We present general algorithms for minimizing sequential finite-state transducers that output strings or numbers. The algorithms are shown to be efficient since in the case of acyclic transducers and for output strings they operate in O(S+|E|+|V|+(|E|-|V|+|F|)x(|Pmax|+1)) steps, where S is the sum of the lengths of all output labels of the resulting transducer, E the set of transitions of the given transducer, V the set of its states, F the set of final states, and Pmax one of the longest of the longest common prefixes of the output paths leaving each state of the transducer. The algorithms apply to a larger class of transducers which includes subsequential transducers.

Abstract. p-subsequential transducers are efficient finite-state transducers with p final outputs used in a variety of applications. Not all transducers admit equivalent p-subsequential transducers however. We briefly describe an existing generalized determinization algorithm for psubsequential transducers and give the first characterization of p-subsequentiable transducers, transducers that admit equivalent p-subsequential transducers. Our characterization shows the existence of an efficient algorithm for testing p-subsequentiability. We have fully implemented the generalized determinization algorithm and the algorithm for testing psubsequentiability. We report experimental results showing that these algorithms are practical in large-vocabulary speech recognition applications. The theoretical formulation of our results is the equivalence of the following three properties for finite-state transducers: determinizability in the sense of the generalized algorithm, p-subsequentiability, and the twins property. 1

This paper describes the FSA Utilities toolbox: a collection of utilities to manipulate finite-state automata and finite-state transducers. Manipulations include determinization (both for finite-state acceptors and finite-state transducers), minimization, composition, complementation, intersection, Kleene closure, etc. Furthermore, various visualization tools are available to browse finite-state automata. The toolbox is implemented in SICStus Prolog.

. We study determinization of weighted finite-state automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomial-time algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide a rigorous analysis of a determinization algorithm of Mohri, with tight bounds for acyclic WFAs. Given that WFAs can expand exponentially when determinized, we explore why those used in ASR tend to shrink. The folklore explanation is that ASR WFAs have an acyclic, multi-partite structure. We show, however, that there exist such WFAs that always incur exponential expansion when determinized. We then introduce a class of WFAs, also with this structure, whose expansion depends on the weights: some weightings cause them to shrink, while others, including random weightings, cause them to expand exponentially. We provide experimental evidence that ASR WFAs exhibit this weight dependence. ...

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Let U be a strictly increasing sequence of integers. By a greedy algorithm, every nonnegative integer has a greedy U-representation. The successor function maps the greedy U-representation of N onto the greedy U-representation of N+1. We characterize the sequences U such that the successor function associated to U is a left, resp. a right sequential function. We also show that the odometer associated to U is continuous if and only if the successor function is right sequential.

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We consider numeration systems where the base is a negative integer, or a complex number which is a root of a negative integer. We give parallel algorithms for addition in these numeration systems, from which we derive on-line algorithms realized by finite automata. A general construction relating addition in base fi and addition in base fi m is given. Results on addition in base fi = m p b, where b is a relative integer, follow. We also show that addition in base the golden ratio is computable by an on-line finite automaton, but is not parallelizable. 1 Introduction A positional numeration system is given by a base and by a set of digits. In the most usual numeration systems, the base is an integer b 2 and the digit set is f0; : : : ; b \Gamma 1g. In order to represent complex numbers without separating the real and the imaginary part, one can use a complex base. For instance, it is known that every complex number can be expressed with base i p 2 and digit set f0; 1g (...

We study the determinization of transducers over infinite words. We consider transducers with all their states final. We give an effective characterization of sequential functions over infinite words. We also describe an algorithm to determinize transducers over infinite words.

Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. Furthermore, the proof is constructive. A collection of examples is given to illustrate the hierarchy of maxplus series with respect to ambiguity.