On Learning Languages from Positive Data and a Limited Number of Short Counterexamples

  • Sanjay Jain
  • Efim Kinber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4005)


We consider two variants of a model for learning languages in the limit from positive data and a limited number of short negative counterexamples (counterexamples are considered to be short if they are smaller that the largest element of input seen so far). Negative counterexamples to a conjecture are examples which belong to the conjectured language but do not belong to the input language. Within this framework, we explore how/when learners using n short (arbitrary) negative counterexamples can be simulated (or simulate) using least short counterexamples or just ‘no’ answers from a teacher. We also study how a limited number of short counterexamples fairs against unconstrained counterexamples. A surprising result is that just one short counterexample (if present) can sometimes be more useful than any bounded number of counterexamples of least size. Most of results exhibit salient examples of languages learnable or not learnable within corresponding variants of our models.


Target Language Initial Sequence Positive Data Negative Data Input Language 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sanjay Jain
    • 1
  • Efim Kinber
    • 2
  1. 1.School of ComputingNational University of SingaporeSingapore
  2. 2.Department of Computer ScienceSacred Heart UniversityFairfieldUSA

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