# Iterated Limiting Recursion and the Program Minimization Problem

@inproceedings{Schubert1974IteratedLR, title={Iterated Limiting Recursion and the Program Minimization Problem}, author={Lenhart K. Schubert}, booktitle={JACM}, year={1974} }

The general problem of finding minimal programs realizing given “program descriptions” is considered, where program descriptions may be of finite or infinite length and may specify arbitrary program properties. The problem of finding minimal programs consistent with finite or infinite input-output lists is a special case (for infinite input-output lists, this is a variant of E. M. Gold's function identification problem). Although most program minimization problems are not recursively solvable…

## 20 Citations

### Limiting Recursion and the Arithmetic Hierarchy

- MathematicsRAIRO Theor. Informatics Appl.
- 1975

A complete characterization of the Kleene hierarchy in terms of the iterated limit opération which fully answers an open problem indicated by Schubert and is interesting in its own right.

### Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms

- Computer Science, MathematicsArXiv
- 2015

It is proved that no algorithm can provide error control on the computational spectral problem or solutions to infinite -dimensional linear systems, and the SCI provides a natural framework for understanding barriers in computations.

### A Calculus of Realizers for EM1 Arithmetic (Extended Abstract)

- Computer ScienceCSL
- 2008

A realizability interpretation of a system for quantifier free arithmetic which is equivalent to the fragment of classical arithmetic without nested quantifiers, which is called EM 1 -arithmetic, is proposed, and any two quantifier-free formulas provably equivalent in classical arithmetic have the same realizer.

### A Calculus of Realizers for EM 1 Arithmetic

- Computer Science
- 2008

We propose a realizability interpretation of a system for quantifier free arithmetic which is equivalent to the fragment of classical arithmetic without nested quantifiers, which we call…

### An Inductive Inference Bibliography

- Computer Science
- 1978

The following pages contain a bibliography of current work in inductive inference, the algorithmic synthesis of programs from examples, to aid researchers interested theoretical aspects of automatic program synthesis.

### A theorem about automatic programming

- Computer ScienceSGAR
- 1975

This paper proposes to focus on systems that "do more" than such systems in the sense that they require less complete information about the programs they are to generate.

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