We study model checking problems for pushdown systems and linear time logics. We show that the global model checking problem (computing the set of configurations, reachable or not, that violate the formula) can be solved in O(g P gP 3 gBgB 3 ) time and O(gP gP 2 gBgB 2 ) space, where gP gP and gBgB are the size of the pushdown system and the size of a Büchi automaton for the negation of the formula. The global model checking problem for reachable configurations can be solved in O(gP gP 4 gBgB 3 ) time and O(gP gP 4 gBgB 2 ) space. In the case of pushdown systems with constant number of control states (relevant for our application), the complexity becomes O(gP gP gBgB 3 ) time and O(gP gP gBgB 2 ) space and O(gP gP 2 gBgB 3 ) time and O(gP gP 2 gBgB 2 ) space, respectively. We show applications of these results in the area of program analysis and present some experimental results.
Recently, pushdown systems (PDSs) have been extended to weighted PDSs, in which each transition is labeled with a value, and the goal is to determine the meet-over-allpaths value (for paths that meet a certain criterion). This paper shows how weighted PDSs yield new algorithms for certain classes of interprocedural dataflow-analysis problems.
Abstract. Recently, pushdown systems (PDSs) have been extended to weighted PDSs, in which each transition is labeled with a value, and the goal is to determine the meet-over-allpaths value (for paths that meet a certain criterion). This paper shows how weighted PDSs yield new algorithms for certain classes of interprocedural dataflow-analysis problems.
Abstract. The automata-theoretic approach to LTL verification relies on an algorithm for finding accepting cycles in a Büchi automaton. Explicit-state model checkers typically construct the automaton "on the fly" and explore its states using depth-first search. We survey algorithms proposed for this purpose and identify two good algorithms, a new algorithm based on nested DFS, and another based on strongly connected components. We compare these algorithms both theoretically and experimentally and determine cases where both algorithms can be useful.
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