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Simulating Weighted Automata over Sequences and Trees with Transformers
International Conference on Artificial Intelligence and StatisticsTransformers are ubiquitous models in the natural language processing (NLP) community and have shown impressive empirical successes in the past few years.
M. Rizvi +3 more
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arXiv.org
We characterize group representations that factor through monomial representations, respectively, block-triangular representations with monomial diagonal blocks, by arithmetic properties.
Antoni Puch, Daniel Smertnig
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We characterize group representations that factor through monomial representations, respectively, block-triangular representations with monomial diagonal blocks, by arithmetic properties.
Antoni Puch, Daniel Smertnig
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2015
Weighted finite automata (WFA) are finite automata whose transitions and states are augmented with some weights, elements of a semiring. A WFA induces a function over strings. The value it assigns to an input string is the semiring sum of the weights of all paths labeled with that string, where the weight of a path is obtained by taking the semiring ...
Borja Balle, Mehryar Mohri
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Weighted finite automata (WFA) are finite automata whose transitions and states are augmented with some weights, elements of a semiring. A WFA induces a function over strings. The value it assigns to an input string is the semiring sum of the weights of all paths labeled with that string, where the weight of a path is obtained by taking the semiring ...
Borja Balle, Mehryar Mohri
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Stochastization of Weighted Automata
2015Nondeterministic weighted finite automata (WFAs) map input words to real numbers. Each transition of a WFA is labeled by both a letter from some alphabet and a weight. The weight of a run is the sum of the weights on the transitions it traverses, and the weight of a word is the minimal weight of a run on it.
Guy Avni, Orna Kupferman
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On the determinization of weighted finite automata
SIAM Journal on Computing, 1998Summary: We study the problem of constructing the deterministic equivalent of a nondeterministic Weighted Finite-state Automaton (WFA). Determinization of WFAs 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 ...
Adam L. Buchsbaum +2 more
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On deterministic weighted automata
Information Processing Letters, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Weighted automata and weighted logics on infinite words
Russian Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manfred Droste, George Rahonis
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Bisimulation metrics and norms for real-weighted automata
Information and Computation, 2020We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale's linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA.
Borja Balle +2 more
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ON WEIGHTED BÜCHI AUTOMATA WITH ORDER-COMPLETE WEIGHTS
International Journal of Algebra and Computation, 2007We investigate Büchi automata with weights for the transitions. Assuming that the weights are taken in a suitable ordered semiring, we show how to define the behaviors of these automata on infinite words. Our main result shows that the formal power series arising in this way are precisely the ones which can be constructed using ω-rational operations ...
Manfred Droste, Ulrike Püschmann
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Weighted Picture Automata and Weighted Logics
Theory of Computing Systems, 2006The author introduces a weighted MSO logic for defining series of pictures; here a picture is a finite rectangular array of symbols from a given (finite) alphabet. The main results of the paper show that the picture series over any commutative semiring definable by this logic are the same as the series recognized by weighted two-dimensional on-line ...
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