202309231609

Tags : Timed Automata

---

Event Clock Automata

Caution

Event Clock Automata are not Timed Automata because of the use of Event Predicting Clocks.

Consider the language $\{aab\}\cup \{abb\}$ where the time gap between accepting the last two characters is $1$.

We can give an Event Recording Automaton for the first word but not for the second word. And we can given an Event Recording Automaton for the second word but not the first one.

Hence both Event Recording Automata and Event Recording Automaton are not powerful enough, and neither of them are more powerful than the other. The Expressive Power Of Event Clock Automata is discussed here.

Now we create an Event Clock Automaton by combining the two. We are allowed to use both Event Recording Clocks and Event Predicting Clocks

Example

Let $L=\{a^{\ast }{b}^{\ast }\}$ such that:

• There exists an $a$ such that the first $b$ is accepted after time $1$
• There exists a $b$ such that it is accepted $1unit$ after the last $a$

Transclude of Drawing-2023-09-23-16.35.03.excalidraw

Event Clock Automata can also be determinized using the subset construction. Event Clock Languages are closed under

• Union
• Intersection
• Complementation

---

References

Event Predicting Automata Event Recording Automata Expressive Power Of Event Clock Automata