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Questions tagged [buchi-automata]

Büchi automata are finite-state automata used to specify languages of infinite strings.

After J.R. Büchi, with an umlaut.

Büchi-automata are given as ordinary finite state automata, but their semantics is to specify infinitary languages, i.e., languages with infinite strings. Such an infinite string is accepted by the automaton iff its run (infinite computation) enters at least one of the final states infinitely often.

Nondeterministic Büchi-automata accept the so-called regular ω-languages. Their deterministic restriction is strictly weaker. In particular, there is no deterministic Büchi automaton that recognizes the language (0+1)*0ω, of infinite words in which 1 occurs only finitely often.

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Equivalence of Büchi automata and linear $\mu$-calculus

It's a known fact that every LTL formula can be expressed by a Büchi $\omega$-automaton. But, apparently, Büchi automata are a more powerful, expressive model. I've heard somewhere that Büchi automata are equivalent to linear-time $\mu$-calculus…
Daniil
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Algorithm to translate a deterministic Büchi automaton to LTL (when possible)

Linear temporal logic and deterministic Büchi automata are incomparable: DBA cannot express $FGa$, and LTL cannot express "at least each odd letter is 'a'". But sometimes it is interesting to know whether the language of a DBA can be expressed in…
Ayrat
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Proving that a (tree) language is not Buchi recognizable

I'm reviewing some notes about tree automata and I'm trying to conclude a proof that the professor left incomplete. The statement is: Let $A = \{a,b\}$ and $T = \{t \in T_A^{\omega} \mid \text{every path in $t$ contains a finite number of $a$}\}$. …
Bakuriu
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Büchi automata: accepting run vs. runs with arbitrarily many final states

I am currently learning about Büchi automata and have a combinatorial question about the acceptance condition. Let $A=(Q,\Sigma,\delta,q_0,F)$ be a (nondeterministic finite) Büchi automaton and $w=w_1w_2w_3\ldots$ an infinite word over $\Sigma$.…
ddd01
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Efficient Algorithm Linear Temporal Logic to Deterministic Rabin Automata

I am trying to construct an equivalent Deterministic Rabin Automata (DRA) given a Linear Temporal Logic (LTL) Formula. One (expensive) way to do this would be to construct an equivalent Non-deterministic Buchi Automata and then determinize it using…
Abhishek Kulkarni
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What is the difference between finite automata and Büchi automata?

as the title suggests, I was struggling to define the differences between finite and Büchi automata and how they are represented. From an assignment I'm working on, this automaton can be depicted as both infinite automaton and Büchi automaton. Can…
Thang Do
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Minimal Deterministic Buchi Automata Product

Problem: Let $\varphi = \varphi_1 \land \varphi_2$ be Deterministic Buchi Automata (DBA) expressible LTL formulas. Let $A$, $A_1$ and $A_2$ be translated DBAs such that ${\cal{L}}(A) = {\cal{L}}(A_1) \cap {\cal{L}}(A_2)$. What can be said about the…
Abhishek Kulkarni
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Is the language with at least as many 0 as 1 on any prefix $\omega$ regular?

Let $L$ be the language of infinite words in $\{0,1\}^\omega$ such that any finite prefix of a word in $L$ has at least as many $0$'s as $1$'s. Is $L$ büchi recognisable? I think that $L$ is not $\omega$ regular, but standard tricks such as…
Jerry Tao
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Are deterministic Büchi automata omega-closed?

As in, given a regular language $V$, does there exist a deterministic Büchi automaton $\mathcal{A}$, or equivalently a regular language $W$ such that $\mathcal{L}(\mathcal{A})=\vec{W}=V^\omega$? For clarity, if $L$ is a finite-word language, then…
giofrida
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Distributivity of $\omega$-regular expressions

Recall that a language is $\omega$-regular if and only if it is recognized by a Büchi automaton. How can I prove that $\qquad (E_1 + E_2).F^\omega$ is equivalent to $\qquad {E_1.(F^\omega)+E_2.(F^\omega)}$ where both expressions are omega regular…
user1325120
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Why are non-deterministic Buchi automata factorially succinct when compared to deterministic Rabin Automata?

I am trying to demonstrate the following idea without success. There are infinitely many $n \in \mathbb{N}$ such that: There is a non-deterministic Buchi automata of size $n$ such that a deterministic Rabin Automata accepting the same language…
Agnishom Chattopadhyay
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Equivalence of states between two "quasi-deterministic" strongly connected Büchi automata accepting the same $\omega$-language

Hope someone can point me to the right direction to solve this problem. Premise. I call quasi-deterministic Büchi automaton (qDBA) a Büchi automaton $B = \langle S, \Sigma, S_0, \delta, F \rangle$, where $S$ is the set of states, $\Sigma$ the…
Davide
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Acceptance conditions when translating LTL to Büchi automaton?

As an exercise in better understanding, I have been implementing the LTL to Generalized Büchi Automaton translation algorithm of Gerth, et al. (which is also discussed in Clarke, et al., Model Checking). What I have ended up with seems incorrect,…
Robert P. Goldman
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What are the steps/tricks/tips to construct a Büchi automaton from a given language?

Let's say I have this language: $(a + bc)^∗((b + c)a^ω + (abb^∗)^ω)$ It seems pretty complicated, where should I begin with if I were to construct a Büchi automaton? I've been doing it the following way with smaller language sets: a $^*$ operator…
Thang Do
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Büchi automaton with modified acceptance condition

Consider a Büchi automaton $\mathcal{A}$ with the modified acceptance condition, that an $\omega$-word $\mathcal{w}$ is accepted by $\mathcal{A}$ iff every run $\rho$ of $\mathcal{A}$ on $\mathcal{w}$ is accepting (rather than at least one run being…
vikraman
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