Franck Guingne

WFSC: a new weighted finite state compiler

This article presents a new tool, WFSC, for creating, manipulating, and applying weighted finite state automata. It inherits some powerful features from Xeroxs non-weighted XFST tool and represents a continuation of Xeroxs work in the field of finite state automata over two decades. The design is generic: algorithms work on abstract components of automata and on a generic abstract semiring, and are independent of their concrete realizations. Applications can access WFSCs functions through an API or create automata through an end-user interface, either from an enumeration of their states and transitions or from rational expressions.

Similarity relations and cover automata

Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate consequences.

A class of rational n -WFSM auto-intersections

Weighted finite-state machines with n tapes describe n-ary rational string relations. The join n-ary relation is very important in applications. It is shown how to compute it via a more simple operation, the auto-intersection. Join and auto-intersection generally do not preserve rationality. We define a class of triples (A,i,j) such that the auto-intersection of the machine A on tapes i and j can be computed by a delay-based algorithm. We point out how to extend this class and hope that it is sufficient for many practical applications.

COVER TRANSDUCERS FOR FUNCTIONS WITH FINITE DOMAIN

Cover automata were introduced a few years ago for designing a compact representation of finite languages. Our aim is to extend this notion to cover transducers for functions with finite domain. Given two alphabets Σ and Ω, and a function α : Σ* → Ω* of order l (the maximal length of a word in the domain of α), a cover transducer for α is any subsequential transducer that realizes the function α when its input is restricted to the set of words of Σ* having a length not greater than l. We study the problem of reducing the number of states of a cover transducer. We report experimental results, from an implementation using WFSC (Weighted Finite State Compiler), a Xerox tool for handling weighted finite state automata and transducers.

WFSM Auto-intersection and Join Algorithms

The join of two n-ary string relations is a main operation regarding to applications. n-Ary rational string relations are realized by weighted finite-state machines with n tapes. We provide an algorithm that computes the join of two machines via a more simple operation, the auto-intersection. The two operations generally do not preserve rationality. A delay-based algorithm is described for the case of a single tape pair, as well as the class of auto-intersections that it handles. It is generalized to multiple tape pairs and some enhancements are discussed.

Acyclic networks maximizing the printing complexity

This article estimates the worst-case running time complexity for traversing and printing all successful paths of a normalized trim acyclic automaton. First, we show that the worst-case structure is a festoon. Then, we prove that the complexity is maximal when we have a distribution of e (Napier constant) outgoing arcs per state on average, and that it can be exponential in the number of arcs.

Running time complexity of printing an acyclic automaton

This article estimates the worst-case running time complexity for traversing and printing all successful paths of a normalized trim acyclic automaton. First, we show that the worst-case structure is a festoon with distribution of arcs on states as uniform as possible. Then, we prove that the complexity is maximum when we have a distribution of e (Napier constant) outgoing arcs per state on average, and that it can be exponential in the number of arcs.