We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i or x i , the values of the counter i respectively after and before the transition, and # is any relational symbol in f=; ; ; ?; !g. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of N (or Z or R depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata. 1 Introduction Finite state automata provide a nice framework for the verification of reactive systems. Their main advantage is the equivalence between recognizability and definability in some decidable logic (e.g. Monadic Second Order Logic or some of its fragments such as tempora...

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Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1 Grammars : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2. Systems of equations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.1 Systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Resolution : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.3 Linear systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.4 Parikh's theorem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

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In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logic by means of deterministic Presburger tree automata (PTA) and show how it can be used to express numerical document queries. Surprisingly, the complexity of satisfiability for the extended logic is asymptotically the same as for the original logic. The non-emptiness for PTAs is in general pspace-complete which is moderate given that it is already pspace-hard to test whether the complement of a regular expression is non-empty. We also identify a subclass of PTAs with a tractable non-emptiness problem. Further, to decide whether a tree t satisfies a formula # is polynomial in the size of # and linear in the size of t.

. Mildly context sensitive grammar formalisms such as multicomponent TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a non-semilinear language. This implies that none of the aforementioned grammar formalisms is strong enough to generate this language. Introduction What we have in mind when we use the term syntactic invariant is, roughly speaking, a property, valid within some (formal) grammar theory, which remains "robust under slight modifications" of this theory. In the following we direct our particular attention to one such property: Semilinearity (of a language). Introducing the definition of semilinearity Parikh proved that any context free language (CFL) is semilinear (see e.g. Parikh 1966). It has been shown that there is a need to go beyond the class of all CFLs, if we want to define a formal language in terms of phr...

We propose an Abstract Interpretation-based static analysis for automatically detecting the dependencies between the names linked to the agents of a mobile system. We focus our study on the mobile systems written in the pi-calculus. We first refine the standard semantics in order to restore the relation between the names and the agents that have declared them. We then abstract the dependency relations that are always satisfied by the names of the agents of a mobile system. That is to say we will detect which names are always pair-wisely equal, and which names have necessarily been declared by the same recursive instance of an agent.

An asynchronous program is one that contains procedure calls which are not immediately executed from the callsite, but stored and “dispatched” in a non-deterministic order by an external scheduler at a later point. We formalize the problem of interprocedural dataflow analysis for asynchronous programs as AIFDS problems, a generalization of the IFDS problems for interprocedural dataflow analysis. We give an algorithm for computing the precise meet-over-valid-paths solution for any AIFDS instance, as well as a demand-driven algorithm for solving the corresponding demand AIFDS instances. Our algorithm can be easily implemented on top of any existing interprocedural dataflow analysis framework. We have implemented the algorithm on top of BLAST, thereby obtaining the first safety verification tool for unbounded asynchronous programs. Though the problem of solving AIFDS instances is EXPSPACE-hard, we find that in practice our technique can efficiently analyze programs by exploiting standard optimizations of interprocedural dataflow analyses.

Strategic games may exhibit symmetries in a variety of ways. A common aspect of symmetry, enabling the compact representation of games even when the number of players is unbounded, is that players cannot (or need not) distinguish between the other players. We define four classes of symmetric games by considering two additional properties: identical payoff functions for all players and the ability to distinguish oneself from the other players. Based on these varying notions of symmetry, we investigate the computational complexity of pure Nash equilibria. It turns out that in all four classes of games equilibria can be found efficiently when only a constant number of actions is available to each player, a problem that has been shown intractable for other succinct representations of multi-player games. We further show that identical payoff functions simplify the search for equilibria, while a growing number of actions renders it intractable. Finally, we show that our results extend to wider classes of threshold symmetric games where players are unable to determine the exact number of players playing a certain action.

Abstract. In order to make multithreaded programming manageable, programmers often follow a design principle where they break the problem into tasks which are then solved asynchronously and concurrently on different threads. This paper investigates the problem of model checking programs that follow this idiom. We present a programming language SPL that encapsulates this design pattern. SPL extends simplified form of sequential Java to which we add the capability of making asynchronous method invocations in addition to the standard synchronous method calls and the ability to execute asynchronous methods in threads atomically and concurrently. Our main result shows that the control state reachability problem for finite SPL programs is decidable. Therefore, such multithreaded programs can be model checked using the counterexample guided abstraction-refinement framework. 1