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2003

On Deterministic Finite Automata and Syntactic Monoid Size, Continued

9 years 19 days ago
On Deterministic Finite Automata and Syntactic Monoid Size, Continued
We continue our investigation on the relationship between regular languages and syntactic monoid size. In this paper we confirm the conjecture on two generator transformation semigroups. We show that for every prime n ≥ 7 there exist natural numbers k and with n = k + such that the semigroup Uk, is maximal w.r.t. its size among all (transformation) semigroups which can be generated with two generators. This significantly tightens the bound on the syntactic monoid size of languages accepted by n-state deterministic finite automata with binary input alphabet. As a by-product of our investigations we are able to determine the maximal size among all semigroups generated by two transformations, where one is a permutation with a single cycle and the other is a non-bijective mapping.
Markus Holzer, Barbara König
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2003
Where DLT
Authors Markus Holzer, Barbara König
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