Topic
ω-automaton
About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.
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TL;DR: It is shown that the problem of checking careful synchronizability of partial finite automata is PSPACE-complete and the problems of checking D1, D2, and D3-directability of nondeterministic finite Automata are PSPACE -complete.
Abstract: We show that the problem of checking careful synchronizability of partial finite automata is PSPACE-complete. Also the problems of checking D 1-, D 2-, and D 3-directability of nondeterministic finite automata are PSPACE-complete; moreover, the restrictions of all these problems to automata with two input letters remain PSPACE-complete.
46 citations
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TL;DR: It is argued that if one wishes a renaissance of automata theory, then one should prefer to return to the investigation of the fundamental, classical problems of Automata theory rather then searching for new applications and defining numerous questionable modifications of basic models.
Abstract: "Automata theory is not over" is the message of this paper. But if one wishes a renaissance of automata theory, then one should prefer to return to the investigation of the fundamental, classical problems of automata theory rather then searching for new applications and defining numerous questionable modifications of basic models. We argue for this opinion here and try co outline a way that could lead to a renaissance of automata theory.
46 citations
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TL;DR: An attempt has been made to characterise a number of exceptional transformations or rules, each of which behaving uniquely, not matching with any other rules, of two dimensional cellular automata with null and periodic boundary conditions.
46 citations
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27 Feb 1997TL;DR: It is proved that every regular expression of size n can be converted into an equivalent nondeterministic finite automaton (NFA) of size O(n(log n)2) in polynomial time.
Abstract: It is proved that every regular expression of size n can be converted into an equivalent nondeterministic finite automaton (NFA) of size O(n(log n)2) in polynomial time. The best previous conversions result in NFAs of worst case size Θ(n2). Moreover, the nonexistence of any linear conversion is proved: we give a language L n described by a regular expression of size O(n) such that every NFA accepting L n is of size Ω(n log n).
46 citations
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01 Jan 2010TL;DR: The NP-completeness of the problem of minimising deterministic automata over finite and infinite words is established, and the introduction of almost equivalence is introduced, an equivalence class for strictly between language equivalence for deterministic \buchi\ or \cobuchi\ automata and language equivalenced automata.
Abstract: In this paper we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic \buchi, \cobuchi, and parity automata play a similar role in the recognition of $\omega$-regular languages. While it is well known that the minimisation of deterministic finite and weak automata is cheap, the complexity of minimising deterministic \buchi\ and parity automata has remained an open challenge. We establish the NP-completeness of these problems. A second contribution of this paper is the introduction of almost equivalence, an equivalence class for strictly between language equivalence for deterministic \buchi\ or \cobuchi\ automata and language equivalence for deterministic finite automata. Two finite automata are almost equivalent if they, when used as a monitor, provide a different answer only a bounded number of times in any run, and we call the minimal such automaton relatively minimal. Minimisation of DFAs, hyper-minimisation, relative minimisation, and the minimisation of deterministic \buchi\ (or \cobuchi) automata are operations of increasing reduction power, as the respective equivalence relations on automata become coarser from left to right. Besides being a natural equivalence relation for finite automata, almost equivalence is language preserving for weak automata, and can therefore also be viewed as a generalisation of language equivalence for weak automata to a more general class of automata. From the perspective of \buchi\ and \cobuchi\ automata, we gain a cheap algorithm for state-space reduction that also turns out to be beneficial for further heuristic or exhaustive state-space reductions put on top of it.
46 citations