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.

Weighted transducers provide a common representation for the components of a speech recognition system. In previous work, we showed that these components can be combined off-line into a single compact recognition transducer that maps directly HMM state sequences to word sequences [11]. The construction of that recognition transducer and its efficiency of use critically depend on the use of a general optimization algorithm, determinization. However, not all weighted automata and transducers used in largevocabulary speech recognition are determinizable. We present a general algorithm that can make an arbitrary weighted transducer determinizable and generalize our previous optimization technique for building an integrated recognition transducer to deal with arbitrary weighted transducers used in speech recognition. We report experimental results in a large-vocabulary speech recognition task, How May I Help You (HMIHY), showing that our generalized technique leads to a recognition transducer that performs as well as our original solution in the case of classical n-gram models while inserting less special symbols, and that it leads to a substantial improvement of the recognition speed, factor of 2.6, in the same task when using a class-based language model.

Finitely subsequential transducers are efficient finite-state transducers with a finite number of final outputs and are used in a variety of applications. Not all transducers admit equivalent finitely subsequential transducers however. We briefly describe an existing generalized determinization algorithm for finitely subsequential transducers and give the first characterization of finitely subsequentiable transducers, transducers that admit equivalent finitely subsequential transducers. Our characterization shows the existence of an efficient algorithm for testing finite subsequentiability. We have fully implemented the generalized determinization algorithm and the algorithm for testing finite subsequentiability. We report

Abstract. In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular decomposition of directed graphs and of 2-structures, but also decomposition by star cutsets. 1

We present a general algorithm, pre-determinization, that makes an arbitrary weighted transducer over the tropical semiring or an arbitrary unambiguous weighted transducer over a cancellative commutative semiring determinizable by inserting in it transitions labeled with special symbols. After determinization, the special symbols can be removed or replaced with ε-transitions. The resulting transducer can be significantly more efficient to use. We report empirical results showing that our algorithm leads to a substantial speed-up in large-vocabulary speech recognition. Our pre-determinization algorithm makes use of an efficient algorithm for testing a general twins property, a sufficient condition for the determinizability of all weighted transducers over the tropical semiring and unambiguous weighted transducers over cancellative commutative semirings. It inserts new transitions just when needed to guarantee that the resulting transducer has the twins property and thus is determinizable. It also uses a single-source shortest-paths algorithm over the min-max semiring for carefully selecting the positions for insertion of new transitions to benefit from the subsequent application of determinization. These positions are proved to be optimal in a sense that we describe.

Abstract—A nondeterministic weighted finite automaton (WFA) maps an input word to a numerical value. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. Many of these applications require the WFAs to be deterministic, or work substantially better when the WFAs are deterministic. Unlike NFAs, which can always be determinized, not all WFAs have an equivalent deterministic weighted automaton (DWFA). In [1], Mohri describes a determinization construction for a subclass of WFA. He also describes a property of WFAs (the twins property), such that all WFAs that satisfy the twins property are determinizable and the algorithm terminates on them. Unfortunately, many natural WFAs cannot be determinized. In this paper we study approximated determinization of WFAs. We describe an algorithm that, given a WFA A and an approximation factor t ≥ 1, constructs a DWFA A ′ that t-determinizes A. Formally, for all words w ∈ Σ ∗ , the value of w in A ′ is at least its value in A and at most t times its value in A. Our construction involves two new ideas: attributing states in the subset construction by both upper and lower residues, and collapsing attributed subsets whose residues can be tightened. The larger the approximation factor is, the more attributed subsets we can collapse. Thus, t-determinization is helpful not only for WFAs that cannot be determinized, but also in cases determinization is possible but results in automata that are too big to handle. In addition, t-determinization is useful for reasoning about the competitive ratio of online algorithms. We also describe a property (the t-twins property) and use it in order to characterize t-determinizable WFAs. Finally, we describe a polynomial algorithm for deciding whether a given WFA has the t-twins property. Index Terms—Weighted automata; Determinization; I.

Weighted transducers provide a common representation for the components of a speech recognition system. In previous work, we showed that these components can be combined off-line into a single compact recognition transducer that maps directly HMM state sequences to word sequences [11]. The construction of that recognition transducer and its efficiency of use critically depend on the use of a general optimization algorithm, determinization. However, not all weighted automata and transducers used in largevocabulary speech recognition are determinizable. We present a general algorithm that can make an arbitrary weighted transducer determinizable and generalize our previous optimization technique for building an integrated recognition transducer to deal with arbitrary weighted transducers used in speech recognition. We report experimental results in a large-vocabulary speech recognition task, How May I Help You (HMIHY), showing that our generalized technique leads to a recognition transducer that performs as well as our original solution in the case of classical  -gram models while inserting less special symbols, and that it leads to a substantial improvement of the recognition speed, factor of ¡£ ¢ ¤ , in the same task when using a class-based language model. 1.