Improved state-space construction in automated verification

Abstract

Verifying system specifications using traditional model-checking techniques rapidly be- comes infeasible as the complexity of the specification becomes non-trivial, due to the state-space explosion problem, wherein the representation of the behaviour of the sys- tem becomes too large to be practically constructable. Thus, we require techniques that collapse the state-space to a manageable size while still preserving the information required for verification of the desired properties. The concept of abstraction provides one effective means of combatting state-space ex- plosion. Essentially, abstraction aims to simplify the behaviour by hiding details that are not directly relevant to the verification task. Within the abstraction framework, the original behaviour of the system is known as the concrete behaviour, and the simplified behaviour the abstract. The precise means of abstraction we consider acts by reducing the set of actions appearing in the abstract behaviour by means of a mapping from each of the set of concrete actions to an abstract action (action renaming) or to the empty word (action hiding). It has been previously shown that when the abstraction fulfils a condition called weak continuation-closure, then the abstract behaviour can be used to decide whether or not the concrete behaviour satisfies a property under a satisfaction relation called satisfaction within fairness, a relation that includes a built-in concept of fairness. The drawback is that the technique requires the construction of the original state-space, which is often infeasible. The main contribution of this thesis is to show that partial-order reduction can be combined with abstraction in such a way that the the abstraction can be used to decide whether the concrete behaviour satisfies a given property within fairness using only a partial-order reduced version of the state-space, which potentially could be orders of magnitude smaller than the full state-space. Attention is also paid to providing practical means for computing this partial-order reduction, and a couple of results in the field of compositional verification are presented.

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