To model Web services handling data from an infinite domain, or with multiple sessions, we introduce fresh-variable automata, a simple extension of finite-state automata in which some transitions are labeled with variables that can be refreshed in some specified states. We prove several closure properties for this class of automata and study their decision problems. We then introduce a notion of simulation that enables us to reduce the Web service composition problem to the construction of a simulation of a target service by the asynchronous product of existing services, and prove that this construction is computable.
Abstract. Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we give two distinct characterizations of undirected graphs of entanglement at most 2. With these characterizations at hand, we present a linear time algorithm to decide whether an undirected graph has this property.
We introduce a framework for computer-aided derivation of multi-scale models. It relies on a combination of an asymptotic method used in the field of partial differential equations with term rewriting techniques coming from computer science. In our approach, a multi-scale model derivation is characterized by the features taken into account in the asymptotic analysis. Its formulation consists in a derivation of a reference model associated to an elementary nominal model, and in a set of transformations to apply to this proof until it takes into account the wanted features. In addition to the reference model proof, the framework includes first order rewriting principles designed for asymptotic model derivations, and second order rewriting principles dedicated to transformations of model derivations. We apply the method to generate a family of homogenized models for second order elliptic equations with periodic coefficients that could be posed in multi-dimensional domains, with possibly multi-domains and/or thin domains.
Parity games are combinatorial representations of closed Boolean µ-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors [3,24] into a µ-calculus [2] whose standard interpretation is over the class of all complete lattices. As done by Berwanger et al. [7,8] for the propositional modal µ-calculus, it is possible to classify parity games into levels of a hierarchy according to the number of fixed-point variables. We ask whether this hierarchy collapses w.r.t. the standard interpretation. We answer this question negatively by providing, for each n ≥ 1, a parity game Gn with these properties: it unravels to a µ-term built up with n fixed-point variables, it is semantically equivalent to no game with strictly less than n − 2 fixed-point variables.Lemma 1.1. If π is a simple path of b-length n, then r n is the vertex closest to the root visited by π. Hence, if a simple path π lies in the subtree of its source, then it is a tree path.We shall deal with trees with back-edges to which a given graph unravels. Definition 1.2.A cover or unravelling of a (finite) directed graph H is a (finite) graph K together with a surjective graph morphism ρ : K −→ H such that for each v ∈ V K , the correspondence sending k to ρ(k) restricts to a bijection fromThe notion of cover of pointed digraphs is obtained from the previous by replacing the surjectivity constraint by the condition that ρ preserves the root of the pointed digraphs. 4
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