Verification with the Undefined: A New Look

Abstract

Partially defined processes have been used in verification for more than a decade. When a notion of “the undefined” is added to a process description formalism, it also has to be added to the semantics, to guarantee that sophisticated verification methods such as compositional LTS construction remain correct. Until now, this has been done for each semantics separately, and the resulting theories have often been quite complicated. In this paper we discuss “the undefined” at the level of strong bisimilarity. We prove a theorem that expresses the correctness of a slightly modified version of compositional LTS construction that utilizes “the undefined”. This method assumes very little about the abstract semantics, and therefore applies to all commonly used semantics. We prove that the assumption it does make is the weakest possible that guarantees correctness. We also describe variants of the method. One of them can be used even if the tools contain no support for “the undefined”.