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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01 Jan 2011
TL;DR: Survey results that compare the recognition power of different variants, consider their basic closure properties and study decidability questions are surveyed.
Abstract: Picture walking automata were introduced by M. Blum and C. Hewitt in 1967 as a generalization of one-dimensional two-way finite automata to recognize pictures, or two-dimensional words. Several variants have been investigated since then, including deterministic, non-deterministic and alternating transition rules; four-, three- and two-way movements; single- and multi-headed variants; automata that must stay inside the input picture, or that may move outside. We survey results that compare the recognition power of different variants, consider their basic closure properties and study decidability questions.
27 citations
22 Jul 2002
TL;DR: An algorithmic calculus of the reachability relations on clock values defined by timed automata is given, by computing unions, compositions and reflexive-transitive closure (star) of "atomic" relations.
Abstract: We give an algorithmic calculus of the reachability relations on clock values defined by timed automata. Our approach is a modular one, by computing unions, compositions and reflexive-transitive closure (star) of "atomic" relations. The essential tool is a new representation technique for n-clock relations - the 2n-automata - and our strategy is to show the closure under union, composition and star of the class of 2n-automata that represent reachability relations in timed automata.
27 citations
27 citations
01 Jan 2011
TL;DR: It is shown that emptiness for such automata is decidable, both over finite and infinite words, under reasonable computability assumptions on the linear order.
Abstract: In this paper we work over linearly ordered data domains equipped with finitely many unary predicates and constants. We consider nondeterministic automata processing words and storing finitely many variables ranging over the domain. During a transition, these automata can compare the data values of the current configuration with those of the previous configuration using the linear order, the unary predicates and the constants.
We show that emptiness for such automata is decidable, both over finite and infinite words, under reasonable computability assumptions on the linear order.
Finally, we show how our automata model can be used for verifying properties of workflow specifications in the presence of an underlying database.
27 citations
16 Sep 2008
TL;DR: It is shown that infinite automata defined using a form of multi-stack rewriting precisely defines double exponential time (more precisely, 2ETime), the class of problems solvable in $2^{2^{O(n)}}$ time, which captures the complexity class qualitatively.
Abstract: Infinite-state automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined using rewriting, and with sets of initial and final states. Infinite-state automata have gained recent interest due to a remarkable result by Morvan and Stirling, which shows that automata with transitions defined using rational rewriting precisely capture context-sensitive ( NLinSpace) languages. In this paper, we show that infinite automata defined using a form of multi-stack rewriting precisely defines double exponential time (more precisely, 2ETime , the class of problems solvable in $2^{2^{O(n)}}$ time). The salient aspect of this characterization is that the automata have no ostensible limits on time nor space, and neither direction of containment with respect to 2ETime is obvious. In this sense, the result captures the complexity class qualitatively, by restricting the power of rewriting.
27 citations