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22
Firstorder definable languages
 Logic and Automata: History and Perspectives, Texts in Logic and Games
, 2008
"... We give an essentially selfcontained presentation of some principal results for firstorder definable languages over finite and infinite words. We introduce the notion of a counterfree Büchi automaton; and we relate counterfreeness to aperiodicity and to the notion of very weak alternation. We al ..."
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Cited by 24 (5 self)
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We give an essentially selfcontained presentation of some principal results for firstorder definable languages over finite and infinite words. We introduce the notion of a counterfree Büchi automaton; and we relate counterfreeness to aperiodicity and to the notion of very weak alternation. We also show that aperiodicity of a regular ∞language can be decided in polynomial space, if the language is specified by some Büchi automaton. 1
Uniform satisfiability problem for local temporal logics over Mazurkiewicz traces
 In CONCUR’05, Lecture Notes in Comp. Science
, 2005
"... Abstract. We continue our study of the complexity of temporal logics over concurrent systems that can be described by Mazurkiewicz traces. In a previous paper (CONCUR 2003), we investigated the class of local and MSO definable temporal logics that capture all known temporal logics and we showed that ..."
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Cited by 14 (4 self)
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Abstract. We continue our study of the complexity of temporal logics over concurrent systems that can be described by Mazurkiewicz traces. In a previous paper (CONCUR 2003), we investigated the class of local and MSO definable temporal logics that capture all known temporal logics and we showed that the satisfiability problem for any such logic is in PSPACE (provided the dependence alphabet is fixed). In this paper, we concentrate on the uniform satisfiability problem: we consider the dependence alphabet (i.e., the architecture of the distributed system) as part of the input. We prove lower and upper bounds for the uniform satisfiability problem that depend on the number of monadic quantifier alternations present in the chosen MSOmodalities. 1
Algebraic recognizability of languages
 In Proc. 29th Int. Symp. Math. Found. of Comp. Sci. (MFCS’04
, 2004
"... Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those ..."
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Cited by 13 (2 self)
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Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. In the beginning was the Word... Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. The notion of recognizable languages is a familiar one, associated with classical theorems by Kleene, Myhill, Nerode, Elgot, Büchi, Schützenberger, etc. It can be approached from several angles: recognizability by automata, recognizability by finite monoids or finiteindex congruences, rational expressions, monadic second
Temporal logics for concurrent recursive programs: Satisfiability and model checking
 In MFCS’11, volume 6907 of LNCS
, 2011
"... Abstract. We develop a general framework for the design of temporal logics for concurrent recursive programs. A program execution is modeled as a partial order with multiple nesting relations. To specify properties of executions, we consider any temporal logic whose modalities aredefinable in monadi ..."
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Cited by 9 (3 self)
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Abstract. We develop a general framework for the design of temporal logics for concurrent recursive programs. A program execution is modeled as a partial order with multiple nesting relations. To specify properties of executions, we consider any temporal logic whose modalities aredefinable in monadic secondorder logic and that, in addition, allows PDLlike path expressions. This captures, in a unifying framework, a wide range of logics defined for ranked and unranked trees, nested words, and Mazurkiewicz traces that have been studied separately. We show that satisfiability and model checking are decidable in EXPTIME and 2EXPTIME, depending on the precise path modalities. 1
Local temporal logic is expressively complete for cograph dependence alphabets
 In Proceedings of LPAR’01, number 2250 in LNAI
, 2001
"... Abstract. Recently, local logics for Mazurkiewicz traces are of increasing interest. This is mainly due to the fact that the satisfiability problem has the same complexity as in the word case. If we focus on a purely local interpretation of formulae at vertices (or events) of a trace, then the satis ..."
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Cited by 9 (7 self)
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Abstract. Recently, local logics for Mazurkiewicz traces are of increasing interest. This is mainly due to the fact that the satisfiability problem has the same complexity as in the word case. If we focus on a purely local interpretation of formulae at vertices (or events) of a trace, then the satisfiability problem of linear temporal logics over traces turns out to be PSPACE–complete. But now the difficult problem is to obtain expressive completeness results with respect to first order logic. The main result of the paper shows such an expressive completeness result, if the underlying dependence alphabet is a cograph, i.e., if all traces are series parallel posets. Moreover, we show that this is the best we can expect in our setting: If the dependence alphabet is not a cograph, then we cannot express all first order properties.
ON LOGICAL HIERARCHIES WITHIN FO2DEFINABLE LANGUAGES
"... Abstract. We consider the class of languages defined in the 2variable fragment of the firstorder logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose le ..."
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Abstract. We consider the class of languages defined in the 2variable fragment of the firstorder logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose levels are varieties of languages (and hence admit an algebraic characterization). Using this algebraic approach, we show that the quantifier alternation hierarchy inside FO2[<] is decidable within one unit. For this purpose, we relate each level of the hierarchy with decidable varieties of languages, which can be defined in terms of iterated deterministic and codeterministic products. A crucial notion in this process is that of condensed rankers, a refinement of the rankers of Weis and Immerman and the turtle languages of Schwentick, Thérien and Vollmer. Many important properties of systems are modeled by finite automata. Frequently, the formal languages induced by these systems are definable
On firstorder fragments for words and Mazurkiewicz traces: A survey
 Developments in Language Theory, 11th International Conference, DLT 2007
"... Abstract. We summarize several characterizations, inclusions, and separations on fragments of firstorder logic over words and Mazurkiewicz traces. The results concerning Mazurkiewicz traces can be seen as generalizations of those for words. It turns out that over traces it is crucial, how easy conc ..."
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Abstract. We summarize several characterizations, inclusions, and separations on fragments of firstorder logic over words and Mazurkiewicz traces. The results concerning Mazurkiewicz traces can be seen as generalizations of those for words. It turns out that over traces it is crucial, how easy concurrency can be expressed. Since there is no concurrency in words, this distinction does not occur there. In general, the possibility of expressing concurrency also increases the complexity of the satisfiability problem. In the last section we prove an algebraic and a language theoretic characterization of the fragment Σ2[E] over traces. Over words the relation E is simply the order of the positions. The algebraic characterization yields decidability of the membership problem for this fragment. For words this result is wellknown, but although our proof works in a more general setting it is quite simple and direct. An essential step in the proof consists of showing that every homomorphism from a free monoid to a finite aperiodic monoid M admits a factorization forest of finite height. We include a simple proof that the height is bounded by 3 M. 1
On firstorder fragments for Mazurkiewicz traces
"... Abstract Mazurkiewicz traces form a model for concurrency. Temporal logic and firstorder logic are important tools in order to deal with the abstract behavior of such systems. Since typical properties can be described by rather simple logical formulas one is interested in logical fragments. One foc ..."
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Abstract Mazurkiewicz traces form a model for concurrency. Temporal logic and firstorder logic are important tools in order to deal with the abstract behavior of such systems. Since typical properties can be described by rather simple logical formulas one is interested in logical fragments. One focus of this paper is unary temporal logic and firstorder logic in two variables. Over words, this corresponds to the variety of finite monoids called DA. However, over Mazurkiewicz traces it is crucial whether traces are given as dependence graphs or as partial orders (over words these notions coincide). The main technical contribution is a generalization of important characterizations of DA from words to dependence graphs, whereas the use of partial orders leads to strictly larger classes. As a consequence we can decide whether a firstorder formula over dependence graphs is equivalent to a firstorder formula in two variables. The corresponding result for partial orders is not known. This difference between dependence graphs and partial orders also affects the complexity of the satisfiability problems for the fragments under consideration: for firstorder formulas in two variables we prove an nexptime upper bound, whereas the corresponding problem for partial orders leads to expspace. Furthermore, we give several separation results for the alternation hierarchy for firstorder logic. It turns out that even for those levels at which one can express the partial order relation in terms of dependence graphs, the fragments over partial orders have more expressive power.
Computing the Reveals Relation in Occurrence Nets
, 2011
"... Topics: Petri net unfoldings are a useful tool to tackle statespace explosion in verification and related tasks. Moreover, their structure allows to access directly the relations of causal precedence, concurrency, and conflict between events. Here, we explore the data structure further, to determin ..."
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Cited by 4 (3 self)
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Topics: Petri net unfoldings are a useful tool to tackle statespace explosion in verification and related tasks. Moreover, their structure allows to access directly the relations of causal precedence, concurrency, and conflict between events. Here, we explore the data structure further, to determine the following relation: event a is said to reveal event b iff the occurrence of a implies that b inevitably occurs, too, be it before, after, or concurrently with a. Knowledge of reveals facilitates in particular the analysis of partially observable systems, in the context of diagnosis, testing, or verification; it can also be used to generate more concise representations of behaviours via abstractions. The reveals relation was previously introduced in the context of fault diagnosis, where it was shown that the reveals relation was decidable: for a given pair a,b in the unfolding U of a safe Petri net N, a finite prefix P of U is sufficient to decide whether or not a reveals b. In this paper, we first considerably improve the bound on P. We then show that there exists an efficient algorithm for computing the relation on a given prefix. We have implemented the algorithm and report on experiments. Structure and behaviour of Petri Nets; partialorder theory of concurrency; automatic analysis 1
From local to global temporal logics over Mazurkiewicz traces
 In honour of Professor Christian Choffrut on the occasion of his 60th birthday
"... We review some results on global and local temporal logic on Mazurkiewicz traces. Our main contribution is to show how to derive the expressive completeness of global temporal logic with respect to first order logic [9] from the similar result on local temporal logic [11]. ..."
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We review some results on global and local temporal logic on Mazurkiewicz traces. Our main contribution is to show how to derive the expressive completeness of global temporal logic with respect to first order logic [9] from the similar result on local temporal logic [11].