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19
Pure future local temporal logics are expressively complete for Mazurkiewicz traces
 Conference version in LATIN 2004, LNCS 2976
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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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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.
Specifying and verifying partial order properties using template MSCs
 In FOSSACS’04, LNCS 2987
, 2004
"... Abstract. Message sequence charts (MSC) are a graphical language for the description of communication scenarios between asynchronous processes. Our starting point is to model systems using an assumeguarantee formalism, in the style of LSCs and Triggered MSCs. We enrich MSCs with the possibility of ..."
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Cited by 8 (3 self)
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Abstract. Message sequence charts (MSC) are a graphical language for the description of communication scenarios between asynchronous processes. Our starting point is to model systems using an assumeguarantee formalism, in the style of LSCs and Triggered MSCs. We enrich MSCs with the possibility of using gaps (template MSC), and show their expressivity. This formalism also allows to express logical formulas. We analyze the modelchecking problem, whose complexity is linear in the size of the system, and ranges from PTIME to EXPSPACE in the size of the template formula. 1
Monitoring Distributed Controllers: When an Efficient LTL Algorithm on Sequences Is Needed to ModelCheck Traces
 of LNCS
, 2006
"... Abstract. It is well known that through code instrumentation, a distributed system’s finite execution can generate a finite trace as a partially ordered set of events. We motivate the need to use LTL modelchecking on sequences and not on traces as defined by Diekert and Gastin, to validate distri ..."
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Abstract. It is well known that through code instrumentation, a distributed system’s finite execution can generate a finite trace as a partially ordered set of events. We motivate the need to use LTL modelchecking on sequences and not on traces as defined by Diekert and Gastin, to validate distributed control systems executions, abstracted by such traces, and present an efficient symbolic algorithm to do the job. It uses the standard method proposed by Vardi and Wolper, which from the LTL formula, builds a monitor that accepts all the bad sequences. We show that, given a monitor and a trace, the problem to check that both the monitor and the trace have a common sequence is NPcomplete in the number of concurrent processes. Our method explores the possible configurations symbolically, since it handles sets of configurations. Moreover, it uses techniques similar to the partial order reduction, to avoid exploring as many execution interleavings as possible. It works very well in practice, compared to the standard exploration method, with or without partial order reduction (which, in practice, does not work well here).
Deciding LTL over Mazurkiewicz traces
, 2003
"... Linear temporal logic (LTL) has become a well established tool for specifying the dynamic behaviour of reactive systems with an interleaving semantics, and the automata–theoretic approach has proven to be a very useful mechanism for performing automatic verification in this setting. Especially alter ..."
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Cited by 5 (2 self)
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Linear temporal logic (LTL) has become a well established tool for specifying the dynamic behaviour of reactive systems with an interleaving semantics, and the automata–theoretic approach has proven to be a very useful mechanism for performing automatic verification in this setting. Especially alternating automata turned out to be a powerful tool in constructing efficient yet simple to understand decision procedures and directly yield further onthefly model checking procedures. In this paper, we exhibit a decision procedure for LTL over Mazurkiewicz traces that generalises the classical automata–theoretic approach to a LTL interpreted no longer over sequences but certain partial orders. Specifically, we construct a (linear) alternating Büchi automaton (ABA) accepting the set of linearisations of traces satisfying the formula at hand. The salient point of our technique is to apply a notion of independencerewriting to formulas of the logic. Furthermore, we show that the class of linear and traceconsistent ABA corresponds exactly to LTL formulas over Mazurkiewicz traces, lifting a similar result from Löding and Thomas formulated in the framework of LTL over words.
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.
Local LTL with past constants is expressively complete for Mazurkiewicz traces
 In Proc. of MFCS’03, number 2747 in LNCS
, 2003
"... Abstract. To obtain an expressively complete lineartime temporal logic (LTL) over Mazurkiewicz traces that is computationally tractable, we need to intepret formulas locally, at individual events in a trace, rather than globally, at configurations. Such local logics necessarily require past modalit ..."
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Abstract. To obtain an expressively complete lineartime temporal logic (LTL) over Mazurkiewicz traces that is computationally tractable, we need to intepret formulas locally, at individual events in a trace, rather than globally, at configurations. Such local logics necessarily require past modalities, in contrast to the classical setting of LTL over sequences. Earlier attempts at defining expressively complete local logics have used very general past modalities as well as filters (sideconditions) that “look sideways ” and talk of concurrent events. In this paper, we show that it is possible to use unfiltered future modalities in conjunction with past constants and still obtain a logic that is expressively complete over traces.
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].
Realizability of Concurrent Recursive Programs
, 2008
"... 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 multistack visibly pushdown automata and Zielonka’s asynchronous automata towards a mod ..."
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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 multistack 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 secondorder 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.