Model checking finite paths and trees

This thesis presents efficient parallel algorithms for checking temporal logic formulas over finite paths and trees. We show that LTL path checking is in AC(logDCFL) and CTL tree checking is in AC(logDCFL). For LTL with pasttime and bounded modalities, which is an exponentially more succinct logic, we show that the path checking problem remains in AC(logDCFL). Our results provide a foundation for efficient algorithms of various applications in monitoring, testing, and verification as well as for query processing for tree-datastructures, e.g. XML documents. The presented path and tree checking algorithms are based on efficient parallel evaluation strategies for monotone Boolean circuits. We reduce the evaluation of product circuits to the problem of evaluating one-input-face monotone planar Boolean circuits: for a monotone Boolean circuit that is a product of a tree and a path, we provide an AC-reduction; for a monotone Boolean circuit that is a product of two trees, we provide an AC-reduction. We develop a classification of Kripke structures with respect to the complexity of LTL model checking: Kripke structures for which the problem is PSPACEcomplete, Kripke structures for which the problem is coNP-complete, and Kripke structures for which the problem is in NC.