Concurrent regular expressions and their relationship to Petri nets
Theoretical Computer Science
Free shuffle algebras in language varieties
Theoretical Computer Science
Text languages in an algebraic framework
Fundamenta Informaticae - Special issue on formal language theory
Formal languages over free binoids
Journal of Automata, Languages and Combinatorics
Series-parallel languages and the bounded-width property
Theoretical Computer Science
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Finite codes over free binoids
Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Regular binoid expressions and regular binoid languages
Theoretical Computer Science
A hierarchy theorem for regular languages over free bisemigroups
Acta Cybernetica
Axiomatizing the identities of binoid languages
Theoretical Computer Science
Acta Cybernetica
Hi-index | 5.23 |
A free binoid Σ*(○, •) over a finite alphabet Σ is a free algebra generated by Σ with two independent associative operators, ○ and •. It has also the same identity λ to both operations. Any element of Σ*(○, •) is denoted uniquely by a sequence of symbols from the extended alphabet E(Σ) = Σ ∪ {○, • (,)}, and any subset of a free binoid is called a binoid language. The set of regular binoid expressions are introduced so that all languages denoted by regular binoid expressions are those which contain finite binoid languages, and closed under five operations, ∪, ○-concatenation, •-concatenation, ○-closure and •-closure. It is shown that for any regular (monoid) expression denoting a binoid language R, there exists a regular binoid expression denoting R. This result together with the main result in a previous paper implies that the class of binoid languages denoted by binoid regular expressions is the same as the class of binoid languages denoted by regular expressions over free binoids.