Regular prefix relations

AbstractWe define a class ofn-ary relations on strings called the regular prefix relations, and give four alternative characterizations of this class:1.the relations recognized by a new type of automaton, the prefix automata,2.the relations recognized by tree automata specialized to relations on strings,3.the relations between strings definable in the second order theory ofk successors,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.

[1]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

[2]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[3]  C. C. Elgot.  Decision problems of finite automata design and related arithmetics , 1961 .

[4]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[5]  Ehud Y. Shapiro.  An Algorithm that Infers Theories from Facts , 1981, IJCAI.

[6]  II Karel ulík,et al.  Abstract families of relations , 1971 .

[7]  Ehud Shapiro,et al.  Algorithmic Program Debugging , 1983 .

[8]  John Doner,et al.  Tree Acceptors and Some of Their Applications , 1970, J. Comput. Syst. Sci..

[9]  Ehud Shapiro,et al.  Inductive Inference of Theories from Facts , 1991, Computational Logic - Essays in Honor of Alan Robinson.

[10]  D. Siefkes.  Review: Michael O. Rabin, Decidability of Second-order Theories and Automata on Infinite Trees , 1972 .

[11]  M. Rabin.  Decidability of second-order theories and automata on infinite trees , 1968 .

[12]  James W. Thatcher,et al.  Generalized finite automata theory with an application to a decision problem of second-order logic , 1968, Mathematical systems theory.

[13]  Ehud Y. Shapiro.  Alternation and the Computational Complexity of Logic Programs , 1984, J. Log. Program..

[14]  Oscar H. Ibarra.  Characterizations of transductions defined by abstract families of transducers , 2005, Mathematical systems theory.