Which finite monoids are syntactic monoids of rational ω-languages

Which finite monoids are syntactic monoids of rational ω-languages

A notion of ω-rigid sets for a finite monoid is introduced. We prove that a finite monoid M is the Arnold's syntactic monoid of some rational ω-language (ω-syntactic for short) if and only if there exists an ω-rigid set for M. This property is shown to be decidable for the finite monoids. Relat...

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Veröffentlicht in:Information processing letters 1992-05, Vol.42 (3), p.127-132
Hauptverfasser: Huy, Phan Trung, Livotsky, Igor, Van, Do Long
Format: Artikel
Sprache:eng
Schlagworte:
Applied sciences
Computer science
control theory
systems
Exact sciences and technology
Formal languages
Language theory and syntactical analysis
syntactic monoid
Theoretical computing
ω-languages
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Zusammenfassung:A notion of ω-rigid sets for a finite monoid is introduced. We prove that a finite monoid M is the Arnold's syntactic monoid of some rational ω-language (ω-syntactic for short) if and only if there exists an ω-rigid set for M. This property is shown to be decidable for the finite monoids. Relationship between the family of ω-syntactic monoids and that of ∗-syntactic monoids (i.e. the syntactic monoids of rational languages of finite words) is established.
ISSN:0020-0190
1872-6119
DOI:10.1016/0020-0190(92)90135-I