# Inductive Inference: Theory and Methods

@article{Angluin1983InductiveIT, title={Inductive Inference: Theory and Methods}, author={Dana Angluin and Carl H. Smith}, journal={ACM Comput. Surv.}, year={1983}, volume={15}, pages={237-269} }

There has been a great deal of theoretical and experimental work in computer science on inductive inference systems, that is, systems that try to infer general rules from examples. However, a complete and applicable theory of such systems is still a distant goal. This survey highlights and explains the main ideas that have been developed in the study of inductive inference, with special emphasis on the relations between the general theory and the specific algorithms and implementations. 154…

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## 932 Citations

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## References

SHOWING 1-10 OF 191 REFERENCES

Toward a Mathematical Theory of Inductive Inference

- Mathematics, Computer ScienceInf. Control.
- 1975

This paper investigates the theoretical capabilities and limitations of a computer to infer such sequences and design Turing machines that in principle are extremely powerful for this purpose and place upper bounds on the capabilities of machines that would do better.

Research in the theory of inductive inference by GDR mathematicians - A survey

- Mathematics, Computer ScienceInf. Sci.
- 1980

Recent results in the theory of inductive inference are summarized. They concern deciphering of automata, language identification, prediction of functions, inference with additional information,…

Some Natural Properties of Strong-Identification in Inductive Inference

- Computer Science, MathematicsTheor. Comput. Sci.
- 1976

The problem of inducing an algorithm for a partial recursive function from the analysis of its graph or loosely speaking of “learning” it, is discussed.

Comparison of Identification Criteria for Machine Inductive Inference

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1983

Abstract A natural ωpLω+1 hierarchy of successively more general criteria of success for inductive inference machines is described based on the size of sets of anomalies in programs synthesized by…

Inductive Inference of Formal Languages from Positive Data

- Computer Science, MathematicsInf. Control.
- 1980

A theorem characterizing when an indexed family of nonempty recursive formal languages is inferrable from positive data is proved, and other useful conditions for inference frompositive data are obtained.

Inference for Regular Bilanguages

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1978

The solution makes use of the Pair-Quere notion of homomorphism of binoids and permits the synthesis of a class of inference algorithms, which this paper studies.

A Formal Theory of Inductive Inference. Part II

- Computer Science, MathematicsInf. Control.
- 1964

1. Summary In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably…

Inductive inference theory: a unified approach to problems in pattern recognition and artificial intelligence

- Computer ScienceIJCAI 1975
- 1975

The theory is used to obtain the a priori probabilities that are necessary in the application of stochastic languages to pattern recognition and A.I. theory to make critical decisions.

Learning and Inductive Inference

- Computer Science
- 1982

A simple model that serves to generate a taxonomy of learning systems is presented and the explication and clarification of four methods of learning single concepts are explained.

Anomaly hierarchies of mechanized inductive inference

- Computer ScienceSTOC
- 1978

An inductive inference machine is defined to be an algorithmic device with no bounds on how much time and memory resource it shall use, which takes as its input the graph of a function, and which, from time to time, as it's receiving its inputs, outputs computer programs.