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

Denys Duchier (1) , Jérôme Durand-Lose (1) , Maxime Senot (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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.

Keywords: Abstract geometrical computation; Signal machine; Q-SAT; Fractal computation; Massive parallelism; Unconventional computation; Unconventional computation.

Domains: Logic in Computer Science [cs.LO]

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⟩