Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Schmid, Todd; Kappé, Tobias; Kozen, Dexter; Silva, Alexandra https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-142118
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Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness

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Abstract

Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that can distinguish between unsuccessful programs performing different actions, by omitting the so-called early termination axiom. We develop an operational (coalgebraic) and denotational (algebraic) semantics and show that they coincide. We then characterize the behaviors of GKAT expressions in this semantics, leading to a coequation that captures the covariety of automata corresponding to these behaviors. Finally, we prove that the axioms of the reduced fragment are sound and complete w.r.t. the semantics, and then build on this result to recover a semantics that is sound and complete w.r.t. the full set of axioms.

BibTeX - Entry

@InProceedings{schmid_et_al:LIPIcs.ICALP.2021.142,
  author =	{Schmid, Todd and Kapp\'{e}, Tobias and Kozen, Dexter and Silva, Alexandra},
  title =	{{Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{142:1--142:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14211},
  URN =		{urn:nbn:de:0030-drops-142118},
  doi =		{10.4230/LIPIcs.ICALP.2021.142},
  annote =	{Keywords: Kleene algebra, program equivalence, completeness, coequations}
}

Keywords: Kleene algebra, program equivalence, completeness, coequations
Seminar: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue date: 2021
Date of publication: 02.07.2021


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