Games for Verification: Algorithmic Issues

This dissertation deals with a number of algorithmic problems motivated by computer aided formal verification of finite state systems. The goal of formal verification is to enhance the design and development of complex systems by providing methods and tools for specifying and verifying correctness of designs. The success of formal methods in practice depends heavily on the degree of automation of development and verification process. This motivates development of efficient algorithms for problems underlying many verification tasks. Two paradigmatic algorithmic problems motivated by formal verification that are in the focus of this thesis aremodel checking and bisimilarity checking. In the thesis game theoretic formulations of the problems are used to abstract away from syntactic and semantic peculiarities of formal models and specification formalisms studied. This facilitates a detailed algorithmic analysis, leading to two novel model checking algorithms with better theoretical or practical performance, and to an undecidability result for a notion of bisimilarity. The original technical contributions of this thesis are collected in three research articles whose revised and extended versions are included in the dissertation. In the first two papers the computational complexity of deciding the winner in parity games is studied. The problem of solving parity games is polynomial time equivalent to the modal mu-calculus model checking. The modal mu-calculus plays a central role in the study of logics for specification and verification of programs. The model checking problem is extensively studied in literature on computer aided verification. The question whether there is a polynomial time algorithm for the modal mu-calculus model checking is one of the most challenging and fascinating open questions in the area. In the first paper a new algorithm is developed for solving parity games, and hence for the modal mu-calculus model checking. The design and analysis of the algorithm are based on a semantic notion of a progress measure. The worst-case running time of the resulting algorithmmatches the best worst-case running time bounds known so far for the problem, achieved by the algorithms due to Browne at al., and Seidl. Our algorithm has better space complexity: it works in small polynomial space; the other two algorithms have exponential worst-case space complexity. In the second paper a novel approach to model checking is pursued, based