Applicative theories for the polynomial hierarchy of time and its levels

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Abstract

In this paper we introduce applicative theories which characterize the polynomial hierarchy of time and its levels. These theories are based on a characterization of the functions in the polynomial hierarchy using monotonicity constraints, introduced by Ben-Amram, Loff, and Oitavem.

MSC

03D15
03D55
03F30
68Q15

Keywords

Computational complexity
Polynomial hierarchy
Levels of the polynomial hierarchy
Applicative theories
Induction schemes

Cited by (0)

Work partially supported by the ESF research project Dialogical Foundations of Semantics within the ESF Eurocores program LogICCC, LogICCC/0001/2007 (funded by the Portuguese Science Foundation, FCT). The first author was also supported by the project Hilbertʼs Legacy in the Philosophy of Mathematics, PTDC/FIL-FCI/109991/2009 from FCT. The second author was also supported by the Fundação para a Ciência e a Tecnologia through the project Functional interpretations of arithmetic and analysis, PTDC/MAT/104716/2008, and PEst OE/MAT/UI0209/2011. This paper is a revised and enlarged—in particular, by the treatment of the levels of the polynomial hierarchy—version of the conference paper [14]. We thank Thomas Strahm and the anonymous referees for valuable comments.