Reversible conservative rational abstract geometrical computation is Turing-universal

Jérôme Durand-Lose (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

In Abstract geometrical computation for black hole computation (MCU '04, LNCS 3354), the author provides a setting based on rational numb ers, abstract geometrical computation, with super-Turing capability. In the present paper, we prove the Turing computing capability of reversible conservative abstract geometrical computation. Reversibility allows backtracking as well as saving energy; it corresponds here to the local reversibility of collisions. Conservativeness corresponds to the preservation of another energy measure ensuring that the number of signals remains bounded. We first consider 2-counter automata enhanced with a stack to keep track of the computation. Then we built a simulation by reversible conservative rational signal machines.

Mots clés: Abstract geometrical computation; Conservativeness; Rational numbers; Reversibility; Turing-computability; 2-counter automata

Domaines: Logique en informatique [cs.LO]; Géométrie algorithmique [cs.CG]; Mathématique discrète [cs.DM]; Complexité [cs.CC]

Jérôme Durand-Lose. Reversible conservative rational abstract geometrical computation is Turing-universal. 2nd Conference on Computability in Europe (CiE '06), Jun 2006, Swansea, United Kingdom. pp.163-172, ⟨10.1007/11780342_18⟩. ⟨hal-00079687⟩