We consider an extension of modal logic with an operator for constructing...

We investigate the model checking problems for guarded first-order and fixed point logics by reducing them to parity games. This approach is known to provide good results for the modal µ-calculus and is very closely related to automata-based methods. To obtain good results also for guarded logics, optimized constructions of games have to be provided. Further, we study the structure of parity games, isolate `easy' cases that admit efficient algorithmic solutions, and determine their relationship to specific fragments of guarded fixed point logics.

We survey evaluation games for first-order logic and least fixed point logics, and discuss their algorithmic complexity.

We show that the problem of computing all contiguous k-ary compositions of a sequence of n values under an associative and commutative operator requires 3 k\Gamma1 k+1 n \Gamma O(k) operations. For the operator max we show in contrast that in the decision tree model the complexity is i 1 + \Theta(1= p k) j n \Gamma O(k). Finally we show that the complexity of the corresponding on-line problem for the operator max is i 2 \Gamma 1 k\Gamma1 j n \Gamma O(k). This work was partially supported by the ESPRIT Long Term Research Program of the EU under contract #20244 (ALCOM-IT). y Supported by the Danish Natural Science Research Council (Grant No. 9400044). z Basic Research in Computer Science, Centre of the Danish National Research Foundation. 1 Introduction Given a sequence of values (x 1 ; x 2 ; : : : ; x n ) from a universe U and an associative binary operator \Phi, we consider the problem of computing all k-ary compositions of contiguous subsequences of length...

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