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: This paper provides a common theoretical framework, based on morphism properties, to previous works of Kameda and Weiner (1970), and of Sengoku (1992), whose issue is the minimization of NFAs.
Abstract: Our aim is to enumerate all NFAs (nondeterministic finite automata) that recognize a given regular language . More precisely, we produce a set 𝔸 of automata such that each automaton A recognizing appears in 𝔸 up to the merging of some states and the addition of some transitions, that is, there is a surjective morphism that maps A onto an automaton of 𝔸. We provide a common theoretical framework, based on morphism properties, to previous works of Kameda and Weiner (1970), and of Sengoku (1992), whose issue is the minimization of NFAs. Our paper gives two incomparable enumeration techniques. Both proceed by enumerating a specific class of grid covers of the automaton map. The first one is related to the canonical automaton introduced by Carrez. The second one is based on new outcomes related to the relationship between grid covers and their projections.
2 citations
TL;DR: In this paper, the authors studied the communication complexity of cellular automata with respect to a new communication complexity problem: each player knows half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by communicating as little as possible between each other.
2 citations
TL;DR: The mortality problem for 2×2 matrices is treated from the automata theory viewpoint and the decidability of the reachability problem is proved for some subclasses of one-dimensional affine automata.
Abstract: The mortality problem for 2×2 matrices is treated from the automata theory viewpoint. This problem is shown to be closely related to the reachability problem for linear and affine automata of low dimensions. The decidability of the reachability problem is proved for some subclasses of one-dimensional affine automata.
2 citations
17 Mar 1995
TL;DR: It is proved that every two-dimensional rectangular automaton A with positive-slope variables has a finite mutual simulation relation, which is the intersection of the region bisimulations defined by the extremal slopes of the variables of A.
Abstract: Many decidability results for hybrid automata rely upon the finite region bisimulation of timed automata [AD94]. Rectangular automata do not have finite bisimulations [Hen95], yet have many decidable verification problems [PV94,HKPV95]. We prove that every two-dimensional rectangular automaton A with positive-slope variables has a finite mutual simulation relation, which is the intersection of the region bisimulations defined by the extremal slopes of the variables of A. While the mutual simulation is infinite for two-dimensional automata with one variable taking both positive and negative slopes, it forms a regular tesselation of the plane, and therefore can be encoded by one counter. As a corollary, we obtain the decidability of model checking linear temporal logic on these automata.
2 citations
TL;DR: This work considers a possible generalization of nondeterministic finite automata to use such automata for describing practical anytime algorithms for the same problems of minimization and to simplify some proofs for algorithms of simplification for usual nondetergetic automata.
Abstract: We consider a possible generalization of nondeterministic finite automata. The goals of this consideration are: to apply some obtained algorithms for various problems of minimization of classical nondeterministic automata; to use such automata for describing practical anytime algorithms for the same problems of minimization; to simplify some proofs for algorithms of simplification for usual nondeterministic automata.
2 citations