Partial Commutation and Traces

Diekert, Volker; Métivier, Yves

doi:10.1007/978-3-642-59126-6_8

Cited by 110 publications

(64 citation statements)

References 45 publications

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“…In other words, there is a one-to-one correspondence between traces and equivalence classes of ∼ e Σ . We remark that visibly pushdown traces are a merge of Mazurkiewicz traces [11] and nested words [3], which, in turn, generalize themselves the notion of a word. Fixing supplies of first-order variables x, y, .…”

Section: Specifying Programs In Mso Logicmentioning

confidence: 80%

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Realizability of concurrent recursive programs

Bollig¹,

Grindei²,

Habermehl

2017

Form Methods Syst Des

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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 recent 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: 80%

“…This set forms a regular word language [11,16] so that the intersection L(F A ) ∩ LexNF is regular, too.…”

Section: ⊓ ⊔mentioning

confidence: 99%

Realizability of concurrent recursive programs

Bollig¹,

Grindei²,

Habermehl

2017

Form Methods Syst Des

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“…Given an independence relation over an alphabet, two strings are said to be equivalent if one can be obtained from the other by repeatedly commuting adjacent independent symbols. An equivalence class of such a type is known as a Mazurkiewicz trace in concurrency theory [Maz87,DM97]. The new compression problem is then to compactly represent an input string if the decompressor is allowed to output any string that is equivalent to the original string.…”

Section: Introductionmentioning

confidence: 99%

Compression of Partially Ordered Strings

Alur

Chaudhuri

Etessami

et al. 2003

CONCUR 2003 - Concurrency Theory

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Abstract. We introduce the problem of compressing partially ordered strings: given string σ ∈ Σ * and a binary independence relation I over Σ, how can we compactly represent an input if the decompressor is allowed to reconstruct any string that can be obtained from σ by repeatedly swapping adjacent independent symbols? Such partially ordered strings are also known as Mazurkiewicz traces, and naturally model executions of concurrent programs. Compression techniques have been applied with much success to sequential program traces not only to store them compactly but to discover important profiling patterns within them. For compression to achieve similar aims for concurrent program traces we should exploit the extra freedom provided by the independence relation. Many popular string compression schemes are grammar-based schemes that produce a small context-free grammar generating uniquely the given string. We consider three classes of strategies for compression of partiallyordered strings: (i) we adapt grammar-based schemes by rewriting the input string σ into an "equivalent" one before applying grammar-based string compression, (ii) we represent the input by a collection of projections before applying (i) to each projection, and (iii) we combine (i) and (ii) with relabeling of symbols. We present some natural algorithms for each of these strategies, and present some experimental evidence that the extra freedom does enable extra compression. We also prove that a strategy of projecting the string onto each pair of dependent symbols can indeed lead to exponentially more succinct representations compared with only rewriting, and is within a factor of |Σ| 2 of the optimal strategy for combining projections with rewriting.

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“…We refer the reader to the survey [10,9] or to the recent articles of Ochmański [17,18,19] for further references.In this paper, we present new advances on two problems of this area. The first problem is well-known and has a very precise statement.…”

mentioning

confidence: 99%

“…We refer the reader to the survey [10,9] or to the recent articles of Ochmański [17,18,19] for further references.…”

mentioning

confidence: 99%

When Does Partial Commutative Closure Preserve Regularity?

Gómez

Guaiana

2008

Automata, Languages and Programming

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The closure of a regular language under commutation or partial commutation has been extensively studied [1,11,12,13], notably in connection with regular model checking [2,3,7] or in the study of Mazurkiewicz traces, one of the models of parallelism [14,15,16,22]. We refer the reader to the survey [10,9] or to the recent articles of Ochmański [17,18,19] for further references.In this paper, we present new advances on two problems of this area. The first problem is well-known and has a very precise statement. The second problem is more elusive, since it relies on the somewhat imprecise notion of robust class. By a robust class, we mean a class of regular languages closed under some of the usual operations on languages, such as Boolean operations, product, star, shuffle, morphisms, inverses of morphisms, residuals, etc. For instance, regular languages form a very robust class, commutative languages (languages whose syntactic monoid is commutative) also form a robust class. Finally, group languages (languages whose syntactic monoid is a finite group) form a semi-robust class: they are closed under Boolean operation, residuals and inverses of morphisms, but not under product, shuffle, morphisms or star.Here are the two problems: The classes considered in this paper are all closed under polynomial operations. Recall that, given a class L of regular languages, the polynomial languages of L are the finite unions of languages of the form L 0 a 1 L 1 · · · a k L k where a 1 , . . . , a k are letters and L 0 , . . . , L k are languages of L. Taking the polynomial closure usually increase robustness. For instance, the class Pol(G) of polynomials of group languages is closed under union, intersection, quotients, product, shuffle and inverses of morphisms. Let I be a partial commutation and let D be its complement in A × A. Our main results on Problems 1 and 2 can be summarized as follows:

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Partial Commutation and Traces

Cited by 110 publications

References 45 publications

Realizability of concurrent recursive programs

Realizability of concurrent recursive programs

Compression of Partially Ordered Strings

When Does Partial Commutative Closure Preserve Regularity?

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