Reducing non-occurrence of specified runtime errors to all-path reachability problems of constrained rewriting

Abstract

A concurrent program with semaphore-based exclusive control can be modeled by a logically constrained term rewrite system. In this paper, we first propose a framework to reduce the non-occurrence of a specified runtime error in the program to an all-path reachability problem of the transformed logically constrained term rewrite system. Here, an all-path reachability problem of the system is a pair of state sets and is demonically valid if every finite execution path starting with a state in the first set and ending with a terminating state includes a state in the second set. Then, we propose a weakened but easily-implementable variant of an existing proof system for all-path reachability problems. As a case study, we deal with the race freedom of concurrent programs with semaphore-based exclusive control.