Reasoning about reversal-bounded counter machines

International audienceIn this paper, we present a short survey on reversal-bounded counter machines. It focuses on the main techniques for model-checking such counter machines with specifications expressed with formulae from some linear-time temporal logic. All the decision procedures are designed by translation into Presburger arithmetic. We provide a proof that is alternative to Ibarra's original one for showing that reachability sets are effectively definable in Presburger arithmetic. Extensions to repeated control state reachability and to additional temporal properties are discussed in the paper. The article is written to the honor of Professor Ewa Orłowska and focuses on several topics that are developped in her works

Modal logics with relative accessibility relations

International audienc

Modal logics with relative accessibility relations

International audienceThis paper presents a systematic study of the logics based on Kripke models with relative accessibility relations as well as a general method for proving their completeness

A Hierarchy of Modal Logics With Relative Accessibility Relations

In this paper we introduce and investigate various classes of multimodal logics based on frames with relative accessibility relations. We discuss their applicability to representation and analysis of incomplete information. We provide axiom systems for these logics and we prove their completeness. 1 Introduction The original motivation for introducing and investigating modal logics with relative accessibility relations comes from the theory of information systems. However, as it is shown in this paper, a number of standard multimodal logics can be uniformly presented and investigated within the general framework of relative relations as well. Information systems are the collections of information items that have the form of descriptions of some objects in terms of their properties. More formally, by an information system we mean a structure S = (OB; AT ; fVAL a : a 2 ATg) such that OB is a nonempty set Philippe Balbiani, [email protected], Laboratoire d'informatique de..