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Solving QSAT in Sublinear Depth

  • Alberto LeporatiEmail author
  • Luca Manzoni
  • Giancarlo Mauri
  • Antonio E. Porreca
  • Claudio Zandron
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11399)

Abstract

Among Open image in new window -complete problems, QSAT, or quantified SAT, is one of the most used to show that the class of problems solvable in polynomial time by families of a given variant of P systems includes the whole Open image in new window . However, most solutions require a membrane nesting depth that is linear with respect to the number of variables of the QSAT instance under consideration. While a system of a certain depth is needed, since depth 1 systems only allows to solve problems in Open image in new window , it was until now unclear if a linear depth was, in fact, necessary. Here we use P systems with active membranes with charges, and we provide a construction that proves that QSAT can be solved with a sublinear nesting depth of order \(\frac{n}{\log n}\), where n is the number of variables in the quantified formula given as input.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alberto Leporati
    • 1
    Email author
  • Luca Manzoni
    • 1
  • Giancarlo Mauri
    • 1
  • Antonio E. Porreca
    • 1
    • 2
  • Claudio Zandron
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanoItaly
  2. 2.Aix Marseille Université, Université de Toulon, CNRS, LISMarseilleFrance

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