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We suggest the first strongly subexponential and purely combinatorial algorithm for solving the mean payoff games problem. It is based on iteratively improving the longest shortest distances to a sink in a possibly cyclic directed graph. We identify a new " controlled " version of the shortest paths problem. By selecting exactly one outgoing edge in each of(More)
We study the containment, satisfiability, and validity problems for conjunctive queries over trees with respect to a schema. We show that conjunctive query containment and validity are 2EXPTIME-complete w.r.t. a schema (DTD or Relax NG). Furthermore, we show that satisfiability for conjunctive queries w.r.t. a schema can be decided in NP. The problem is(More)
We suggest a new randomized algorithm for solving parity games with worst case time complexity roughly min O n 3 · n k + 1 k , 2 O(√ n log n) , where n is the number of vertices and k the number of colors of the game. This is comparable with the previously known algorithms when the number of colors is small. However, the subexponential bound is an advantage(More)
We give a simple, direct, and constructive proof of memoryless determinacy for parity and mean payoo games. First, we prove by induction that the ÿnite duration versions of these games, played until some vertex is repeated, are determined and both players have memoryless winning strategies. In contrast to the proof of Ehrenfeucht and Mycielski, Internat.(More)
The complexity of solving infinite games, including parity, mean payoff, and simple stochastic, is an important open problem in verification, automata, and complexity theory. In this paper, we develop an abstract setting for studying and solving such games, based on function optimization over certain discrete structures. We introduce new classes of(More)
The complexity of containment and satisfiability of conjunc-tive queries over finite, unranked, labeled trees is studied with respect to the axes Child , NextSibling, their transitive and reflexive closures, and Following. For the containment problem a trichotomy is presented, classifying the problems as in PTIME, coNP-complete, or Π P 2-complete. For the(More)
We prove that minimizing finite automata is NP-hard for almost all classes of automata that extend the class of deterministic finite automata. More specifically, we show that minimization is NP-hard for all finite automata classes that subsume the class of δNFAs which accept strings of length at most three. Here, δNFAs are the finite automata that are(More)