The Suffix Tree of a Tree and Minimizing Sequential Transducers

This paper gives a linear-time algorithm for the construction of thesuffix tree of a tree. The suffix tree of a tree is used to obtain an efficientalgorithm for the minimization of sequential transducers

Logical and Algebraic Characterizations of Rational Transductions

Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic congruences allows to decide whether a regular language is aperiodic. We lift this decidability result to rational transductions, i.e., word-to-word functions defined by finite state transducers. In this context, logical and algebraic characterizations have also been proposed. Our main result is that one can decide if a rational transduction (given as a transducer) is in a given decidable congruence class. We also establish a transfer result from logic-algebra equivalences over languages to equivalences over transductions. As a consequence, it is decidable if a rational transduction is first-order definable, and we show that this problem is PSPACE-complete

Degree of Sequentiality of Weighted Automata

Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA. For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE -complete

Automata Minimization: a Functorial Approach

In this paper we regard languages and their acceptors - such as deterministic or weighted automata, transducers, or monoids - as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: A) We provide sufficient conditions on the output category so that minimization of the corresponding automata is guaranteed. B) We show how to lift adjunctions between the categories for output values to adjunctions between categories of automata. C) We show how this framework can be instantiated to unify several phenomena in automata theory, starting with determinization, minimization and syntactic algebras. We provide explanations of Choffrut's minimization algorithm for subsequential transducers and of Brzozowski's minimization algorithm in this setting.Comment: journal version of the CALCO 2017 paper arXiv:1711.0306

Normalization of Sequential Top-Down Tree-to-Word Transducers

International audienceWe study normalization of deterministic sequential top-down tree-to-word transducers (STWs), that capture the class of deterministic top-down nested-word to word transducers. We identify the subclass of earliest STWs (eSTWs) that yield normal forms when minimized. The main result of this paper is an effective normalization procedure for STWs. It consists of two stages: we first convert a given STW to an equivalent eSTW, and then, we minimize the eSTW. Keywords: formal language theory, tree automata, transformations, XML databases, XSLTExtended Version: A long version is available here.</p