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.2023.37
URN: urn:nbn:de:0030-drops-190313
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/19031/
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Li, Yong ; Schewe, Sven ; Vardi, Moshe Y.

Singly Exponential Translation of Alternating Weak Büchi Automata to Unambiguous Büchi Automata

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LIPIcs-CONCUR-2023-37.pdf (0.8 MB)

Abstract

We introduce a method for translating an alternating weak Büchi automaton (AWA), which corresponds to a Linear Dynamic Logic (LDL) formula, to an unambiguous Büchi automaton (UBA). Our translations generalise constructions for Linear Temporal Logic (LTL), a less expressive specification language than LDL. In classical constructions, LTL formulas are first translated to alternating very weak automata (AVAs) - automata that have only singleton strongly connected components (SCCs); the AVAs are then handled by efficient disambiguation procedures. However, general AWAs can have larger SCCs, which complicates disambiguation. Currently, the only available disambiguation procedure has to go through an intermediate construction of nondeterministic Büchi automata (NBAs), which would incur an exponential blow-up of its own. We introduce a translation from general AWAs to UBAs with a singly exponential blow-up, which also immediately provides a singly exponential translation from LDL to UBAs. Interestingly, the complexity of our translation is smaller than the best known disambiguation algorithm for NBAs (broadly (0.53n)ⁿ vs. (0.76n)ⁿ), while the input of our construction can be exponentially more succinct.

BibTeX - Entry

@InProceedings{li_et_al:LIPIcs.CONCUR.2023.37,
  author =	{Li, Yong and Schewe, Sven and Vardi, Moshe Y.},
  title =	{{Singly Exponential Translation of Alternating Weak B\"{u}chi Automata to Unambiguous B\"{u}chi Automata}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{37:1--37:17},
  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 =		{https://drops.dagstuhl.de/opus/volltexte/2023/19031},
  URN =		{urn:nbn:de:0030-drops-190313},
  doi =		{10.4230/LIPIcs.CONCUR.2023.37},
  annote =	{Keywords: B\"{u}chi automata, unambiguous automata, alternation, weak, disambiguation}
}

Keywords: Büchi automata, unambiguous automata, alternation, weak, disambiguation
Collection: 34th International Conference on Concurrency Theory (CONCUR 2023)
Issue Date: 2023
Date of publication: 07.09.2023

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