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.CONCUR.2023.28
URN: urn:nbn:de:0030-drops-190225
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Groote, Jan Friso ; Willemse, Tim A. C.

Real Equation Systems with Alternating Fixed-Points

LIPIcs-CONCUR-2023-28.pdf (0.8 MB)


We introduce the notion of a Real Equation System (RES), which lifts Boolean Equation Systems (BESs) to the domain of extended real numbers. Our RESs allow arbitrary nesting of least and greatest fixed-point operators. We show that each RES can be rewritten into an equivalent RES in normal form. These normal forms provide the basis for a complete procedure to solve RESs. This employs the elimination of the fixed-point variable at the left side of an equation from its right-hand side, combined with a technique often referred to as Gauß-elimination. We illustrate how this framework can be used to verify quantitative modal formulas with alternating fixed-point operators interpreted over probabilistic labelled transition systems.

BibTeX - Entry

  author =	{Groote, Jan Friso and Willemse, Tim A. C.},
  title =	{{Real Equation Systems with Alternating Fixed-Points}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-190225},
  doi =		{10.4230/LIPIcs.CONCUR.2023.28},
  annote =	{Keywords: Real Equation System, Solution method, Gau{\ss}-elimination, Model checking, Quantitative modal mu-calculus}

Keywords: Real Equation System, Solution method, Gauß-elimination, Model checking, Quantitative modal mu-calculus
Collection: 34th International Conference on Concurrency Theory (CONCUR 2023)
Issue Date: 2023
Date of publication: 07.09.2023

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