Stéphane Demri

LTL with the Freeze Quantifier and Register Automata

Temporal logics, first-order logics, and automata over data words have recently attracted considerable attention. A data word is a word over a finite alphabet, together with a datum (an element of an infinite domain) at each position. Examples include timed words and XML documents. To refer to the data, temporal logics are extended with the freeze quantifier, first-order logics with predicates over the data domain, and automata with registers or pebbles. We investigate relative expressiveness and complexity of standard decision problems for LTL with the freeze quantifier (LTLdarr), 2-variable first-order logic (FO2) over data words, and register automata. The only predicate available on data is equality. Previously undiscovered connections among those formalisms, and to counter automata with incrementing errors, enable us to answer several questions left open in recent literature. We show that the future-time fragment of LTLdarr which corresponds to FO2 over finite data words can be extended considerably while preserving decidability, but at the expense of non-primitive recursive complexity, and that most of further extensions are undecidable. We also prove that surprisingly, over infinite data words, LTLdarr without the until operator, as well as nonemptiness of one-way universal register automata, are undecidable even when there is only 1 register

Logical Analysis of Indiscernibility

In this paper we explain the role of indiscernibility in the analysis of vagueness of concepts and in concept learning. We develop deduction methods that enable us making inferences from incomplete information in the presence of indiscernibility.

Complexity of Simple Dependent Bimodal Logics

We characterize the computational complexity of simple dependent bimodal logics. We define an operator ⊕ ⊆ between logics that almost behaves as the standard joint operator ⊕ except that the inclusion axiom ([2]{tt p} Rightarrow [1] {tt p}) is added. Many multimodal logics from the literature are of this form or contain such fragments. For the standard modal logics K,T,B,S4 and S5 we study the complexity of the satisfiability problem of the joint in the sense of ⊕ ⊆ . We mainly establish the PSPACE upper bounds by designing tableaux-based algorithms in which a particular attention is given to the formalization of termination and to the design of a uniform framework. Reductions into the packed guarded fragment with only two variables introduced by M. Marx are also used. E. Spaan proved that K ⊕ ⊆ S5 is EXPTIME-hard. We show that for (langle {cal L}_1,{cal L}_2 rangle in {K,T,B} times {S4,S5}), ({cal L}_1 oplus_{subseteq} {cal L}_2) is also EXPTIME-hard.

The complexity of propositional linear temporal logics in simple cases

It is well-known that model-checking and satisfiability for PLTL are PSPACE-complete. By contrast, very little is known about whether there exist some interesting fragments of PLTL with a lower worst-case complexity. Such results would help understand why PLTL model-checkers are successfully used in practice.

The Effects of Bounding Syntactic Resources on Presburger LTL

We study decidability and complexity issues for fragments of LTL with Presburger constraints by restricting the syntactic resources of the formulae (the class of constraints, the number of variables and the distance between two states for which counters can be compared) while preserving the strength of the logical operators. We provide a complete picture refining known results from the literature, in some cases pushing forward the known decidability limits. By way of example, we show that model-checking formulae from LTL with quantifier-free Presburger arithmetic over one-counter automata is only PSPACE-complete. In order to establish the PSPACE upper bound, we show that the nonemptiness problem for Buchi one-counter automata taking values in Z and allowing zero tests and sign tests, is only NLOGSPACE-complete.

A class of decidable information logics

Abstract For a class of propositional information logics defined from Pawlaks information systems, the validity problem is proved to be decidable using a significant variant of the standard filtration technique. Decidability is proved by showing that each logic has the strong finite model property and by bounding the size of the models. The logics in the scope of this paper are characterized by classes of Kripke-style structures with interdependent relations pairwise satisfying the Gargovs local agreement condition and closed under the so-called restriction operation. They include Gargovs data analysis logic with local agreement and Nakamuras logic of graded modalities. The last part of the paper is devoted to the definition of complete Hubert-style axiomatizations for subclasses of the introduced logics, thus providing evidence that such logics are subframe logics in Wolters sense.

A Class of Information Logics with a Decidable Validity Problem

For a class of prepositional information logics defined from Pawlaks information systems, the validity problem is proved to be decidable using a significant variant of the standard filtration technique. Actually the decidability is proved by showing that each logic has the strong finite model property and by bounding the size of the models. The logics in the scope of this paper are characterized by classes of Kripkestyle structures with interdependent equivalence relations and closed by the so-called restriction operation. They include Gargovs data analysis logic with local agreement and Nakamuras logic of graded modalities.

The Covering and Boundedness Problems for Branching Vector Addition Systems

The covering and boundedness problems for nbranching vector addition systems nare shown complete for doubly-exponential time.

Temporal logics on strings with prefix relation

We show that linear-time temporal logic over concrete domains made of finite strings and the prefix relation admits a PSpace-complete satisfiability problem. Actually, we extend a known result with the concrete domain made of the set of natural numbers and the greater than relation (corresponding to the singleton alphabet case) and we solve an open problem mentioned in several publications. Since the prefix relation is not a total ordering, it is not possible to take advantage of existing techniques dedicated to temporal logics with concrete domains that are essentially linearly ordered structures. Instead, we introduce an adequate encoding of string constraints into length constraints that allows us to reduce the problem on strings to the problem on natural numbers. To do so, we also propose an extended version of the logic on strings that is able to compare lengths of longest common prefixes and for which the satisfiability problem is shown in PSpace. Finally, we show how to lift the result for the branching-time case in order to get decidability when the underlying temporal logic is CTL.

Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic

We show that model-checking flat counter systems over CTL* (with arithmetical constraints on counter values) has the same complexity as the satisfiability problem for Presburger arithmetic. The lower bound already holds with the temporal operator EF only, no arithmetical constraints in the logical language and with guards on transitions made of simple linear constraints. This complements our understanding of model-checking flat counter systems with linear-time temporal logics, such as LTL for which the problem is already known to be (only) NP-complete with guards restricted to the linear fragment.