Unification and Logarithmic Space

Clément Aubert (1) , Marc Bagnol (1)

1 Logique de la Programmation

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction. We show how unification can be used to build a model of computation by means of specific subalgebras associated to finite permutations groups. We then prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. We also show that the construction can naturally represent pointer machines, an intuitive way of understanding logarithmic space computing.

Mots clés: Complexité implicite; Unification; Espace logarithmique; Théorie de la démonstration; Machines à pointeurs; Géométrie de l'Interaction

Domaines: Logique en informatique [cs.LO]

Clément Aubert, Marc Bagnol. Unification and Logarithmic Space. Joint International Conference, RTA-TLCA 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 14-17, 2014. Proceedings, Jul 2014, Vienne, Austria. pp.77-92, ⟨10.1007/978-3-319-08918-8_6⟩. ⟨hal-01005698⟩