Towards the Construction of an Abstract State-Space from a Partial-Order Representation of the Concrete One

Abstract

When analysing a concurrent program in order to verify its correctness one faces a severe complexity problem: state-spaces corresponding to concurrent programs become tremendously large. To cope with this problem of state-space explosion, two different types of approaches have been established: abstraction techniques and partial-order methods. Abstraction aims at reducing the number of states by reducing the diversity of actions of a program. Partial-order methods reduce a state-space by ignoring particular interleavings of concurrent behavioural patterns. However, abstraction still faces the intricateness of an exhaustive state-space construction and partial-order methods, by ignoring certain patterns of actions, are not suitable for proving some property classes such as liveness properties.We combine in this paper abstraction with a partial-order approach. The aim is to use a partial-order method in the analysis phase of a concurrent program to construct only a reduced concrete state-space of the program. The reduced state-space then has to contain sufficient information about the program needed to construct the abstract state-space. The abstract state-space is then used to prove properties of the program.