We introduce weighted regular tree grammars with storage as combination of (a) regular tree grammars with storage and (b) weighted tree automata over multioperator monoids. Each weighted regular tree grammar with storage generates a weighted tree language, which is a mapping from the set of trees to the multioperator monoid. We prove that, for multioperator monoids canonically associated to par...

Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalizing two results on regula...

We investigate the relationship between regular languages and syntactic monoid size. In particular, we consider the transformation monoids of n-state (minimal) deterministic finite automata. We show tight upper bounds on the syntactic monoid size, proving that an nstate deterministic finite automaton with singleton input alphabet (input alphabet with at least three letters, respectively) induce...

In this study, Bruck-Reilly extension of a ternary monoid is defined. Additionally, some results about construction are given which belongs to one the classes semigroups; regular, inverse, orthodox and strongly regular.

We develop an algebraic theory for languages of data words. We prove that, under certain conditions, a language of data words is definable in first-order logic if and only if its syntactic monoid is aperiodic. 1 Introduction This paper is an attempt to combine two fields. The first field is the algebraic theory of regular languages. In this theory, a regular language is represented by its synta...

Let M be a submonoid of the free monoid A∗, and let X ⊆ M be a variable length code (for short a code). X is weakly M-complete if any word in M is a factor of some word in X∗ [J. Néraud, C. Selmi, Free monoid theory: maximality and completeness in arbitrary submonoids, Internat. J. Algorithms Comput. 13(5) (2003) 507–516]. Given a code X ⊆ M , we are interested in the construction of a weakly M...

Let Σ = X ∪ X = {x1, x2, ..., xm, x −1 1 , x 2 , ..., x m } and let G be a group with set of generators Σ. Let L(G) = {ω ∈ Σ∗ | ω ≡ e (mod G)} ⊆ Σ∗ be the group language representing G, where Σ∗ is a free monoid over Σ and e is the identity in G. The problem of determining whether a context-free language is subset of a group language is discussed. Polynomial algorithms are presented for testing...