        • Theorems about Stopping Times
        • There is a non-trivial proof for reflexivity of equality in Circle
        • Threshold Equivalence
        • Threshold Languages
        • Tietze Extension Theorem
        • Time and Space Hierarchy Theorems
        • Time Petri Net
        • Time Table Planning
        • Timed Automata Alternate Definition
        • Timed Automata Homework 1
        • Timed Automata Plan
        • Timed Automata with Diagonal Constraints
        • TOC Problem Set 1 (not graded)
        • Top is Complete and Cocomplete
        • Topological Groups
        • Topological Invariants
        • Topological Semantics for LTL
        • Topological Space of Paths in a Timed Automata is Baire
        • Topological Spaces
        • Topological Spaces as Frames
        • Topology over Finite Paths in a Timed Automata
        • Torsion submodule
        • Total Spaces (HoTT)
        • Total Unimodularity
        • Trace and Norm
        • Traces of Powers of Adjacency Matrices
        • Train Track Crossing for Timed Automata
        • Trakhtenbrot's Encoding of Turing Machine
        • Trakhtenbrot's Theorem
        • Transitive Sets
        • Translating Haskell Programs to Lambda Calculus
        • Translation Scheme from Haskell to Lambda Calculus for Definitions
        • Translation Scheme from Haskell to Lambda Calculus for Expressions
        • Translation Scheme from Haskell to Lambda Calculus for Some RHS only options
        • Transport
        • Transport over a function between families
        • Transports in a Family of Paths
        • Transpose of a Weighted Automata
        • Travelling Salesman Problem
        • Tree Decomposition
        • Tree Decomposition and Size of the Tree
        • Tree Decomposition Lemma 1
        • Tree Decomposition of k-connected Graphs
        • Tree Packing
        • Tree Path Maxima Problem
        • Tree Width
        • Trees (Automata Theory)
        • Triangular Graphs
        • Trigonometric Functions
        • TTAS Lock
        • Tube Lemma
        • TUE 7 Lec Notes
        • Turing Machine Configuration
        • Turing Machines
        • Turing Machines with multiple tapes
        • Two Stacks
        • Two Variable Adjunction
        • Two-Way Infinite Tape Turing Machine
        • Tychonoff's Theorem
        • Type Inhabitation in P-SPACE
        • Type of a Set and a Relation
        • Type of Natural Number Algebra
        • Type of W-Algebras
        • Type Theoretic Axiom of Choice
        • Type Theoretic Rosetta Stone
        • Type Theory vs Set Theory
        • Typed Combinatory Logic
        • Types are Higher Groupoids
        • Types of Modules
        • Uncapacitated Facility location
        • Uncountable Cardinalities
        • Undecidability of the Halting Problem
        • Undecidability of the Membership Problem
        • Uniform Definition of Haskell Functions
        • Uniform Topology
        • union of disjoint intervals giving an interval length
        • Unique construction of Adjunction
        • Uniqueness of fourier series
        • Uniqueness of functions created using induction principle
        • Uniqueness Principle for Sigma Types
        • Unit and Counit as Singleton and Evaluation
        • Unit and Counit as Universal Arrows
        • Units (Rings)
        • Univalence
        • Univalence Implies Function Extensionality
        • Univalence Implies Weak Function Extensionality
        • Universal Elements are Universal Elements
        • Universal Finite Automaton
        • Universal Property (Mac Lane)
        • Universal Property (Riehl)
        • Universal Property of Polynomial Rings
        • Universal Property of Products and Coproducts
        • Universal Turing Machine
        • Universality is Decidable for One-Clock Timed Automata
        • Universality of Concurrent Object Class
        • Universe with circle is not a groupoid
        • Universes
        • Unraked Tree Automata
        • Unranked Trees in Logic
        • Untiming Timed Automata
        • Untitled
        • Updatable Timed Automata
        • Updatable Timed Automata with only update being x=x-1
        • Updatable Timed Automata with only x=c and x=y updates
        • Updatable Timed Automata without Diagonal Constraints and c in N
        • Urysohn Lemma
        • Urysohn Metrization Theorem
        • Valuation of a P-name
        • Variable Rule for Match Function
        • Vertex Cover Problem
        • Vertical and Horizontal Composition of Natural Transformations
        • Von Neumann Ordinals
        • W-Types
        • W-Types are the initial element in the category of W-Algebras
        • Weak Function Extensionality
        • Weakly initial objects and joint weakly initial sets
        • Web of Reductions
        • Weighted Automata
        • Weighted Automata as Formal Power Series
        • Weighted Automata on Series
        • Well Structured Transition Systems
        • Well-Preorder
        • What are Differential equations
        • What is Topology
        • WHILE programs
        • Why Differential Equations
        • Winning Arena for Büchi Games
        • Winning Arena for Parity Games
        • Winning Arena for Rabin Games
        • Winning Arena for Rabin Games - Fail
        • Winning Arena for Reachability Games
        • Winning Condition for Games on Graphs
        • Winning Strategy for Büchi Games
        • Winning Strategy for Player 1 in Banach-Mazur games
        • Winning Strategy for Player 2 in Banach-Mazur games
        • Winning Strategy for Reachability Games
        • Word Problem for Finitely Presented Groups is Undecidable
        • Word Problem for Finitely Presented Groups is Undecidable Lemma 1
        • ww where w is any word
        • Yoneda Embedding
        • Yoneda Lemma
        • Zero Divisors
        • Zig-Zag Product Construction of Expander Graphs
        • Zone Automata
        • Zone Automata Example
        • Model Repair of Time Petri Nets
        • Model repair planning
        • Revisiting Complexity of First-Order and Monadic Second Order Logic
        • Verification of MST
        • Weak Alternating Automata are not that Weak
        • Weak Alternating Automata are not that Weak Presentation
        • Advances in Algorithmic Meta Theorems
        • Automated Verification of Test Input Generators
        • Codes - Madhur Tulsiani
        • concurrent stochastic games
        • Conterfactual Explanations for MITL Violation
        • Discrete Time Markov Chain
        • Greybox Learning of Languages Recognizable by Event Recording Automata
        • Guruswami
        • HyperPropertiers
        • Muller LTL Formulas
        • Percolation Thoery
        • Synchronized Distributed Games
        • Three views on LIA
    Home

    ❯

    MOC

    ❯

    0-Atlas

    Jul 22, 20251 min read

    Atlas


    Info

    Well Hello! This the location where you come to when you are trying to find notes that you have created.

    If this note is note helpful then please contact me and let me know what you are looking for.


    Courses

    Current

    • Weighted Automata and Transducers
    • Finite Model Theory
    • Topics in Algorithms
    • Intro to Martingales
    • Homotopy Type Theory

    All

    • Algebraic Automata Theory
    • Complexity Theory
    • Concurrent Programming
    • Games on Graphs
    • Implementation of Functional Programming Languages
    • Infinite State Verification
    • Logic
    • Logic, Automata and Games
    • Measure Theoretic Probability
    • Set Theory
    • Software Verification and Analysis
    • Undecidability in Algebra and Topology

    Study Topics

    • Category Theory
    • Topology via Logic
    • Logic
    • Measure Theoretic Probability
    • Set Theory
    • Complexity Theory

    Presentations

    • Independence of CH - Dana Scott
    • Revisiting Complexity of First-Order and Monadic-Second-Order Logic


    Graph View

    • Atlas
    • Courses
    • Study Topics
    • Presentations

    Backlinks

    • index

    Created with Quartz v4.4.0 © 2025

    • GitHub