No abstract

There has been much interest in decision procedures for testing satisfiability of formulas in various systems of temporal logic. This is due to the potential applications of such decision procedures to the mechanical synthesis of concurrent programs from their specifications.However, formulae of classical temporal logics can express specifications of only a fixed number of processes. Thus, their use in mechanical synthesis suffers from two limitations, viz., the state explosion problem and their inability to describe dynamic systems, ones in which the number of processes could vary to adapt to external demands. In this paper, we present an indexed temporal logic, Indexed Simplified Computation Tree Logic (Indexed SCTL), that can be used to specify programs with arbitrarily many similar processes. With a view to synthesizing such programs mechanically from specifications, we pose two new decision problems: almost always satisfiability and almost always unsatisfiability. We show that both these problems are decidable for Indexed SCTL, and, in fact, that every Indexed SCTL specification is either almost always satisfiable, i.e., it can be realized by a concurrent program provided that the number of constituent processes exceeds a certain value that depends on the specification (and is determined by our decision procedure), or is almost always unsatisfiable,i.e., no concurrent program with more than a certain number (which, again, is determined by the decision procedure) of processes can ever realize the specification. Finally, we show how our results could be used to automate the synthesis of a concurrent system that meets a desired Indexed SCTL specification which is almost always satisfiable.

We introduce two systems concepts: bounded response-time and self-stabilization in the context of rule-based programs. These concepts are essential for the design of rule-based programs which must be highly fault-tolerant and perform in a real-time environment.The mechanical analysis of programs for these two properties will be discussed. We have also applied our techniques to analyze a NASA application.

No abstract

No abstract