Weighted Automata Algorithms

Mohri, Mehryar

doi:10.1007/978-3-642-01492-5_6

Cited by 145 publications

(152 citation statements)

References 42 publications

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“…1 is a weighted finite-state automaton. Requirements on the types of weights that can be used in weights automata are well-established [13]. For many algorithms, including the forward algorithm, the requirement is that the weights are in a semiring.…”

Section: Computing Derivatives With the Expectation Semiringmentioning

confidence: 99%

Efficient decoding with generative score-spaces using the expectation semiring

Dalen

Ragni

Gales

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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State-of-the-art speech recognisers are usually based on hidden Markov models (HMMs). They model a hidden symbol sequence with a Markov process, with the observations independent given that sequence. These assumptions yield efficient algorithms, but limit the power of the model. An alternative model that allows a wide range of features, including word-and phone-level features, is a log-linear model. To handle, for example, word-level variable-length features, the original feature vectors must be segmented into words. Thus, decoding must find the optimal combination of segmentation of the utterance into words and word sequence. Features must therefore be extracted for each possible segment of audio. For many types of features, this becomes slow. In this paper, long-span features are derived from the likelihoods of word HMMs. Derivatives of the log-likelihoods, which break the Markov assumption, are appended. Previously, decoding with this model took cubic time in the length of the sequence, and longer for higher-order derivatives. This paper shows how to decode in quadratic time.

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Section: Computing Derivatives With the Expectation Semiringmentioning

confidence: 99%

Efficient decoding with generative score-spaces using the expectation semiring

Dalen

Ragni

Gales

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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“…A weighted finite-state transducer or automaton (FST or FSA) can be viewed as a PDT or PDA where the open and close parentheses alphabets are empty; see [16] for a stand-alone definition.…”

Section: Pushdown Automata and Transducersmentioning

confidence: 99%

“…We also assume that T 2 has no input-ǫ transitions. When T 2 has input-ǫ transitions, an epsilon filter [16,3] generalized to handle parentheses can be used.…”

Section: Compositionmentioning

confidence: 99%

“…Transitions labeled by non-parenthesis are treated as in Mohri [16] 2 ) in the worst case, where N denotes the maximal number of times a state is inserted in the queue for a given call of GetDistance. Assuming the cost of a queue operation is Γ (n) for a queue containing n elements, the worst-case time complexity of the algorithm can then be expressed as O(N |T | 3 Γ (|T |)).…”

Section: Shortest Distance and Shortest Pathmentioning

confidence: 99%

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A Pushdown Transducer Extension for the OpenFst Library

Allauzen

Riley

2012

Implementation and Application of Automata

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Abstract. Pushdown automata are devices that can efficiently represent context-free languages, have natural weighted versions, and combine naturally with finite automata. We describe a pushdown transducer extension to OpenFst, a weighted finite-state transducer library. We present several weighted pushdown algorithms, some with clear finite-state analogues, describe their library usage and give some applications of these methods to recognition, parsing and translation.

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“…Deterministic WAs are ACRAs with one register, and algorithms exist to compute the state complexity and for minimization [10]. Mohri [11] presents a comprehensive survey of the field. Recent work on the quantitative analysis of programs [5] also uses weighted automata, but does not deal with minimization or with notions of regularity.…”

Section: Introductionmentioning

confidence: 99%

Decision Problems for Additive Regular Functions

Alur

Raghothaman

2013

Automata, Languages, and Programming

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Abstract. Additive Cost Register Automata (ACRA) map strings to integers using a finite set of registers that are updated using assignments of the form "x := y + c" at every step. The corresponding class of additive regular functions has multiple equivalent characterizations, appealing closure properties, and a decidable equivalence problem. In this paper, we solve two decision problems for this model. First, we define the register complexity of an additive regular function to be the minimum number of registers that an ACRA needs to compute it. We characterize the register complexity by a necessary and sufficient condition regarding the largest subset of registers whose values can be made far apart from one another. We then use this condition to design a pspace algorithm to compute the register complexity of a given ACRA, and establish a matching lower bound. Our results also lead to a machine-independent characterization of the register complexity of additive regular functions. Second, we consider two-player games over ACRAs, where the objective of one of the players is to reach a target set while minimizing the cost. We show the corresponding decision problem to be exptime-complete when the costs are non-negative integers, but undecidable when the costs are integers.

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Weighted Automata Algorithms

Cited by 145 publications

References 42 publications

Efficient decoding with generative score-spaces using the expectation semiring

Efficient decoding with generative score-spaces using the expectation semiring

A Pushdown Transducer Extension for the OpenFst Library

Decision Problems for Additive Regular Functions

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