4 research outputs found
Syntactic Complexity of R- and J-Trivial Regular Languages
The syntactic complexity of a regular language is the cardinality of its
syntactic semigroup. The syntactic complexity of a subclass of the class of
regular languages is the maximal syntactic complexity of languages in that
class, taken as a function of the state complexity n of these languages. We
study the syntactic complexity of R- and J-trivial regular languages, and prove
that n! and floor of [e(n-1)!] are tight upper bounds for these languages,
respectively. We also prove that 2^{n-1} is the tight upper bound on the state
complexity of reversal of J-trivial regular languages.Comment: 17 pages, 5 figures, 1 tabl
On Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)
Eilenberg correspondence, based on the concept of syntactic monoids, relates
varieties of regular languages with pseudovarieties of finite monoids. Various
modifications of this correspondence related more general classes of regular
languages with classes of more complex algebraic objects. Such generalized
varieties also have natural counterparts formed by classes of finite automata
equipped with a certain additional algebraic structure. In this survey, we
overview several variants of such varieties of enriched automata.Comment: In Proceedings AFL 2014, arXiv:1405.527
On Varieties of Ordered Automata
The Eilenberg correspondence relates varieties of regular languages to
pseudovarieties of finite monoids. Various modifications of this correspondence
have been found with more general classes of regular languages on one hand and
classes of more complex algebraic structures on the other hand. It is also
possible to consider classes of automata instead of algebraic structures as a
natural counterpart of classes of languages. Here we deal with the
correspondence relating positive -varieties of languages to
positive -varieties of ordered automata and we present various
specific instances of this correspondence. These bring certain well-known
results from a new perspective and also some new observations. Moreover,
complexity aspects of the membership problem are discussed both in the
particular examples and in a general setting