We introduce a class of tree automata that perform tests on a memory that is updated using function symbol application and projection. The language emptiness problem for this class of tree automata is shown to be in DEXPTIME.

Abstract. We study the control reachability problem in the Dolev-Yao model of cryptographic protocols when principals are represented by tail recursive processes with generated names. We propose a conservative approximation of the problem by reduction to a non-standard collapsed operational semantics and we introduce checkable syntactic conditions entailing the equivalence of the standard and the collapsed semantics. Then we introduce a conservative and decidable set-based analysis of the collapsed operational semantics and we characterize a situation where the analysis is exact.

We present an automated abstract verification method for infinite-state systems specified by logic programs (which are a uniform and intermediate layer to which diverse formalisms such as transition systems, pushdown processes and while programs can be mapped). We establish connections between: logic program semantics and CTL properties, set-based program analysis and pushdown processes, and also between model checking and constraint solving, viz. theorem proving. We show that set-based analysis can be used to compute supersets of the values of program variables in the states that satisfy a given CTL property.

We show that the first-order theory of structural subtyping of non-recursive types is decidable, as a consequence of a more general result on the decidability of term powers of decidable theories.

. Set constraints is a suitable formalism for static analysis of programs. However, it is known that the complexity of set constraint problems in the most general cases is very high (NEXPTIME-completeness of the satisfiability test). Lots of works are involved in finding more tractable subclasses. In this paper, we investigate two classes of set constraints shown to be useful for program analysis: the first one is an extension of definite set constraints including the main feature of quantified set expressions. We will show that the satisfiability problem for this class is EXPTIME- complete. The second one concerns constraints of the form X ` exp, where exp is built with function symbols, the intersection and union connectives and projection operators. The dual aspects of those two classes allows to find a common approach for solving both of them. This approach uses as basic tool tree automata, which are suitable both for computation and representing the solution of those solving prob...

We show that the first-order theory of structural subtyping of non-recursive types is decidable. Let Σ be a language consisting of function symbols (representing type constructors) and C a decidable structure in the relational language L containing a binary relation ≤. C represents primitive types; ≤ represents a subtype ordering. We introduce the notion of Σ-term-power of C, which generalizes the structure arising in structural subtyping. The domain of the Σ-term-power of C is the set of Σ-terms over the set of elements of C. We show that the decidability of the first-order theory of C implies the decidability of the first-order theory of the Σterm-power of C. This result implies the decidability of the first-order theory of structural subtyping of non-recursive types.

We exhibit a rich class of Horn clauses, which we call H1 , whose least models, though possibly infinite, can be computed effectively. We show that

In this paper, we introduce the class of co-definite set constraints. This is a natural subclass of set constraints which, when satisfiable, have a greatest solution. It is practically motivated by the set-based analysis of logic programs with the greatest-model semantics. We present an algorithm solving co-definite set constraints and show that their satisfiability problem is DEXPTIME-complete. 1 Introduction Set constraints and set-based analysis form an established research topic. It combines theoretical investigations ranging from expressiveness and decidability to program semantics and domain theory, with direct practical applications to type inference, optimization and verification of imperative, functional, logic and reactive programs (see [1, 14, 20] for overviews). In set-based analysis, the problem of reasoning about runtime properties of programs is transferred to the problem of solving set constraints. The design of a system for a particular program analysis problem (for a...

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Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular record descriptions. We introduce the constraint system FT of ordering constraints interpreted over feature trees. Under the view that feature trees represent symbolic information, the relation corresponds to the information ordering ("carries less information than"). We present two algorithms in cubic time, one for the satisfiability problem and one for the entailment problem of FT . We show that FT has the independence property. We are thus able to handle negative conjuncts via entailment and obtain a cubic algorithm that decides the satisfiability of conjunctions of positive and negated ordering constraints over feature trees. Furthermore, we reduce the satisfiability problem of Dorre's weak subsumption constraints to the satisfiability problem of FT and improve the complexity bound for solving weak subsumption constraints from O(n^5) to O(n³).