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289
Learning Subsequential Transducers for Pattern Recognition Interpretation Tasks
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1993
"... AbstractThe “interpretation ” framework in pattern recognition (PR) arises in the many cases in which the more classical paradigm of “classification ” is not properly applicable generally because the number of classes is rather large or simply because the concept of “class ” does not hold. A very g ..."
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Cited by 114 (17 self)
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AbstractThe “interpretation ” framework in pattern recognition (PR) arises in the many cases in which the more classical paradigm of “classification ” is not properly applicable generally because the number of classes is rather large or simply because the concept of “class ” does not hold. A very general way of representing the results of interpretations of given objects or data is in terms of sentences of a “semantic language ” in which the actions to be performed for each different object or datum are described. Interpretation can therefore be conveniently formalized through the concept of formal transduction, giving rise to the central PR problem of how to automatically learn a transducer from a training set of examples of the desired inputoutput behavior. This paper presents a formalization of the stated transducer learning problem, as well as an effective and efficient method for the inductive learning of an important class of transducers, namely, the class of subsequential transducers. The capabilities of subsequential transductions are illustrated through a series of experiments that also show the high effectiveness of the proposed learning method in obtaining very accurate and compact transducers for the corresponding tasks. Index TermsFormal languages, inductive inference, learning, rational transducers, subsequential functions, syntactic pattern recognition. I.
Graph Kernels
, 2007
"... We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexit ..."
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Cited by 101 (9 self)
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n 6) to O(n 3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixedpoint methods that take O(dn 3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for ddimensional edge kernels, and O(n 4) in the infinitedimensional case; on sparse graphs these algorithms only take O(n 2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to Rconvolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semidefinite.
FiniteState SpeechToSpeech Translation
, 1997
"... A fully integrated approach to SpeechInput Language Translation in limiteddomain applications is presented. The mapping from the input to the output language is modeled in terms of a finite state translation model which is learned from examples of inputoutput sentences of the task considered. Thi ..."
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Cited by 81 (15 self)
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A fully integrated approach to SpeechInput Language Translation in limiteddomain applications is presented. The mapping from the input to the output language is modeled in terms of a finite state translation model which is learned from examples of inputoutput sentences of the task considered. This model is tightly integrated with standard acousticphonetic models of the input language and the resulting global model directly supplies, through Viterbi search, an optimal outputlanguage sentence for each input language utterance. Several extensions to this framework, recently developed to cope with the increasing difficulty of translation tasks, are reviewed. Finally, results for a task in the framework of hotel frontdesk communication, with a vocabulary of about 700 words, are reported.
ContextFree Languages and PushDown Automata
 HANDBOOK OF FORMAL LANGUAGES
, 1997
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Undecidable Problems of Decentralized Observation and Control
, 2001
"... We introduce a new notion of decentralized observability for discreteevent systems, which we call joint observability. We prove that checking joint observability of a regular language w.r.t. one observer is decidable, whereas for two (or more) observers the problem becomes undecidable. Based on thi ..."
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Cited by 52 (4 self)
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We introduce a new notion of decentralized observability for discreteevent systems, which we call joint observability. We prove that checking joint observability of a regular language w.r.t. one observer is decidable, whereas for two (or more) observers the problem becomes undecidable. Based on this result, we show that a related decentralized control problem is also undecidable. We finally provide an extensive study relating our work to existing work in the literature.
Directed Replacement
, 1996
"... This paper introduces to the finitestate calculus a family of directed replace operators. In contrast ..."
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Cited by 49 (11 self)
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This paper introduces to the finitestate calculus a family of directed replace operators. In contrast
Numeration systems, linear recurrences, and regular sets
 Inform. and Comput
, 1994
"... A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2,... expresses a nonnegative integer n as a sum n = � i j=0 ajuj. In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1,...) = g, then every sufficiently large mult ..."
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Cited by 38 (5 self)
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A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2,... expresses a nonnegative integer n as a sum n = � i j=0 ajuj. In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1,...) = g, then every sufficiently large multiple of g has some representation. If the lexicographic ordering on the representations is the same as the usual ordering of the integers, we say the numeration system is orderpreserving. In particular, if u0 = 1, then the greedy representation, obtained via the greedy algorithm, is orderpreserving. We prove that, subject to some technical assumptions, if the set of all representations in an orderpreserving numeration system is regular, then the sequence u = (uj)j≥0 satisfies a linear recurrence. The converse, however, is not true. The proof uses two lemmas about regular sets that may be of independent interest. The first shows that if L is regular, then the set of lexicographically greatest strings of every length in L is also regular. The second shows that the number of strings of length n in a regular language L is bounded by a constant (independent of n) iff L is the finite union of sets of the form xy ∗ z. 1
Kleene algebra with tests: Completeness and decidability
 IN PROC. OF 10TH INTERNATIONAL WORKSHOP ON COMPUTER SCIENCE LOGIC (CSL’96
, 1996
"... Kleene algebras with tests provide a rigorous framework for equational specification and verification. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra w ..."
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Cited by 37 (15 self)
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Kleene algebras with tests provide a rigorous framework for equational specification and verification. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra with tests and *continuous Kleene algebra with tests over languagetheoretic and relational models. We also show decidability. Cohen's reduction of Kleene algebra with hypotheses of the form r = 0 to Kleene algebra without hypotheses is simplified and extended to handle Kleene algebras with tests.
The equivalence problem of multitape finite automata
 Theoretical Computer Science
, 1991
"... Using a result of B.H. Neumann we extend Eilenberg’s Equality Theorem to a general result which implies that the multiplicity equivalence problem of two (nondeterministic) multitape finite automata is decidable. As a corollary we solve a long standing open problem in automata theory, namely, the equ ..."
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Cited by 33 (2 self)
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Using a result of B.H. Neumann we extend Eilenberg’s Equality Theorem to a general result which implies that the multiplicity equivalence problem of two (nondeterministic) multitape finite automata is decidable. As a corollary we solve a long standing open problem in automata theory, namely, the equivalence problem for multitape deterministic finite automata. The main theorem states that there is a finite test set for the multiplicity equivalence of finite automata over conservative monoids embeddable in a fully ordered group. 1