Solving Q-SAT in bounded space and time by geometrical computation

Abstract : Abstract geometrical computation can solve PSPACE-com\-plete problems efficiently: any quantified boolean formula, instance of Q-SAT -- the problem of satisfiability of quantified boolean formula -- can be decided in bounded space and time with simple geometrical constructions involving only drawing parallel lines on an Euclidean space-time. Complexity as the maximal length of a sequence of consecutive segments is quadratic. We use the continuity of the real line to cover all the possible boolean valuations by a recursive tree structure relying on a fractal pattern: an exponential number of cases are explored simultaneously by a massive parallelism.
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Submitted on : Tuesday, July 5, 2011 - 4:07:19 PM
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Denys Duchier, Jérôme Durand-Lose, Maxime Senot. Solving Q-SAT in bounded space and time by geometrical computation. Models of computability in context, 7th Int. Conf. Computability in Europe, Jun 2011, Sofia, Bulgaria. pp.76-86. ⟨hal-00605661⟩



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