Jean-Marc Talbot

Finite-Control Mobile Ambients

We define a finite-control fragment of the ambient calculus, a formalism for describing distributed and mobile computations. A series of examples demonstrates the expressiveness of our fragment. In particular, we encode the choice-free, finite-control, synchronous ?-calculus. We present an algorithm for model checking this fragment against the ambient logic (without composition adjunct). This is the first proposal of a model checking algorithm for ambients to deal with recursively-defined, possibly nonterminating, processes. Moreover, we show that the problem is PSPACE-complete, like other fragments considered in the literature. Finite-control versions of other process calculi are obtained via various syntactic restrictions. Instead, we rely on a novel type system that bounds the number of active ambients and outputs in a process; any typable process has only a finite number of derivatives.

Model checking mobile ambients

We settle the complexity bounds of the model checking problem for the ambient calculus with public names against the ambient logic. We show that if either the calculus contains replication or the logic contains the guarantee operator, the problem is undecidable. In the case of the replication-free calculus and guarantee-free logic we prove that the problem is PSPACE-complete. For the complexity upper bound, we devise a new representation of processes that remains of polynomial size during process execution; this allows us to keep the model checking procedure in polynomial space. Moreover, we prove PSPACE-hardness of the problem for several quite simple fragments of the calculus and the logic; this suggests that there are no interesting fragments with polynomial-time model checking algorithms.

Automata and logics for unranked and unordered trees

In this paper, we consider the monadic second order logic (MSO) and two of its extensions, namely Counting MSO (CMSO) and Presburger MSO (PMSO), interpreted over unranked and unordered trees. We survey classes of tree automata introduced for the logics PMSO and CMSO as well as other related formalisms; we gather results from the literature and sometimes clarify or fill the remaining gaps between those various formalisms. Finally, we complete our study by adapting these classes of automata for capturing precisely the expressiveness of the logic MSO.

When ambients cannot be opened

We investigate expressiveness of a fragment of the ambient calculus, a formalism for describing distributed and mobile computations. More precisely, we study expressiveness of the pure and public ambient calculus from which the capability open has been removed, in terms of the reachability problem of the reduction relation. Surprisingly, we show that even for this very restricted fragment, the reachability problem is not decidable. At a second step, for a slightly weaker reduction relation, we prove that reachability can be decided by reducing this problem to markings reachability for Petri nets. Finally, we show that the name-convergence problem as well as the model-checking problem turn out to be undecidable for both the original and the weaker reduction relation.

N-ary queries by tree automata

We investigate n-ary node selection queries in trees by successful runs of tree automata. We show that run-based n-ary queries capture MSO, contribute algorithms for enumerating answers of n-ary queries, and study the complexity of the problem. We investigate the subclass of run-based n-ary queries by unambiguous tree automata.

Set-Based Analysis for Logic Programming and Tree Automata

Compile-time program analysis aims to extract from a program properties useful for efficient implementations and sofware verification. A property of interest is the computational semantics of a program. For decidability reasons, only an approximation of this semantics can be computed. Set-based analysis [Hei92a] provides an elegant and accurate method for this. In the logic programming framework, this computation can be related to type inference [MR85]. In [FSVY91], a simpler presentation based on program transformation and algorithms on alternating tree automata is proposed. Unfortunately, the authors focussed on type checking (i.e. a membership test to the approximate semantics). We propose in this paper a new method to achieve set-based analysis reusing the main transformation described in [FSV Y91]. The main tool for both computation and representation of the result of set-based analysis is tree automata. This leads to a global and coherent presentation of the problem of set-based analysis combined with the simplicity of [FSVY91]. We obtain also a complexity characterization for the problem and our method. We expect that this tree automaton approach will lead to an efficient implementation, contrary to the first conclusions of [FSVY91].

TREE AUTOMATA WITH GLOBAL CONSTRAINTS

We define tree automata with global equality and disequality constraints (TAGED). TAGEDs can test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, they are equipped with an equality relation and a disequality relation on states, so that whenever two subtrees t and t′ evaluate (in an accepting run) to two states which are in the (dis)equality relation, they must be (dis)equal. We study several properties of TAGEDs, and prove emptiness decidability of for several expressive subclasses of TAGEDs.

Entailment of atomic set constraints is PSPACE-complete

The complexity of set constraints has been extensively studied over the last years and was often found quite high. At the lower end of expressiveness, there are atomic set constraints which are conjunctions of inclusions t/sub 1//spl sube/t/sub 2/ between first-order terms without set operators. It is well-known that satisfiability of atomic set constraints can be tested in cubic time. Also, entailment of atomic set constraints has been claimed decidable in polynomial time. We refute this claim. We show that entailment between atomic set constraints can express validity of quantified boolean formulas and is this PSPACE hard. For infinite signatures, we also present a PSPACE-algorithm for solving atomic set constraints with negation. This proves that entailment of atomic set constraints is PSPACE-complete for infinite signatures. In case of finite signatures, this problem is even DEXPTIME-hard.

A Generalised Twinning Property for Minimisation of Cost Register Automata

Weighted automata (WA) extend finite-state automata by associating with transitions weights from a semiring

Tree Automata with Global Constraints

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