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  1. Home > Articles & Issues >
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  3. A note on a recent a ...
Article

A note on a recent attempt to improve the Pin-Frankl bound

François Gonze (1), Raphaël M. Jungers (1), Avraham N. Trahtman (2)
(1) Institute of Information and Communication Technologies, Electronics and Applied Mathematics
(2) Department of Mathematics [Ramat Gan]
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Imported on
December 2, 2014
Published on
April 26, 2015
Last modified on
March 31, 2025
Volume 17
vol. 17:1
Automata, Logic and Semantics
DOI
10.46298/dmtcs.2101
License
https://about.hal.science/hal-authorisation-v1
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A note on a recent attempt to improve the Pin-Frankl bound

François Gonze (1), Raphaël M. Jungers (1), Avraham N. Trahtman (2)
(1) Institute of Information and Communication Technologies, Electronics and Applied Mathematics
(2) Department of Mathematics [Ramat Gan]
Abstract
We provide a counterexample to a lemma used in a recent tentative improvement of the Pin-Frankl bound for synchronizing automata. This example naturally leads us to formulate an open question, whose answer could fix the line of the proof, and improve the bound.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Automata
  • Synchronization
  • Cerny’s conjecture
Mathematics Subject Classification 2020
  • 05C20 - Directed graphs (digraphs), tournaments
  • 05C70 - Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
  • 05C83 - Graph minors
Cited by

Source: OpenCitations

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