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Descriptive Complexity of Deterministic Polylogarithmic Time

  • Flavio FerrarottiEmail author
  • Senén González
  • José María Turull Torres
  • Jan Van den Bussche
  • Jonni Virtema
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11541)

Abstract

We propose a logical characterization of problems solvable in deterministic polylogarithmic time (\(\mathrm {PolylogTime}\)). We introduce a novel two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. In the course of proving that our logic indeed captures \(\mathrm {PolylogTime}\) on finite ordered structures, we introduce a variant of random-access Turing machines that can access the relations and functions of the structure directly. We investigate whether an explicit predicate for the ordering of the domain is needed in our logic. Finally, we present the open problem of finding an exact characterization of order-invariant queries in \(\mathrm {PolylogTime}\).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Software Competence Center HagenbergHagenbergAustria
  2. 2.Universidad Nacional de La MatanzaBuenos AiresArgentina
  3. 3.Hasselt UniversityHasseltBelgium

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