The Book of Traces

Diekert, Volker; Rozenberg, Grzegorz

doi:10.1142/2563

Cited by 351 publications

(267 citation statements)

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“…In other words, there is a one-to-one correspondence between nested traces and equivalence classes of ∼ Σ . We remark that nested traces are a merge of Mazurkiewicz traces [10] and nested words [3], which, in turn, generalize themselves the notion of a word.…”

Section: Specifying Programs In Mso Logicmentioning

confidence: 75%

Realizability of Concurrent Recursive Programs

Bollig

Grindei

Habermehl

2009

Foundations of Software Science and Computational Structures

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Abstract. We define and study an automata model of concurrent recursive programs. An automaton consists of a finite number of pushdown systems running in parallel and communicating via shared actions. Actually, we combine multi-stack visibly pushdown automata and Zielonka's asynchronous automata towards a model with an undecidable emptiness problem. However, a reasonable restriction allows us to lift Zielonka's Theorem to this recursive setting and permits a logical characterization in terms of a suitable monadic second-order logic. Building on results from Mazurkiewicz trace theory and work by La Torre, Madhusudan, and Parlato, we thus develop a framework for the specification, synthesis, and verification of concurrent recursive processes.

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Section: Specifying Programs In Mso Logicmentioning

confidence: 75%

Realizability of Concurrent Recursive Programs

Bollig

Grindei

Habermehl

2009

Foundations of Software Science and Computational Structures

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“…This model has a solid theoretical foundation based on the theory of Mazurkiewicz traces [9,4]. The key property of asynchronous automata, known as Zielonka's theorem, is that every regular trace language can be represented by a deterministic asynchronous automaton [15].…”

Section: Introductionmentioning

confidence: 99%

Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata

Genest

Gimbert

Muscholl

et al. 2010

Automata, Languages and Programming

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Abstract. Asynchronous automata are parallel compositions of finitestate processes synchronizing over shared variables. A deep theorem due to Zielonka says that every regular trace language can be represented by a deterministic asynchronous automaton. In this paper we improve the construction, in that the size of the obtained asynchronous automaton is polynomial in the size of a given DFA and simply exponential in the number of processes. We show that our construction is optimal within the class of automata produced by Zielonka-type constructions. In particular, we provide the first non trivial lower bound on the size of asynchronous automata.

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“…During the last two decades, this topic has attracted much attention, and several notions of graph-language recognisability have been developed [15,4,25,7,10,8,6].…”

Section: Introductionmentioning

confidence: 99%

“…Robust notions of recognisability are available, in particular, for partially ordered sets which serve as models for concurrent computation [7,17].…”

Section: Introductionmentioning

confidence: 99%

Automata on Directed Graphs: Edge Versus Vertex Marking

Berwanger

Janin

2006

Lecture Notes in Computer Science

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Abstract. We investigate two models of finite-state automata that operate on rooted directed graphs by marking either vertices (V-automata) or edges (E-automata). Runs correspond to locally consistent markings and acceptance is defined by means of regular conditions on the paths emanating from the root. Comparing the expressive power of these two notions of graph acceptors, we show that E-automata are more expressive than V-automata. Moreover, we prove that E-automata are at least as expressive as the µ-calculus. Our main result implies that every MSOdefinable tree language can be recognised by E-automata with uniform runs, that is, runs that do not distinguish between isomorphic subtrees.

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The Book of Traces

Cited by 351 publications

References 0 publications

Realizability of Concurrent Recursive Programs

Realizability of Concurrent Recursive Programs

Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata

Automata on Directed Graphs: Edge Versus Vertex Marking

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