On the basis of run semantics and breadth-first algebraic semantics, the algebraic characterizations for a classes of formal power series over complete strong bimonoids are investigated in this paper. As recognizers, weighted pushdown automata with final states (WPDAs for short) and empty stack (WPDAs[Formula: see text]) are shown to be equivalent based on run semantics. Moreover, it is demonst...

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [BR82; EK03], i.e. mappings from trees to a semiring K. A widely studied class of tree series is the class of rational (or recognizable) tree series which can be defined either in an algebraic way or by means of multiplicity tree automata. We argue that ...

We next want to construct a much larger ring in which infinite sums of multiples of elements of S are allowed. In order to insure that multiplication is well-defined, from now on we assume that S has the following additional property: (#) For all s ∈ S, {(s1, s2) ∈ S × S : s1s2 = s} is finite. Thus, each element of S has only finitely many factorizations as a product of two elements. For exampl...

In a recent paper we introduced Parikh slender languages and series as a generalization of slender languages de ned and studied by Andra siu, Dassow, P aun and Salomaa. Results concerning Parikh slender series can be applied in ambiguity proofs of context-free languages. In this paper an algorithm is presented for deciding whether or not a given N-algebraic series is Parikh slender. Category: F...

Gabrielov’s famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization of the concept of ideals in power series rings. hh july 31, 2017 Introduction In the Séminaire Henri Cartan of 1960/61, Grothendieck posed the question whether analytically ...

A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).

We characterize the dependence on doublets of the cohomology of an arbitrary nilpotent differential s (including BRST differentials and classical linearized Slavnov-Taylor (ST) operators) in terms of the cohomology of the doublets-independent component of s. All cohomologies are computed in the space of local integrated formal power series. We drop the usual assumption that the counting operato...