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21
Weighted automata and weighted logics
 In Automata, Languages and Programming – 32nd International Colloquium, ICALP 2005
, 2005
"... Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We g ..."
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Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize Büchi’s and Elgot’s fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with our weighted logic. We also consider weighted firstorder logic and show that aperiodic series coincide with the firstorder definable ones, if the semiring is locally finite, commutative and has some aperiodicity property. 1
Skew and infinitary formal power series
, 2005
"... We investigate finitestate systems with weights. Departing from the classical theory, in this paper the weight of an action does not only depend on the state of the system, but also on the time when it is executed; this reflects the usual human evaluation practices in which later events are conside ..."
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Cited by 16 (4 self)
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We investigate finitestate systems with weights. Departing from the classical theory, in this paper the weight of an action does not only depend on the state of the system, but also on the time when it is executed; this reflects the usual human evaluation practices in which later events are considered less urgent and carry less weight than close events. We first characterize the terminating behaviors of such systems in terms of rational formal power series. This generalizes a classical result of Schützenberger. Secondly, we deal with nonterminating behaviors and their weights. This includes an extension of the Büchiacceptance condition from finite automata to weighted automata and provides a characterization of these nonterminating behaviors in terms of ωrational formal power series. This generalizes a classical theorem of Büchi.
On the Determinization of Weighted Automata
 Journal of Automata, Languages and Combinatorics
, 2005
"... In the paper, we generalize an algorithm and some related results by Mohri [25] for determinization of weighted finite automata (WFA) over the tropical semiring. We present the underlying mathematical concepts of his algorithm in a precise way for arbitrary semirings. We define a class of semirings ..."
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In the paper, we generalize an algorithm and some related results by Mohri [25] for determinization of weighted finite automata (WFA) over the tropical semiring. We present the underlying mathematical concepts of his algorithm in a precise way for arbitrary semirings. We define a class of semirings in which we can show that the twins property is sufficient for the termination of the algorithm. We also introduce singlevalued WFA and give a partial correction of a claim by Mohri [25] by showing several characterizations of singlevalued WFA, e.g., the formal power series computed by a singlevalued WFA is subsequential iff it has bounded variation. Also, it is decidable in polynomial time whether a given WFA over the tropical semiring is singlevalued. 1
Deciding unambiguity and sequentiality from a finitely ambiguous maxplus automaton
 THEORET. COMPUT. SCI
, 2004
"... Finite automata with weights in the maxplus semiring are considered. The main result is: it is decidable whether a series that is recognized by a finitely ambiguous maxplus automaton is unambiguous, or is sequential. Furthermore, the proof is constructive. A collection of examples is given to illu ..."
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Finite automata with weights in the maxplus semiring are considered. The main result is: it is decidable whether a series that is recognized by a finitely ambiguous maxplus 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 Finite Automata over Strong Bimonoids
, 2008
"... We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid sa ..."
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We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions. Moreover, we show that in this case the given weighted automata can be determinized.
Computing the Threshold for qGram Filters
 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory (SWAT 2002), 2368 of LNCS:348–357
, 2002
"... Abstract. A popular and much studied class of filters for approximate string matching is based on finding common qgrams, substrings of length q, between the pattern and the text. A variation of the basic idea uses gapped qgrams and has been recently shown to provide significant improvements in pra ..."
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Abstract. A popular and much studied class of filters for approximate string matching is based on finding common qgrams, substrings of length q, between the pattern and the text. A variation of the basic idea uses gapped qgrams and has been recently shown to provide significant improvements in practice. A major difficulty with gapped qgram filters is the computation of the socalled threshold which defines the filter criterium. We describe the first general method for computing the threshold for qgram filters. The method is based on a carefully chosen precise statement of the problem which is then transformed into a constrained shortest path problem. In its generic form the method leaves certain parts open but is applicable to a large variety of qgram filters and may be extensible even to other classes of filters. We also give a full algorithm for a specific subclass. For this subclass, the algorithm has been implemented and used succesfully in an experimental comparison. 1
Rigorous Approximated Determinization of Weighted Automata
"... 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 deterministi ..."
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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 tdeterminizes 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, tdeterminization 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, tdeterminization is useful for reasoning about the competitive ratio of online algorithms. We also describe a property (the ttwins property) and use it in order to characterize tdeterminizable WFAs. Finally, we describe a polynomial algorithm for deciding whether a given WFA has the ttwins property. Index Terms—Weighted automata; Determinization; I.
On the Determinizability of Weighted Automata and Transducers
 In Proceedings of the workshop Weighted Automata: Theory and Applications (WATA
, 2002
"... Finite automata are classical computational devices used in a variety of largescale applications [1]. Finitestate transducers are automata whose transitions are labeled with both an input and an output label. Some applications in text, speech and image processing require more general devices, weig ..."
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Finite automata are classical computational devices used in a variety of largescale applications [1]. Finitestate transducers are automata whose transitions are labeled with both an input and an output label. Some applications in text, speech and image processing require more general devices, weighted automata, to account for the variability of the input data and to rank various output hypotheses [7, 9, 8]. A weighted automaton is a finite automaton in which each transition is labeled with some weight in addition to the usual symbol. Weighted automata and transducers provide a common representation for each component of a complex system used in these applications and admit general algorithms such as composition which can be used to combine these components. The time efficiency of these systems is substantially increased when deterministic or subsequential machines are used [9] and the size of these machines can be further reduced using general minimization algorithms [9, 10]. A weighted automaton or transducer is deterministic or subsequential if it has a unique initial state and if no two transitions leaving the same state share the same input label. A general determinization algorithm for weighted automata and transducers was given by [9]. The algorithm outputs a deterministic machine equivalent to the input weighted automaton or transducer and is an extension of the classical subset construction used for unweighted finite automata. But, unlike the case of unweighted automata, not all finitestate transducers or weighted automata and transducers can be determinized using this algorithm. In fact, some machines do not admit any equivalent deterministic one. Thus, it is important to design an algorithm for testing the determinizability of finitestate transducers and weighted automata.
On the Equivalence of Weighted Finitestate Transducers
"... Although they can be topologically different, two distinct transducers may actually recognize the same rational relation. Being able to test the equivalence of transducers allows to implement such operations as incremental minimization and iterative composition. This paper presents an algorithm for ..."
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Although they can be topologically different, two distinct transducers may actually recognize the same rational relation. Being able to test the equivalence of transducers allows to implement such operations as incremental minimization and iterative composition. This paper presents an algorithm for testing the equivalence of deterministic weighted finitestate transducers, and outlines an implementation of its applications in a prototype weighted finitestate calculus tool.