Interval-valued computations and their connection with PSPACE

Authors:
Benedek Nagy;Sándor Vályi
Affiliations:
Department of Computer Science, Faculty of Informatics, University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary and Reasearch Group on Mathematical Lingusitics, Rovira i Virgili University, Ta ...;Department of Computer Science, Faculty of Informatics, University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

At the conference CiE 2005, the first author introduced a new model for analog computations, namely interval-valued computations. In this model, computations work on the so-called interval-valued bytes, which are special subsets of the interval [0,1) rather than a finite sequence of bits. The question was posed there, which complexity is needed to solve PSPACE-complete problems in this paradigm. In this paper, after formalizing the computational model, we answer this question. We show that the validity problem of quantified propositional formulae is decidable by a linear interval-valued computation. As a consequence, all polynomial space problems are decidable by a polynomial interval-valued computation. Furthermore, it is proven that PSPACE coincides with the class of languages which are decidable by a restricted polynomial interval-valued computation.