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Characterizing PAClearnability of Semilinear Sets
 Inform. and Comput
, 1998
"... The learnability of the class of lettercounts of regular languages (semilinear sets) and other related classes of subsets of N d with respect to the distributionfree learning model of Valiant (PAClearning model) is characterized. Using the notion of reducibility among learning problems due to P ..."
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The learnability of the class of lettercounts of regular languages (semilinear sets) and other related classes of subsets of N d with respect to the distributionfree learning model of Valiant (PAClearning model) is characterized. Using the notion of reducibility among learning problems due to Pitt and Warmuth called "prediction preserving reducibility," and a special case thereof, a number of positive and partially negative results are obtained. On the positive side the class of semilinear sets of dimension 1 or 2 is shown to be learnable when the integers are encoded in unary. On the neutral to negative side it is shown that when the integers are encoded in binary the learning problem for semilinear sets as well as a class of subsets of Z d much simpler than semilinear sets is as hard as learning DNF, a central open problem in the field. A number of hardness results for related learning problems are also given. 3 Most of the research reported herein was conducted while the aut...
Commutation Problems on Sets of Words and Formal Power Series
, 2002
"... We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generaliza ..."
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We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generalizations of the semilinear languages, and we study their behaviour under rational operations, morphisms, Hadamard product, and difference. Turning to commutation on sets of words, we then study the notions of centralizer of a language  the largest set commuting with a language , of root and of primitive root of a set of words. We answer a question raised by Conway more than thirty years ago  asking whether or not the centralizer of any rational language is rational  in the case of periodic, binary, and ternary sets of words, as well as for rational ccodes, the most general results on this problem. We also prove that any code has a unique primitive root and that two codes commute if and only if they have the same primitive root, thus solving two conjectures of Ratoandromanana, 1989. Moreover, we prove that the commutation with an ccode X can be characterized similarly as in free monoids: a language commutes with X if and only if it is a union of powers of the primitive root of X.
Algebra and language theory
 Bull. London Math. Soc
, 1975
"... In the early days of highspeed computers there was a hope that it would be possible to program a computer to translate from one language to another, and this led to an intensive study of language structure. The result has been disappointing in that we are still far from making translations by compu ..."
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In the early days of highspeed computers there was a hope that it would be possible to program a computer to translate from one language to another, and this led to an intensive study of language structure. The result has been disappointing in that we are still far from making translations by computer, but that is no cause for
Submitted exclusively to the London Mathematical Society DOI: 10.1112/S0000000000000000 GROUPS WITH CONTEXTFREE COWORD PROBLEM
"... We study the class of cocontextfree groups. We define a cocontextfree group to be one whose coword problem (the complement of its word problem) is contextfree. This class is larger than the subclass of contextfree groups, being closed under the taking of finite direct products, restricted sta ..."
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We study the class of cocontextfree groups. We define a cocontextfree group to be one whose coword problem (the complement of its word problem) is contextfree. This class is larger than the subclass of contextfree groups, being closed under the taking of finite direct products, restricted standard wreath products with contextfree top groups, and passing to finitely generated subgroups and finite index overgroups. But we do not know of other examples of cocontextfree groups. We prove that the only examples amongst polycyclic groups or the BaumslagSolitar groups are virtually abelian. We do this by proving that languages with certain purely arithmetical properties cannot be contextfree; this result may be of independent interest. 1.
Observability Properties of Petri Nets
, 2000
"... In this paper we discuss the problem of estimating the marking of a Place/Transition net based on event observation. We assume that the net structureisknown while the initial marking is unknown. We define several observability properties and show how they can beproved. In particular we set up a hie ..."
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In this paper we discuss the problem of estimating the marking of a Place/Transition net based on event observation. We assume that the net structureisknown while the initial marking is unknown. We define several observability properties and show how they can beproved. In particular we set up a hierarchy considering the possibility that the above properties are satisfied by a net N starting from an initial marking M 0 , by a net N starting from any initial marking M reachable from an initial marking M 0 , or by a net N starting from any marking in N m ,where m is the number of places of the net. 1 Introduction This paper presents a set of analytical tools to determine the observability properties of Petri nets, i.e., algorithms to determine under which conditions it is possible to reconstruct the marking of a Place/Transition net based on eventobservation. Observability is widely studied by automatic control researchers. It is a fundamental property because it allows one to estim...
ON SEMILINEARITY IN FORMAL POWER SERIES ION PETRE
"... A notion of semilinearity isintroduced for formal power series as a natural generalization of semilinear languages over a commutative monoid. Some closure properties of the semilinear languages are established also for formal power series. In this way, a classical result due to Eilenberg and Schutze ..."
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A notion of semilinearity isintroduced for formal power series as a natural generalization of semilinear languages over a commutative monoid. Some closure properties of the semilinear languages are established also for formal power series. In this way, a classical result due to Eilenberg and Schutzenberger and some results due to Ginsburg are extended to series. We also prove that Parikh's theorem does not hold for series unless some rather constraining conditions are considered. 1
Learning Parallel Systems by Regular Trace Languages
"... We study the problem of learning by examples the structure of regular trace languages, a useful formalization of systems or programs of concurrent operations. Negative results are showed about traces with empty and total concurrency, and we compare them with a positive result derived from a work by ..."
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We study the problem of learning by examples the structure of regular trace languages, a useful formalization of systems or programs of concurrent operations. Negative results are showed about traces with empty and total concurrency, and we compare them with a positive result derived from a work by N. Abe, about trace languages generated by commutative regular languages. 1 Introduction In this work we search a way to predict the structure of an unknown trace language by seeing only examples from it. Trace languages are a way to model the behaviour of concurrent systems. Now suppose to be observing a running system in its operations, and to know which atomic operation it can do in parallel. Our aim would be to understand which high level operation it is doing, in terms of structure of the sequence of operations beyond the parallelization of atomic operations. In other words, we think of a complex operation as a sequential program, but some atomic operations in it can be done in paralle...
doi:10.1112/S002461070500654X GROUPS WITH CONTEXTFREE COWORD PROBLEM
"... This paper is made available online in accordance with publisher policies. Please scroll down to view the document itself. Please refer to the repository record for this item and our policy information available from the repository home page for further information. To see the final version of this ..."
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This paper is made available online in accordance with publisher policies. Please scroll down to view the document itself. Please refer to the repository record for this item and our policy information available from the repository home page for further information. To see the final version of this paper please visit the publisher’s website. Access to the published version may require a subscription.