Automatic Functions, Linear Time and Learning

  • John Case
  • Sanjay Jain
  • Samuel Seah
  • Frank Stephan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


The present work determines the exact nature of linear time computable notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time notions permit full learnability for learning in the limit of automatic classes (families of languages which are uniformly recognised by a finite automaton). In particular it is shown that a function is automatic iff there is a one-tape Turing machine with a left end which computes the function in linear time where the input before the computation and the output after the computation both start at the left end. It is known that learners realised as automatic update functions are restrictive for learning. In the present work it is shown that one can overcome the problem by providing work-tapes additional to a resource-bounded base tape while keeping the update-time to be linear in the length of the largest datum seen so far. In this model, one additional such worktape provides additional learning power over the automatic learner model and the two-work-tape model gives full learning power.


Turing Machine Inductive Inference Finite Automaton Input Symbol Input Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • John Case
    • 1
  • Sanjay Jain
    • 2
  • Samuel Seah
    • 3
  • Frank Stephan
    • 2
    • 3
  1. 1.Department of Computer and Information SciencesUniversity of DelawareNewarkUnited States of America
  2. 2.Department of Computer ScienceNational University of SingaporeSingaporeRepublic of Singapore
  3. 3.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore

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