Symeon Bozapalidis

Equational Elements in Additive Algebras

Abstract. Let K and Γ be a semiring and a finite ranked alphabet, respectively. We consider K -Γ -algebras with additive carriers and fully multilinear operations. The free objects in this category are the K -Γ -algebras

Weighted grammars and Kleene's theorem

K\langle \langle T_{\Gamma} (X)\rangle \rangle

Effective construction of the synthetic algebra of a recognizable series on trees

of formal power series on trees with coefficients in K . We study equational elements in such structures. More precisely we establish the following classical result of Mezei and Wright: the equational elements of

The rank of a formal tree power series

K\langle \langle T_{\Gamma} \rangle \rangle

Context-Free Series on Trees

are the recognizable formal power series, whereas each equational element of an additive K -Γ -algebra

Alphabetic tree relations

\cal A

Graph automata

is the image via the unique morphism

Représentations matricielles des séries d'arbre reconnaissables

H_{\cal A}: K \langle \langle T_{\Gamma} \rangle \rangle \rightarrow {\cal A}

Fuzzy tree language recognizability

of a recognizable formal power series. As a consequence we get closure of the family Eq(

Recognizability of graph and pattern languages

\cal A