The success of model checking is largely based on its ability to efficiently locate errors in software designs. If an error is found, a model checker produces a trail that shows how the error state can be reached, which greatly facilitates debugging. However, while current model checkers find error states efficiently, the counterexamples are often unnecessarily lengthy, which hampers error explanation. This is due to the use of "naive" search algorithms in the state space exploration. In this paper we present approaches to the use of heuristic search algorithms in explicit-state model checking. We present the class of A * directed search algorithms and propose heuristics together with bitstate compression techniques for the search of safety property violations. We achieve great reductions in the length of the error trails, and in some instances render problems analyzable by exploring a much smaller number of states than standard depth-first search. We then suggest an improvement of the nested depth-first search algorithm and show how it can be used together with A * to improve the search for liveness property violations. Our approach to directed explicit-state model checking has been implemented in a tool set called HSF-SPIN. We provide experimental results from the protocol validation domain using HSF-SPIN.

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We provide an overview of the organization and results of the deterministic part of the 4th International Planning Competition, i.e., of the part concerned with evaluating systems doing deterministic planning. IPC-4 attracted even more competing systems than its already large predecessors, and the competition event was revised in several important respects. After giving an introduction to the IPC, we briefly explain the main differences between the deterministic part of IPC-4 and its predecessors. We then introduce formally the language used, called PDDL2.2 that extends PDDL2.1 by derived predicates and timed initial literals. We list the competing systems and overview the results of the competition. The entire set of data is far too large to be presented in full. We provide a detailed summary; the complete data is available in an online appendix. We explain how we awarded the competition prizes.

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