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Algorithmic Frontiers of Fairness
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
College Notes
Excalidraw
Drawing 2025-01-07 12.06.37.excalidraw
FSTTCS
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
MOC
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
Notes
(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
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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
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Rank of a module
Rank-k m,l Types MSO
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Ranked Tree Automata
Ranked Trees in Logic
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Rational Relations as Weighted Automata
Rational Series
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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
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Reflective subcategories create limits and contain colimits
Reflective Subcategory
Region Automata Alternate Definition
Regular Permutation Groups
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Relative Strength of ZF- and ZF
Removable Singularities in Analytic Functions
Repeated Events
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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
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Retractions
Retracts (HoTT)
Right Congruent Equivalence Relation
Ring
Ring Homomorphisms
Rules for Higher Inductive Types
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S^1
Sankalp Talk - Ax Grothediek Raw
Satisfiability in First Order Logic
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Search vs Decision for NP complete problems
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Semi Ring
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Set Cover Problem
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Set of Languages accepted by Büchi Automata are exactly Omega-Regular
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Sigma Types respect Universal Properties
sigma-paradise
Similar description of inductive types lead to equal types
similar tunes
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Size of subsets of Reals
Slice Category Strictly Creates Limits
Slide Plan
Small Progress Measures
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Smallest Filter Heyting Algebras
Snake Lemma
Solution of a differential equation
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Some Algorithms for finding the Minimum Spanning Trees
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Some Contractible Types
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Some Problems in Computational Algebra
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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
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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
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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)
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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
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Model Repair of Time Petri Nets
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Weak Alternating Automata are not that Weak Presentation
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Model repair planning
Jul 22, 2025
1 min read
Have to present whatever I have done
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