article

Learning regular languages using RFSAs

Authors:

François Denis,

Aurélien Lemay,

Alain TerlutteAuthors Info & Claims

Theoretical Computer Science, Volume 313, Issue 2

Pages 267 - 294

https://doi.org/10.1016/j.tcs.2003.11.008

Published: 17 February 2004 Publication History

Abstract

Residual languages are important and natural components of regular languages and several grammatical inference algorithms naturally rely on this notion. In order to identify a given target language L, classical inference algorithms try to identify words which define identical residual languages of L. Here, we study whether it could be interesting to perform a tighter analysis by identifying inclusion relations between the residual languages of L. We consider the class of Residual Finite State Automata (RFSAs). An RFSA A is a NonDeterministic Automaton whose states corresponds to residual languages of the language L_A it recognizes. The inclusion relations between residual languages of L_A can be naturally materialized on A. We prove that the class of RFSAs is not polynomially characterizable. We lead some experiments which show that when a regular language is randomly drawn by using a nondeterministic representation, the number of inclusion relations between its residual languages is very important. Moreover, its minimal RFSA representation is much smaller than its minimal DFA representation. Finally, we design a new learning algorithm, DeLeTe2, based on the search for the inclusion relations between the residual languages of the target language. We give sufficient conditions for the identifiability of the target language. We experimentally compare the performance of DeLeTe2 to those of classical inference algorithms.

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Cited By

Jastrząb TLardeux FMonfroy EHong JPark J(2024)Classifying Words with 3-sort AutomataProceedings of the 39th ACM/SIGAPP Symposium on Applied Computing10.1145/3605098.3636142(787-788)Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1145/3605098.3636142
Jastrząb TLardeux FMonfroy E(2023)Inference of Over-Constrained NFA of Size to Efficiently and Systematically Derive NFA of Size k for Grammar LearningComputational Science – ICCS 202310.1007/978-3-031-35995-8_10(134-147)Online publication date: 3-Jul-2023
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Index Terms

Learning regular languages using RFSAs
1. Computing methodologies
  1. Artificial intelligence
    1. Natural language processing
  2. Machine learning
    1. Learning paradigms
2. Theory of computation
  1. Formal languages and automata theory
    1. Grammars and context-free languages
  2. Models of computation
    1. Computability

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 313, Issue 2

Special issue: Algorithmic learning theory

17 February 2004

138 pages

ISSN:0304-3975

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Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 17 February 2004

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Cited By

Jastrząb TLardeux FMonfroy EHong JPark J(2024)Classifying Words with 3-sort AutomataProceedings of the 39th ACM/SIGAPP Symposium on Applied Computing10.1145/3605098.3636142(787-788)Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1145/3605098.3636142
Jastrząb TLardeux FMonfroy E(2023)Inference of Over-Constrained NFA of Size to Efficiently and Systematically Derive NFA of Size k for Grammar LearningComputational Science – ICCS 202310.1007/978-3-031-35995-8_10(134-147)Online publication date: 3-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-35995-8_10
Berndt SLiśkiewicz MLutter MReischuk R(2022)Learning residual alternating automataInformation and Computation10.1016/j.ic.2022.104981289:PAOnline publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1016/j.ic.2022.104981
Chu WChen SBonsangue M(2022)Non-linear Optimization Methods for Learning Regular DistributionsFormal Methods and Software Engineering10.1007/978-3-031-17244-1_4(54-70)Online publication date: 24-Oct-2022
https://dl.acm.org/doi/10.1007/978-3-031-17244-1_4
An JZhan BZhan NZhang M(2021)Learning Nondeterministic Real-Time AutomataACM Transactions on Embedded Computing Systems10.1145/347703020:5s(1-26)Online publication date: 22-Sep-2021
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Jastrząb T(2019)A Comparison of Selected Variable Ordering Methods for NFA InductionComputational Science – ICCS 201910.1007/978-3-030-22750-0_73(741-748)Online publication date: 12-Jun-2019
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Berndt SLiśkiewicz MLutter MReischuk RSingh SMarkovitch S(2017)Learning residual alternating automataProceedings of the Thirty-First AAAI Conference on Artificial Intelligence10.5555/3298483.3298494(1749-1755)Online publication date: 4-Feb-2017
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Wang XGulwani SSingh R(2016)FIDEX: filtering spreadsheet data using examplesACM SIGPLAN Notices10.1145/3022671.298403051:10(195-213)Online publication date: 19-Oct-2016
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Jastrzab T(2016)On Parallel Induction of Nondeterministic Finite AutomataProcedia Computer Science10.1016/j.procs.2016.05.31880:C(257-268)Online publication date: 1-Jun-2016
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