We consider one aspect of the problem of specification and verification of reactive real-time systems which involve operations and constraints concerning time. Time is continuous what is motivated by specifications of hybrid systems. Our goal is to try to find a framework that is based on applied first order logic that permits to represent the verification problem directly, completely and conservatively , and that is apt to describe interesting decidable classes, maybe showing way to feasible algorithms. To achieve this goal (...) we use a first order timed logic that is an extension of a decidable theory of reals with timed functions. This logic permits, on the one hand, to rewrite directly and completely requirements and, on the other hand, to describe executions of various timed algorithms—here we consider block Gurevich abstract state machines because of their theoretical clarity and sufficient expressive power. Then we describe one decidable class of the verification problem that is based on notions reflecting finiteness properties of systems of control. These notions may be of independent interest, as, in particular, they give a way to describe a limited usage of arithmetics preserving decidability that is not covered by existing model-theoretic approaches. As an example we consider the generalized railroad crossing problem that we analyze in its entirety. (shrink)

The paper describes a decidable class of verification problems expressed in first order timed logic. To specify programs we useState Machines. It is known that Abstract State Machines and first order timed logic are two very powerful formalisms apt to represent verification problems for timed distributed systems. However, the general verification problem represented in this way is undecidable. Prior, some decidable classes of verification problems were described in semantical properties that are in their turn undecidable. The decidable class of the (...) present paper is described in syntactical terms. Though it admits no functions, only predicates, it is of practical interest and we give an example illustrating possible applications. (shrink)

We describe a decidable class of formulas in a first order timed logic that covers a good amount of properties of real-time distributed systems. Earlier we described a decidable class based on some finiteness properties, and sketched a decidable class in a weaker logic that captures periodicity properties, though without complete proof. The new feature of the decidable class presented here is to be able to treat parametric properties, in particular, properties that concern an arbitrary number of processes as compared (...) to the just mentioned class that could express only properties for a fixed, explicitly given number of processes. As before the properties may use non-trivial arithmetics. We also state another important feature of the class: if a verification formula is not true then our algorithm gives a quantifier-free description of all its counter-models of the complexity involved in the definition of the decidable class and that is quite representative. In conclusion we discuss theoretical and practical issues of the complexity and some open questions. (shrink)