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Regular prefix relations

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Abstract

We define a class ofn-ary relations on strings called the regular prefix relations, and give four alternative characterizations of this class:

  1. 1.

    the relations recognized by a new type of automaton, the prefix automata,

  2. 2.

    the relations recognized by tree automata specialized to relations on strings,

  3. 3.

    the relations between strings definable in the second order theory ofk successors,

  4. 4.

    the smallest class containing the regular sets and the prefix relation, and closed under the Boolean operations, Cartesian product, projection, explicit transformation, and concatenation with Cartesian products of regular sets.

We give concrete examples of regular prefix relations, and a pumping argument for prefix automata. An application of these results to the study of inductive inference of regular sets is described.

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References

  1. Karel Culik II. Abstract families of relations.J. Comp. Sys. Sci. 5:596–606, 1971.

    Google Scholar 

  2. John Doner. Tree acceptors and some of their applications.J. Comp. Sys. Sci. 4:406–451, 1970.

    Google Scholar 

  3. Calvin C. Elgot. Decision problems of finite automata design and related arithmetics.Trans. Am. Math. Soc. 98:21–51, 1961.

    Google Scholar 

  4. E. Mark Gold. Language identification in the limit.Inform. Contr. 10:447–474, 1967.

    Google Scholar 

  5. J. E. Hopcroft and J. D. Ullman.Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.

  6. Oscar H. Ibarra. Characterizations of transductions defined by abstract families of transducers.Math. Sys. Theory 5:271–281, 1971.

    Google Scholar 

  7. Michael O. Rabin. Decidability of second-order theories and automata on infinite trees.Trans. Am. Math. Soc. 141:1–35, 1969.

    Google Scholar 

  8. E. Shapiro. An algorithm that infers theories from facts. In Seventh IJCAI, pages 446–451, IJCAI, 1981.

  9. E. Shapiro. Algorithmic Program Debugging. Ph.D. thesis, Yale University Computer Science Dept., 1982. Also issued as Report #237.

  10. E. Shapiro. Alternation and the computational complexity of logic programs. Technical Report, Yale University Computer Science Dept., Report #239, 1982.

  11. E. Shapiro. Inductive inference of theories from facts. Technical Report, Yale University Computer Science Dept., Report #192, 1981.

  12. J. W. Thatcher and J. B. Wright. Generalized finite automata theory with an application to a decision problem of second-order logic.Math. Sys. Theory 2:57–81, 1968.

    Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, Yale University, 06520, New Haven, Conn., USA

    Dana Angluin

  2. Department of Mathematics and Statistics, Queen's University, K7L 3N6, Kingston, Canada

    Douglas N. Hoover

Authors
  1. Dana Angluin
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  2. Douglas N. Hoover
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Additional information

Support from the National Science Foundation under grant number MCS-8002447.

Support from an NSERC Canada Postdoctoral Fellowship.

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Angluin, D., Hoover, D.N. Regular prefix relations. Math. Systems Theory 17, 167–191 (1984). https://doi.org/10.1007/BF01744439

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  • DOI: https://doi.org/10.1007/BF01744439

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