Indexed Family

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Sanjay Jain - One of the best experts on this subject based on the ideXlab platform.

  • On an open problem in classification of languages
    Journal of Experimental & Theoretical Artificial Intelligence, 2001
    Co-Authors: Sanjay Jain
    Abstract:

    Smith, Wichagen and Zeugmann (1997) showed an interesting connection between learning with bounded number of mind changes from informants and classification from informant. They showed that if an Indexed Family of languages L is learnable via informants, using at most m mind changes, then one can partition 2 N , the class of all languages, into m + 2 subclasses L 1,…,L m + 2.

  • Synthesizing Learners Tolerating Computable Noisy Data
    Journal of Computer and System Sciences, 2001
    Co-Authors: John Case, Sanjay Jain
    Abstract:

    An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an Indexed Family of recursive languages (by definition) generates a sequence of decision procedures defining the Family. F. Stephan's model of noisy data is employed, in which, roughly, correct data crops up infinitely often and incorrect data only finitely often. In a computable universe, all data sequences, even noisy ones, are computable. New to the present paper is the restriction that noisy data sequences be, nonetheless, computable. This restriction is interesting since we may live in a computable universe. Studied, then, is the synthesis from indices for r.e. classes and for Indexed families of recursive languages of various kinds of noise-tolerant language-learners for the corresponding classes or families Indexed, where the noisy input data sequences are restricted to being computable. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The main positive result is: grammars for each Indexed Family can be learned behaviorally correctly from computable, noisy, positive data. The proof of another positive synthesis result yields, as a pleasant corollary, a strict subset-principle or telltale style characterization, for the computable noise-tolerant behaviorally correct learnability of grammars from positive and negative data, of the corresponding families Indexed.

  • ALT - Synthesizing noise-tolerant language learners
    Theoretical Computer Science, 2001
    Co-Authors: John Case, Sanjay Jain, Arun Sharma
    Abstract:

    An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an Indexed Family of languages (by definition) generates a sequence of decision procedures defining the Family. F. Stephen's model of noisy data is empoloyed, in which, roughly, correct data crops up infintely often, and incorrect data only finitely often. Studied, then, is the synthesis from indices for r.e. classes and for Indexed families of languages of various kinds of noise-tolerant language-learners for the corresponding classes or families Indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The proofs of most of the positive resutls yield, as pleasant corollaries, strict subset-principle or tell-tale style characterization for the noise-tolerant learn-ability of the corresponding classes or families Indexed.

  • The synthesis of language learners
    Information and Computation, 1999
    Co-Authors: Ganesh R. Baliga, John Case, Sanjay Jain
    Abstract:

    Abstract An index for an r.e. class of languages (by definition) is a procedure which generates a sequence of grammars defining the class. An index for an Indexed Family of languages (by definition) is a procedure which generates a sequence of decision procedures defining the Family. Studied is the metaproblem of synthesizing from indices for r.e. classes and for Indexed families of languages various kinds of language learners for the corresponding classes or families Indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The negative results essentially provide lower bounds for the positive results. The proofs of some of the positive results yield, as pleasant corollaries, subset-principle or tell-tale style characterizations for the learnability of the corresponding classes or families Indexed. For example, the Indexed families of recursive languages that can be behaviorally correctly identified from positive data are surprisingly characterized by Angluin's condition 2 (the subset principle for circumventing overgeneralization).

  • MINIMAL CONCEPT IDENTIFICATION AND RELIABILITY
    International Journal of Foundations of Computer Science, 1998
    Co-Authors: Sanjay Jain
    Abstract:

    Identification, by algorithmic devices, of grammars for languages from positive data is a well studied problem. In this paper we are mainly concerned about the learnability of Indexed families of uniformly recursive languages. Mukouchi introduced the notion of minimal and reliable minimal concept inference from positive data. He left open a question about whether every Indexed Family of uniformly recursive languages that is minimally inferable is also reliably minimally inferable. We show that this is not the case.

John Case - One of the best experts on this subject based on the ideXlab platform.

  • ALT - Synthesizing noise-tolerant language learners
    Theoretical Computer Science, 2001
    Co-Authors: John Case, Sanjay Jain, Arun Sharma
    Abstract:

    An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an Indexed Family of languages (by definition) generates a sequence of decision procedures defining the Family. F. Stephen's model of noisy data is empoloyed, in which, roughly, correct data crops up infintely often, and incorrect data only finitely often. Studied, then, is the synthesis from indices for r.e. classes and for Indexed families of languages of various kinds of noise-tolerant language-learners for the corresponding classes or families Indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The proofs of most of the positive resutls yield, as pleasant corollaries, strict subset-principle or tell-tale style characterization for the noise-tolerant learn-ability of the corresponding classes or families Indexed.

  • Synthesizing Learners Tolerating Computable Noisy Data
    Journal of Computer and System Sciences, 2001
    Co-Authors: John Case, Sanjay Jain
    Abstract:

    An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an Indexed Family of recursive languages (by definition) generates a sequence of decision procedures defining the Family. F. Stephan's model of noisy data is employed, in which, roughly, correct data crops up infinitely often and incorrect data only finitely often. In a computable universe, all data sequences, even noisy ones, are computable. New to the present paper is the restriction that noisy data sequences be, nonetheless, computable. This restriction is interesting since we may live in a computable universe. Studied, then, is the synthesis from indices for r.e. classes and for Indexed families of recursive languages of various kinds of noise-tolerant language-learners for the corresponding classes or families Indexed, where the noisy input data sequences are restricted to being computable. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The main positive result is: grammars for each Indexed Family can be learned behaviorally correctly from computable, noisy, positive data. The proof of another positive synthesis result yields, as a pleasant corollary, a strict subset-principle or telltale style characterization, for the computable noise-tolerant behaviorally correct learnability of grammars from positive and negative data, of the corresponding families Indexed.

  • The synthesis of language learners
    Information and Computation, 1999
    Co-Authors: Ganesh R. Baliga, John Case, Sanjay Jain
    Abstract:

    Abstract An index for an r.e. class of languages (by definition) is a procedure which generates a sequence of grammars defining the class. An index for an Indexed Family of languages (by definition) is a procedure which generates a sequence of decision procedures defining the Family. Studied is the metaproblem of synthesizing from indices for r.e. classes and for Indexed families of languages various kinds of language learners for the corresponding classes or families Indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The negative results essentially provide lower bounds for the positive results. The proofs of some of the positive results yield, as pleasant corollaries, subset-principle or tell-tale style characterizations for the learnability of the corresponding classes or families Indexed. For example, the Indexed families of recursive languages that can be behaviorally correctly identified from positive data are surprisingly characterized by Angluin's condition 2 (the subset principle for circumventing overgeneralization).

  • ALT - Synthesizing Learners Tolerating Computable Noisy Data
    Lecture Notes in Computer Science, 1998
    Co-Authors: John Case, Sanjay Jain
    Abstract:

    An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an Indexed Family of languages (by definition) generates a sequence of decision procedures defining the Family. F. Stephan's model of noisy data is employed, in which, roughly, correct data crops up infinitely often, and incorrect data only finitely often. In a completely computable universe, all data sequences, even noisy ones, are computable. New to the present paper is the restriction that noisy data sequences be, nonetheless, computable! Studied, then, is the synthesis from indices for r.e. classes and for Indexed families of languages of various kinds of noise-tolerant language-learners for the corresponding classes or families Indexed, where the noisy input data sequences are restricted to being computable. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The main positive result is surprisingly more positive than its analog in the case the noisy data is not restricted to being computable: grammars for each Indexed Family can be learned behaviorally correctly from computable, noisy, positive data! The proof of another positive synthesis result yields, as a pleasant corollary, a strict subset-principle or telltale style characterization, for the computable noise-tolerant behaviorally correct learnability of grammars from positive and negative data, of the corresponding families Indexed.

Sibylle Schupp - One of the best experts on this subject based on the ideXlab platform.

  • a pattern for static reflection on fields sharing internal representations in Indexed Family containers
    International Conference on Software and Data Technologies, 2007
    Co-Authors: Andreas Priesnitz, Sibylle Schupp
    Abstract:

    Reflection allows defining generic operations in terms of the constituents of objects. These definitions incur overhead if reflection takes place at run time, which is the common case in popular languages. If performance matters, some compile-time means of reflection is desired to obviate that penalty. Furthermore, the information provided by static reflection can be utilised for class generation, e.g., to optimize internal representation. We demonstrate how to provide static reflection on class field properties by means of generic components in an OO language with static meta-programming facilities. Surprisingly, a major part of the solution is not specific to the particular task of providing reflection. We define the internal representation of classes by a reworked implementation of a generic container that models the concept of a statically Indexed Family. The proposed features of this implementation are also beneficial to its use as a common container.

  • ICSOFT (PL/DPS/KE/MUSE) - A PATTERN FOR STATIC REFLECTION ON FIELDS - Sharing Internal Representations in Indexed Family Containers
    2007
    Co-Authors: Andreas Priesnitz, Sibylle Schupp
    Abstract:

    Reflection allows defining generic operations in terms of the constituents of objects. These definitions incur overhead if reflection takes place at run time, which is the common case in popular languages. If performance matters, some compile-time means of reflection is desired to obviate that penalty. Furthermore, the information provided by static reflection can be utilised for class generation, e.g., to optimize internal representation. We demonstrate how to provide static reflection on class field properties by means of generic components in an OO language with static meta-programming facilities. Surprisingly, a major part of the solution is not specific to the particular task of providing reflection. We define the internal representation of classes by a reworked implementation of a generic container that models the concept of a statically Indexed Family. The proposed features of this implementation are also beneficial to its use as a common container.

Robin Adams - One of the best experts on this subject based on the ideXlab platform.

  • TYPES - Formalized metatheory with terms represented by an Indexed Family of types
    Lecture Notes in Computer Science, 2006
    Co-Authors: Robin Adams
    Abstract:

    It is possible to represent the terms of a syntax with binding constructors by a Family of types, Indexed by the free variables that may occur. This approach has been used several times for the study of syntax and substitution, but never for the formalization of the metatheory of a typing system. We describe a recent formalization of the metatheory of Pure Type Systems in Coq as an example of such a formalization. In general, careful thought is required as to how each definition and theorem should be stated, usually in an unfamiliar ‘big-step' form; but, once the correct form has been found, the proofs are very elegant and direct.

  • formalized metatheory with terms represented by an Indexed Family of types
    Types for Proofs and Programs, 2004
    Co-Authors: Robin Adams
    Abstract:

    It is possible to represent the terms of a syntax with binding constructors by a Family of types, Indexed by the free variables that may occur. This approach has been used several times for the study of syntax and substitution, but never for the formalization of the metatheory of a typing system. We describe a recent formalization of the metatheory of Pure Type Systems in Coq as an example of such a formalization. In general, careful thought is required as to how each definition and theorem should be stated, usually in an unfamiliar ‘big-step' form; but, once the correct form has been found, the proofs are very elegant and direct.

Andreas Priesnitz - One of the best experts on this subject based on the ideXlab platform.

  • a pattern for static reflection on fields sharing internal representations in Indexed Family containers
    International Conference on Software and Data Technologies, 2007
    Co-Authors: Andreas Priesnitz, Sibylle Schupp
    Abstract:

    Reflection allows defining generic operations in terms of the constituents of objects. These definitions incur overhead if reflection takes place at run time, which is the common case in popular languages. If performance matters, some compile-time means of reflection is desired to obviate that penalty. Furthermore, the information provided by static reflection can be utilised for class generation, e.g., to optimize internal representation. We demonstrate how to provide static reflection on class field properties by means of generic components in an OO language with static meta-programming facilities. Surprisingly, a major part of the solution is not specific to the particular task of providing reflection. We define the internal representation of classes by a reworked implementation of a generic container that models the concept of a statically Indexed Family. The proposed features of this implementation are also beneficial to its use as a common container.

  • ICSOFT (PL/DPS/KE/MUSE) - A PATTERN FOR STATIC REFLECTION ON FIELDS - Sharing Internal Representations in Indexed Family Containers
    2007
    Co-Authors: Andreas Priesnitz, Sibylle Schupp
    Abstract:

    Reflection allows defining generic operations in terms of the constituents of objects. These definitions incur overhead if reflection takes place at run time, which is the common case in popular languages. If performance matters, some compile-time means of reflection is desired to obviate that penalty. Furthermore, the information provided by static reflection can be utilised for class generation, e.g., to optimize internal representation. We demonstrate how to provide static reflection on class field properties by means of generic components in an OO language with static meta-programming facilities. Surprisingly, a major part of the solution is not specific to the particular task of providing reflection. We define the internal representation of classes by a reworked implementation of a generic container that models the concept of a statically Indexed Family. The proposed features of this implementation are also beneficial to its use as a common container.