A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fi xed set C of Boolean functions. We consider the problem of determining whether two given constraint satisfaction instances are equivalent in the sense that they possess the same sets of satisfying assignments. We prove a Dichotomy Theorem by showing that for all sets C of allowed constraints, this problem is either polynomial-time solvable or coNP-complete, and we give a simple criterion to determine which case holds. Another equivalence problem...

Let B 1/2 denote the class of languages having dot-depth 1=2, i.e., the class of languages that can we written as finite unions of languages u 0 A + u 1 A + \Delta \Delta \Delta un\Gamma1 A + un , where u i 2 A and n 0. A language has dot--depth one if and only if it is in the Boolean closure of B 1/ . We examine the structure of the class of dot--depth one languages with respect to Boolean operations and identify an infinite family of Boolean hierarchies inside this class. In particular, we show that 1. the union of these hierarchies amounts to the Boolean hierarchy over B 1/2 , 2. all emerging inclusions are strict, 3. the membership problems for all classes in each hierarchy are decidable and 4. a given language can exactly be located in this landscape.

In the early nineties of the previous century, leaf languages were introduced as a means for the uniform characterization of many complexity classes, mainly in the range between P (polynomial time) and PSPACE (polynomial space). It was shown that the separability of two complexity classes can be reduced to a combinatorial property of the corresponding dening leaf languages. In the present paper, it is shown that every separation obtained in this way holds for every generic oracle in the sense of Blum and Impagliazzo. We obtain several consequences of this result, regarding, e.g., simultaneous separations and universal oracles, resource-bounded genericity, and type-2 complexity. Keywords: computational and structural complexity, leaf language, oracle separation, generic oracle, type-2 complexity theory. 1

We take a look at the second part of the robot-selflocalization-problem. The hypotheses generated in a solution of the first part of the problem will be efficient reduced with the movement of the robot. A practical approach is described, using realistic paths and imprecise sensors. It operates on voronoi edges and voronoi vertices and can handle polygons with indiscribed obstacles. A new decision strategy will be discussed different from strategy MDL. Estimations will be given for time and space complexities and for the competitve ratio.

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