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DOI: 10.4230/LIPIcs.MFCS.2023.7

Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes

Authors: Antonis Achilleos and Aggeliki Chalki

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

We present quantitative logics with two-step semantics based on the framework of quantitative logics introduced by Arenas et al. (2020) and the two-step semantics defined in the context of weighted logics by Gastin & Monmege (2018). We show that some of the fragments of our logics augmented with a least fixed point operator capture interesting classes of counting problems. Specifically, we answer an open question in the area of descriptive complexity of counting problems by providing logical characterisations of two subclasses of #P, namely SpanL and TotP, that play a significant role in the study of approximable counting problems. Moreover, we define logics that capture FPSPACE and SpanPSPACE, which are counting versions of PSPACE.

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Antonis Achilleos and Aggeliki Chalki. Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{achilleos_et_al:LIPIcs.MFCS.2023.7,
  author =	{Achilleos, Antonis and Chalki, Aggeliki},
  title =	{{Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.7},
  URN =		{urn:nbn:de:0030-drops-185412},
  doi =		{10.4230/LIPIcs.MFCS.2023.7},
  annote =	{Keywords: descriptive complexity, quantitative logics, counting problems, #P}
}

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Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes

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