On Deterministic Finite Automata and Syntactic Monoid Size, ...
Reference
Markus Holzer and Barbara König. On deterministic finite automata and syntactic monoid size, continued. In Proc. of DLT '03 (Developments in Language Theory), pages 349–360. Springer-Verlag, 2003. LNCS 2710.
Abstract
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
there exist natural numbers
and
with
such that the semigroup
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
-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.
Suggested BibTeX entry:
@inproceedings{HK03,
author = {Markus Holzer and Barbara K{\"o}nig},
booktitle = {Proc. of DLT '03 (Developments in Language Theory)},
note = {{LNCS} 2710},
pages = {349--360},
publisher = {Springer-Verlag},
title = {On Deterministic Finite Automata and Syntactic Monoid Size, Continued},
year = {2003}
}
