13 research outputs found
Automata on infinite biposets
Bisemigroups are algebras equipped with two independent associative operations. Labeled finite sp-biposets may serve as a possible representation of the elements of the free bisemigroups. For finite sp-biposets, an accepting device, called parenthesizing automaton, was introduced in [6], and it was proved that its expressive power is equivalent to both algebraic recognizability and monadic second order definability. In this paper, we show, how this concept of parenthesizing automaton can be generalized for infinite biposets in a way that the equivalence of regularity (defined by acceptance with automata), recognizability (defined by homomorphisms and finite ω-bisemigroups) and MSO-definability remains true
A hierarchy theorem for regular languages over free bisemigroups
In this article a question left open in [2] is answered. In particular, we show that it is essential that in the definition of parenthesizing automata an arbitrary number of parentheses can be used. Moreover, we prove that the classes Regm of languages accepted by a parenthesizing automaton with at most m pairs of parentheses form a strict hierarchy. In fact, this hierarchy is proper for all alphabets
Weighted Logics for Nested Words and Algebraic Formal Power Series
Nested words, a model for recursive programs proposed by Alur and Madhusudan,
have recently gained much interest. In this paper we introduce quantitative
extensions and study nested word series which assign to nested words elements
of a semiring. We show that regular nested word series coincide with series
definable in weighted logics as introduced by Droste and Gastin. For this we
establish a connection between nested words and the free bisemigroup. Applying
our result, we obtain characterizations of algebraic formal power series in
terms of weighted logics. This generalizes results of Lautemann, Schwentick and
Therien on context-free languages
Free De Morgan Bisemigroups and Bisemilattices
We give a geometric representation of free De Morgan bisemigroups, free commutative De Morgan bisemigroups and free De Morgan bisemilattices, using labeled graphs
Definable transductions and weighted logics for texts
AbstractA text is a word together with an additional linear order on it. We study quantitative models for texts, i.e. text series which assign to texts elements of a semiring. We introduce an algebraic notion of recognizability following Reutenauer and Bozapalidis as well as weighted automata for texts combining an automaton model of Lodaya and Weil with a model of Ésik and Németh. After that we show that both formalisms describe the text series definable in a certain fragment of weighted logics as introduced by Droste and Gastin. In order to do so, we study certain definable transductions and show that they are compatible with weighted logics
Learning Pomset Automata.
We extend the L⋆ algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata
Learning Pomset Automata
We extend the L* algorithm to learn bimonoids recognising pomset languages.
We then identify a class of pomset automata that accepts precisely the class of
pomset languages recognised by bimonoids and show how to convert between
bimonoids and automata