Static Backward Slicing of Non-deterministic Programs and Systems

Abstract

A theory of slicing non-deterministic programs and systems is developed. Non-deterministic programs and systems are represented as non-deterministic program graphs (NDPGs) that allow arbitrary non-deterministic branching to be expressed. Structural and semantic relationships that must exist between an NDPG and (1) its non-termination insensitive (weak) slices and (2) its non-termination sensitive (strong) slices are defined. Weak and strong commitment closure are introduced. These are the NDPG equivalents of being closed under non-termination sensitive and non-termination insensitive control dependence; properties defined on subsets of vertices of the equivalent deterministic structure: the control flow graph. It is proved that if a subset of the vertices of an NDPG is both data dependence closed and (weak/strong) commitment closed, then the resulting induced graph will, indeed, satisfy our structural and semantic requirements. O ( n 3 ) algorithms for computing minimal data and weak/strong commitment closed sets are given. The resulting induced graphs are thus guaranteed to be weak and strong slices, respectively. It is demonstrated, with examples, that programs written in Dijkstra's non-deterministic guarded command language (DNGCL) can be converted to NDPGs to which our slicing algorithms can then be applied. It is proved that the resulting slices (NDPGs) can always be converted back to valid DNGCL programs, highlighting the applicability of our approach to slicing at the source code level.