Compositional Model Checking of Partially Ordered State Spaces

Symbolic trajectory evaluation (STE) — a model checking technique based on partial orderrepresentations of state spaces — has been shown to be an effective model checking techniquefor large circuit models. However, the temporal logic that it supports is restricted, and as with allverification techniques has significant performance limitations. The demand for verifying largercircuits, and the need for greater expressiveness requires that both these problems be examined.The thesis develops a suitable logical framework for model checking partially ordered statespaces: the temporal logic TL and its associated satisfaction relations, based on the quaternarylogic . TL is appropriate for expressing the truth of propositions about partially ordered statespaces, and has suitable technical properties that allow STE to support a richer temporal logic.Using this framework, verification conditions called assertions are defined, a generalised ver-sion of STE is developed, and three STE-based algorithms are proposed for investigation. Ad-vantages of this style of proof include: models of time are incorporated; circuits can be de-scribed at a low level; and correctness properties are expressed at a relatively high level.A primary contribution of the thesis is the development of a compositional theory for TLassertions. This compositional theory is supported by the partial order representation of statespace. To show the practical use of the compositional theory, two prototype verification sys-tems were constructed, integrating theorem proving and STE. Data is manipulated efficientlyby using binary decision diagrams as well as symbolic data representation methods. Simpleheuristics and a flexible interface reduce the human cost of verification.Experiments were undertaken using these prototypes, including verifying two circuits fromthe IFIP WG 10.5 Benchmark suite. These experiments showed that the generalised STE al-gorithms were effective, and that through the use of the compositional theory it is possible toverify very large circuits completely, including detailed timing properties.