On the Inference of Approximate Programs

Abstract A more powerful criterion of successful inductive inference is studied. This criterion considers the inference successful when the result is a program which computes the function to be inferred everywhere, except on a sparse (but infinite) subset of its domain. In previous work, sparse was taken to mean finite. Relationships with previously defined criteria are examined. Royer [19] considered the same issues and independently obtained some of our results.

[1]  Carl H. Smith,et al.  On the Complexity of Inductive Inference , 1986, Inf. Control..

[2]  Leonard Pitt,et al.  Probabilistic inductive inference , 1989, JACM.

[3]  Daniel N. Osherson,et al.  Criteria of Language Learning , 1982, Inf. Control..

[4]  Manuel Blum,et al.  Toward a Mathematical Theory of Inductive Inference , 1975, Inf. Control..

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

[6]  Paul Young,et al.  An introduction to the general theory of algorithms , 1978 .

[7]  Leonard Pitt,et al.  A Characterization of Probabilistic Inference , 1984, FOCS.

[8]  Carl H. Smith,et al.  The Power of Pluralism for Automatic Program Synthesis , 1982, JACM.

[9]  Robert P. Daley.  On the Error Correcting Power of Pluralism in BC-Type Inductive Inference , 1983, Theoretical Computer Science.

[10]  Keh-Jiann Chen,et al.  Tradeoffs in machine inductive inference , 1981 .

[11]  James S. Royer,et al.  Inductive Inference of Approximations , 1986, Inf. Control..

[12]  Carl H. Smith,et al.  Probability and Plurality for Aggregations of Learning Machines , 1988, Inf. Comput..

[13]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[14]  Keh-Jiann Chen.  Tradeoffs in the Inductive Inference of Nearly Minimal Size Programs , 1982, Inf. Control..

[15]  Rusins Freivalds,et al.  On the Power of Probabilistic Strategies in Inductive Inference , 1984, Theor. Comput. Sci..

[16]  John Case,et al.  Machine Inductive Inference and Language Identification , 1982, ICALP.

[17]  Manuel Blum,et al.  A Machine-Independent Theory of the Complexity of Recursive Functions , 1967, JACM.

[18]  John Case,et al.  Comparison of Identification Criteria for Machine Inductive Inference , 1983, Theor. Comput. Sci..

[19]  Rolf Wiehagen.  Limes-Erkennung rekursiver Funktionen durch spezielle Strategien , 1975, J. Inf. Process. Cybern..

[20]  Karlis Podnieks.  Computational complexity of prediction strategies , 1977 .