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Equivalence Problems for Boolean Constraint Satisfaction
, 2001
"... 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 p ..."
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Cited by 5 (2 self)
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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 polynomialtime solvable or coNPcomplete, and we give a simple criterion to determine which case holds. Another equivalence problem...
Boolean Hierarchies inside DotDepth One
, 1999
"... Let B 1/2 denote the class of languages having dotdepth 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 dotdepth one if and only if it is in the Boolean clo ..."
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Cited by 3 (1 self)
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Let B 1/2 denote the class of languages having dotdepth 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 dotdepth one if and only if it is in the Boolean closure of B 1/ . We examine the structure of the class of dotdepth 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.
Generic Separations and Leaf Languages
 Mathematical Logic Quaterly
, 2001
"... 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 ..."
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Cited by 1 (1 self)
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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, resourcebounded genericity, and type2 complexity. Keywords: computational and structural complexity, leaf language, oracle separation, generic oracle, type2 complexity theory. 1
Practical Strategies for Hypotheses Elimination on the SelfLocalization Problem
, 1999
"... We take a look at the second part of the robotselflocalizationproblem. 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 vo ..."
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Cited by 1 (0 self)
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We take a look at the second part of the robotselflocalizationproblem. 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.