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Logical Definability on Infinite Traces
 Theoretical Computer Science
, 1993
"... The main results of the present paper are the equivalence of definability by monadic secondorder logic and recognizability for real trace languages, and that firstorder definable, starfree, and aperiodic real trace languages form the same class of languages. This generalizes results on infinite w ..."
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Cited by 31 (4 self)
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The main results of the present paper are the equivalence of definability by monadic secondorder logic and recognizability for real trace languages, and that firstorder definable, starfree, and aperiodic real trace languages form the same class of languages. This generalizes results on infinite words and on finite traces to infinite traces. It closes an important gap in the different characterizations of recognizable languages of infinite traces. 1 Introduction In the late 70's, A. Mazurkiewicz introduced the notion of trace as a suitable mathematical model for concurrent systems [16] (for surveys on this topic see also [1, 6, 10, 17]). In this framework, a concurrent system is seen as a set \Sigma of atomic actions together with a fixed irreflexive and symmetric independence relation I ` \Sigma \Theta \Sigma. The relation I specifies pairs of actions which can be carried out in parallel. It generates an equivalence relation on the set of sequential observations of the system. As ...
Deterministic Asynchronous Automata for Infinite Traces
 Acta Informatica
, 1993
"... This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite tra ..."
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Cited by 13 (3 self)
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This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by some Idiamond deterministic Muller automaton. 1 Introduction A. Mazurkiewicz introduced the concept of traces as a suitable semantics for concurrent systems [Maz77]. A concurrent system is given by a set of atomic actions \Sigma = fa; b; c; : : :g together with an independence relation I ` \Sigma \Theta \Sigma, which specifies pairs of actions which can be performed concurrently. This leads to an equivalence relation on \Sigma generated by the independence relation I. More precisely, if a and b denote independent...
On the complementation of asynchronous cellular Büchi automata
 Theoretical Computer Science
, 1996
"... We present direct subset automata constructions for asynchronous (asynchronous cellular, resp.) automata. This provides a solution to the problem of direct determinization for automata with distributed control for languages of finite traces. We use the subset automaton construction and apply Kla ..."
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Cited by 1 (0 self)
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We present direct subset automata constructions for asynchronous (asynchronous cellular, resp.) automata. This provides a solution to the problem of direct determinization for automata with distributed control for languages of finite traces. We use the subset automaton construction and apply Klarlund's progress measure technique in order to complement nondeterministic asynchronous cellular Buchi automata for infinite traces.