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.2023.32
URN: urn:nbn:de:0030-drops-190268
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Martens, Jan ; Groote, Jan Friso

Computing Minimal Distinguishing Hennessy-Milner Formulas is NP-Hard, but Variants are Tractable

LIPIcs-CONCUR-2023-32.pdf (0.9 MB)


We study the problem of computing minimal distinguishing formulas for non-bisimilar states in finite LTSs. We show that this is NP-hard if the size of the formula must be minimal. Similarly, the existence of a short distinguishing trace is NP-complete. However, we can provide polynomial algorithms, if minimality is formulated as the minimal number of nested modalities, and it can even be extended by recursively requiring a minimal number of nested negations. A prototype implementation shows that the generated formulas are much smaller than those generated by the method introduced by Cleaveland.

BibTeX - Entry

  author =	{Martens, Jan and Groote, Jan Friso},
  title =	{{Computing Minimal Distinguishing Hennessy-Milner Formulas is NP-Hard, but Variants are Tractable}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{32:1--32:17},
  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-190268},
  doi =		{10.4230/LIPIcs.CONCUR.2023.32},
  annote =	{Keywords: Distinguishing behaviour, Hennessy-Milner logic, NP-hardness}

Keywords: Distinguishing behaviour, Hennessy-Milner logic, NP-hardness
Collection: 34th International Conference on Concurrency Theory (CONCUR 2023)
Issue Date: 2023
Date of publication: 07.09.2023
Supplementary Material: Software: archived at:

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