Aubert, Clément and Bagnol, Marc - Unification and Logarithmic Space

lmcs:4552 - Logical Methods in Computer Science, July 31, 2018, Volume 14, Issue 3 -
Unification and Logarithmic Space

Authors: Aubert, Clément and Bagnol, Marc

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 rooted in proof theory and more specifically linear logic and geometry of interaction. We show how to build a model of computation in the unification algebra and then, by means of a syntactic representation of finite permutations in the algebra, we prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. Finally, we show that the construction naturally corresponds to pointer machines, a convenient way of understanding logarithmic space computation.

Volume: Volume 14, Issue 3
Published on: July 31, 2018
Submitted on: May 31, 2018
Keywords: Computer Science - Logic in Computer Science,03D15, 68N17,F.1.3,F.4.1


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