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State Complexity of Testing Divisibility

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object , Other literature type 07 Aug 2010Embargo end date: 01 Aug 2010 Belgium English Publisher:Open Publishing AssociationJournal:Electronic Proceedings in Theoretical Computer Science, volume 31, pages 48-57 (eissn: 2075-2180, Copyright policy )
Authors: Charlier, Emilie; Rampersad, Narad; Rigo, Michel; Waxweiler, Laurent;

doi: 10.4204/eptcs.31.7 , 10.48550/arxiv.1008.1668

arXiv: 1008.1668

handle: 2268/64877

State Complexity of Testing Divisibility

Abstract

Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m >= 2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of the multiples of m in the Fibonacci system is exactly 2m^2.

In Proceedings DCFS 2010, arXiv:1008.1270

Country
Belgium
Related Organizations
Keywords

Sciences informatiques, FOS: Computer and information sciences, Periodicity, Formal Languages and Automata Theory (cs.FL), Physique, chimie, mathématiques & sciences de la terre, Numeration system, Computer Science - Formal Languages and Automata Theory, QA75.5-76.95, Computer science, Automata, Engineering, computing & technology, Ingénierie, informatique & technologie, Mathématiques, Divisibility criterion, Physical, chemical, mathematical & earth Sciences, Electronic computers. Computer science, F.4.3, State complexity, QA1-939, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
gold