License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.133
URN: urn:nbn:de:0030-drops-181858
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18185/
Go to the corresponding LIPIcs Volume Portal

Lichter, Moritz

Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting

pdf-format:
LIPIcs-ICALP-2023-133.pdf (0.8 MB)

Abstract

At the core of the quest for a logic for Ptime is a mismatch between algorithms making arbitrary choices and isomorphism-invariant logics. One approach to tackle this problem is witnessed symmetric choice. It allows for choices from definable orbits certified by definable witnessing automorphisms.
We consider the extension of fixed-point logic with counting (IFPC) with witnessed symmetric choice (IFPC+WSC) and a further extension with an interpretation operator (IFPC+WSC+I). The latter operator evaluates a subformula in the structure defined by an interpretation. When similarly extending pure fixed-point logic (IFP), IFP+WSC+I simulates counting which IFP+WSC fails to do. For IFPC+WSC, it is unknown whether the interpretation operator increases expressiveness and thus allows studying the relation between WSC and interpretations beyond counting.
In this paper, we separate IFPC+WSC from IFPC+WSC+I by showing that IFPC+WSC is not closed under FO-interpretations. By the same argument, we answer an open question of Dawar and Richerby regarding non-witnessed symmetric choice in IFP. Additionally, we prove that nesting WSC-operators increases the expressiveness using the so-called CFI graphs. We show that if IFPC+WSC+I canonizes a particular class of base graphs, then it also canonizes the corresponding CFI graphs. This differs from various other logics, where CFI graphs provide difficult instances.

BibTeX - Entry

@InProceedings{lichter:LIPIcs.ICALP.2023.133,
  author =	{Lichter, Moritz},
  title =	{{Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{133:1--133:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18185},
  URN =		{urn:nbn:de:0030-drops-181858},
  doi =		{10.4230/LIPIcs.ICALP.2023.133},
  annote =	{Keywords: witnessed symmetric choice, interpretation, fixed-point logic, counting, CFI graphs, logic for PTime}
}

Keywords: witnessed symmetric choice, interpretation, fixed-point logic, counting, CFI graphs, logic for PTime
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI