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Noise-tolerant efficient inductive synthesis of regular expressions from good examples

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Abstract

We present an almost linear time method of inductive synthesis restoring simple regular expressions from one representative (good) example. In particular, we consider synthesis of expressions of star-height one, where we allow one union operation under each iteration, and synthesis of expressions without union operations from examples that may contain mistakes. In both cases we provide sufficient conditions defining precisely the class of target expressions and the notion of good examples under which the synthesis algorithm works correctly, and present the proof of correctness. In the case of expressions with unions the proof is based on novel results in the combinatorics of words. A generalized algorithm that can synthesize simple expressions containing unions from noisy examples is implemented as a computer program. Computer experiments show that the algorithm is quite practical and may have applications in genome informatics.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia, 29 Rainis Blvd., LV-1459, Riga, Latvia

    Alvis Br−azma & K−arlis Čer−ans

Authors
  1. Alvis Br−azma
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  2. K−arlis Čer−ans
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Additional information

Alvis Br−azma: He received the Ph.D. degree in computer science from Moscow State University in 1988, and the M. S. degree in mathematics from the University of Latvia in 1982. He has worked at the University of Latvia, at New Mexico State University, and at Helsinki University. Since 1995 he is an Associate Professor at the University of Latvia. He has publications on program synthesis, machine learning, string algorithms, graph drawing, and computational biology. His current scientific interests are machine learning applications in computational biology including automatic pattern discovery in biological data.

K−arlis Čer−ans: He received the Dr.sc.comp. degree from the University of Latvia in 1992. Since 1995 he is an Associate Professor at the University of Latvia. His main research interests are in programming theory: specification and analysis of real time systems, and algorithmic analysis problems for exteded automata (infinite state systems). He has publications also in the fields of inductive inference of recursive functions, and machine learning.

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Br−azma, A., Čer−ans, K. Noise-tolerant efficient inductive synthesis of regular expressions from good examples. New Gener Comput 15, 105–140 (1997). https://doi.org/10.1007/BF03037562

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  • DOI: https://doi.org/10.1007/BF03037562

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