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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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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 infinit ..."
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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...
A Domain for Concurrent Termination: A Generalization of Mazurkiewicz traces
 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming (ICALP'95), Szeged (Hungary) 1995, number 944 in Lecture Notes in Computer Science
, 1994
"... This paper generalizes the concept of Mazurkiewicz traces to a fuzzy description of a concurrent process, where a known prefix is given in a first component and a second alphabetic component yields necessary information about future actions. This allows to define a good semantic domain where the ..."
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This paper generalizes the concept of Mazurkiewicz traces to a fuzzy description of a concurrent process, where a known prefix is given in a first component and a second alphabetic component yields necessary information about future actions. This allows to define a good semantic domain where the concatenation is continuous with respect to the Scott and to the Lawson topology. For this we define the notion of ff\Gamma and of ffi trace. We show various mathematical results proving thereby the soundness of our approach. Our theory is a proper generalization of the theory of finite and infinite words (with explicit termination) and of the theory of finite and infinite (real and complex) traces. We make use of trace theory, domain theory, and topology. 1 Introduction The theory of Mazurkiewicz traces has been recognized as an important tool for investigating concurrent systems, overviews are in [Maz87, AR88, Per89, Die90, DR95]. The underlying idea is that for a given alphabet...
A Hierarchy of Partial Order Temporal Properties
 In Proc. Temporal Logic, LNCS
, 1994
"... We propose a classification of partial order temporal properties into a hierarchy, which is a generalization of the safetyprogress hierarchy of Chang, Manna and Pnueli. The classes of the hierarchy are characterized through three views: languagetheoretic, topological and temporal. Instead of the d ..."
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We propose a classification of partial order temporal properties into a hierarchy, which is a generalization of the safetyprogress hierarchy of Chang, Manna and Pnueli. The classes of the hierarchy are characterized through three views: languagetheoretic, topological and temporal. Instead of the domain of strings, we take the domain of Mazurkiewicz traces as a basis for our considerations. For the languagetheoretic view, we propose operations on trace languages which define the four main classes of properties: safety, guarantee, persistence and response. These four classes are shown to correspond precisely to the two lower levels of the Borel hierarchy of the Scott topology of the domain of traces relativized to the infinite traces. In addition, a syntactic characterization of the classes is provided in terms of a sublogic of the Generalized Interleaving Set Temporal Logic GISTL (an extension of ISTL). 1 Introduction Recently, Chang, Manna and Pnueli [CMP93] proposed a classificati...
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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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.