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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27 Jun 2004
TL;DR: The concept of lattice-valued regular expressions is introduced and it is shown that such expressions become not only the necessary tool for the analysis and synthesis of fuzzy automata, but give rise to a recursive generation of the family of fuzzy languages accepted by fuzzy Automata from certain simple fuzzy languages.
Abstract: In this study, we introduce the concept of lattice-valued regular expressions. Such expressions become not only the necessary tool for the analysis and synthesis of fuzzy automata, but give rise to a recursive generation of the family of fuzzy languages accepted by fuzzy automata from certain simple fuzzy languages. The equivalence between lattice-valued regular expressions and lattice-valued finite automata is demonstrated. We also show that the family of fuzzy languages accepted by deterministic lattice-valued finite automata (abbreviated as DLA) is not closed under Kleene closure operation. Similarly, we show that in general the family of fuzzy languages accepted by (nondeterministic) lattice-valued finite automata (abbreviated as LA) is not closed under complement operation. These two findings form an essential difference between lattice-valued finite automata and classical finite automata. We also elaborate on regular expressions produced by DLA.
8 citations
TL;DR: Haskell code is developed for two ways to list the strings of the language defined by a regular expression: directly by set operations and indirectly by converting to and simulating an equivalent automaton.
Abstract: Haskell code is developed for two ways to list the strings of the language defined by a regular expression: directly by set operations and indirectly by converting to and simulating an equivalent automaton. The exercise illustrates techniques for dealing with infinite ordered domains and leads to an effective standard form for nondeterministic finite automata.
8 citations
27 Jun 2005
TL;DR: A class of acyclic automata for which it is easy-to-find a regular expression that has linear size is presented, and those automata are called UDR, which is characterized by properties of its underlying digraph.
Abstract: Computing short regular expressions equivalent to a given finite automaton is a hard task. We present a class of acyclic automata for which it is easy-to-find a regular expression that has linear size. We call those automata UDR. A UDR automaton is characterized by properties of its underlying digraph. We give a characterisation theorem and an efficient algorithm to determine if an acyclic automaton is UDR, that can be adapted to compute an equivalent short regular expression.
8 citations
24 Mar 2012
TL;DR: New and explicit Ramsey-based algorithms for the universality and inclusion problem for nondeterministic parity automata are developed and it is shown that the speed-up in the asymptotic worst-case gained through the new and direct methods is exponential in the number of priorities in the parity Automata.
Abstract: Parity automata are a generalisation of Buchi automata that have some interesting advantages over the latter, e.g. determinisability, succinctness and the ability to express certain acceptance conditions like the intersection of a Buchi and a co-Buchi condition directly as a parity condition. Decision problems like universality and inclusion for such automata are PSPACE-complete and have originally been tackled via explicit complementation only. Ramsey-based methods are a later development that avoids explicit complementation but relies on an application of Ramsey's Theorem for its correctness. In this paper we develop new and explicit Ramsey-based algorithms for the universality and inclusion problem for nondeterministic parity automata. We compare them to Ramsey-based algorithms which are obtained from translating parity automata into Buchi automata first and then applying the known Ramsey-based analysis procedures to the resulting automata. We show that the speed-up in the asymptotic worst-case gained through the new and direct methods is exponential in the number of priorities in the parity automata. We also show that the new algorithms are much more efficient in practice.
8 citations
TL;DR: This work considers timed automata with more general enabling regions coupling the continuous and discrete dynamics than those previously considered, and provides a necessary condition for the existence of a finite state reduction.
Abstract: We consider a class of hybrid dynamical systems and obtain conditions under which the behavior of these systems can be reduced to a finite state automaton. Specifically, we consider timed automata with more general enabling regions coupling the continuous and discrete dynamics than those previously considered. We provide a necessary condition for the existence of a finite state reduction, together with examples showing that this condition is not sufficient. We then give two sufficient conditions that provide a large class of systems with general enabling regions which admit finite reductions.
8 citations