Abstraction for verification and refutation in model checking

Model checking is an automated technique for deciding whether a computer program satisfies a temporal property. Abstraction is the key to scaling model checking to industrial-sized problems, which approximates a large (or infinite) program by a smaller abstract model and lifts the model checking result over the abstract model back to the original program. In this thesis, we study abstraction in model checking based on \emph{exact-approximation}, which allows for verification and refutation of temporal properties within the same abstraction framework. Our work in this thesis is driven by problems from both practical and theoretical aspects of exact-approximation. We first address challenges of effectively applying symmetry reduction to \emph{virtually} symmetric programs. Symmetry reduction can be seen as a \emph{strong} exact-approximation technique, where a property holds on the original program if and only if it holds on the abstract model. In this thesis, we develop an efficient procedure for identifying virtual symmetry in programs. We also explore techniques for combining virtual symmetry with symbolic model checking. Our second study investigates model checking of \emph{recursive} programs. Previously, we have developed a software model checker for non-recursive programs based on exact-approximating predicate abstraction. In this thesis, we extend it to reachability and non-termination analysis of recursive programs. We propose a new program semantics that effectively removes call stacks while preserving reachability and non-termination. By doing this, we reduce recursive analysis to non-recursive one, which allows us to reuse existing abstract analysis in our software model checker to handle recursive programs. A variety of \emph{partial} transition systems have been proposed for construction of abstract models in exact-approximation. Our third study conducts a systematic analysis of them from both semantic and logical points of view. We analyze the connection between semantic and logical consistency of partial transition systems, compare the expressive power of different families of these formalisms, and discuss the precision of model checking over them. Abstraction based on exact-approximation uses a uniform framework to prove correctness and detect errors of computer programs. Our results in this thesis provide better understanding of this approach and extend its applicability in practice.