Learning Subclasses of Formal Languages

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Learning Subclasses of Formal Languages

• Third Progress Seminar
• Laxminarayana J A

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Plan of Presentation

• Motivation
• Introduction
• Inference Methods
• TDRL TDELL TDCFG TSDLL
• Applications
• XML Pseudoknots
• Conclusion

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Motivation

• Growing Influence of Grammatical Inference.
• The class of Terminal Distinguishable Languages
• Scope to design efficient Algorithms
• Identification of suitable Applications
• Back

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Introduction

• Grammatical inference
• Formal languages
• Chomsky hierarchy
• Inductive inference
• Identification in limit
• Terminal distinguishable languages
• Back

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Grammatical Inference
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Formal Languages

• A formal grammar G has four components.
• A set of symbols ?, called terminals
• A set of symbols N, called non-terminals with the
  restriction that ? and N are disjoint
• A special non-terminal symbol S , called a start
  symbol
• A set of production rules P , where each
  production of the form ? ? ?

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Chomsky Hierarchy

• Noam Chomsky defined classes of grammars
• Type 0 Recursively Enumerable Languages
  (Unrestricted Grammars)
• Type 1 Context Sensitive Languages (Context
  Sensitive Grammars)
• Type 2 Context Free Languages (Context Free
  Grammars)
• Type 3 Regular Languages (Regular Grammars)

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Inductive Inference

• Proposed by Angluin, 1983
• Deductive and Inductive Inference
• Identification by enumeration and Identification
  in Limit
• Specifying Inference Problems
• Class of Rules , Hypothesis Space ,
• Set of examples, inference methods.
• Criteria for evaluating and comparing inference
  methods.

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Golds Results

• The class of phrase structure languages is
  learnable from positive and negative samples.
• Not even the class of Regular languages is
  learnable from positive samples alone.
• Any language class which contains all finite
  languages and at least one infinite language
  (super finite language class) is NOT identifiable
  in the limit from positive samples.
• The finite cardinality languages class is
  identifiable from positive samples.

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Angluins Results

• Angluin1980 proposed that a language class
  that contains some finite languages and some
  infinite languages is identifiable from positive
  samples alone.
• Angluin proposed an efficient characterizable
  method using which one can learn many interesting
  classes of languages. Examples are
• Parenthesis Language, Pattern Language
• K-Reversible Language and TDR Language
• Back

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Terminal Distinguishable Languages

• Based on structural information (skeleton)
• Good algebraic and grammatical characteristics.
• Good incremental behaviour
• Based on three properties Backward determinism,
  Terminal completeness, Terminal dissimilarity
• Back

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Conclusion

• Inference algorithms based on tabular approach
  and union-find approach has been successfully
  implemented and shown to have advantages like
  simplicity and minimization of computational
  overhead.
• A novel way of identifying a subclass of CFG in
  GNF from positive samples is presented and shown
  to have good convergence property.
• An inference model is proposed to identify a
  TSDLG using error correcting approach.
• Suitability of the grammatical inference
  techniques are demonstrated with the help of
  applications like XML Document analysis and
  Pseudoknot identification.
• Back.