# Learning by Erasing

**DOI:**https://doi.org/10.1007/978-1-4419-1428-6_766

## Synonyms

## Definition

Learning by erasing as proposed by Lange et al. (1996) is a class of methods used in inductive inference, a research area started by Gold (1967). We consider learning where an algorithmic device inputs data and produces a sequence of programs such that this sequence can be interpreted as a correct program consistent with the given data. For Gold (1967) the sequence was supposed to be an infinite sequence such that all of its members (but a finite number of them) equal one correct program. For learning-by-erasing algorithms the interpretation of the infinite resulting sequence is different. The sequence is to contain all possible programs with some exceptions. Namely, one minimal program among those missing is assumed to be the result.

## Theoretical Background

When you have eliminated the impossible, whatever remains, however improbable, must be the truth. The scientific method in problem solving is in the process of putting forth a hypothesis and...

## References

- Freivalds, R., Karpinski, M., & Smith, C. H. (1994). Co-learning of total recursive functions.
*Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory (COLT 1994)*, ACM, New Brunswick, pp. 190–197.Google Scholar - Gierasimczuk, N. (2009).
*Learning by erasing in dynamic epistemic logic*(LNCS, Vol. 1181, pp. 362–373). Berlin/Heidelberg: Springer.Google Scholar - Gold, E. M. (1967). Language identification in the limit.
*Information and Control, 10*, 447–474.Google Scholar - Jain, S., Osherson, D., Royer, J. S., & Sharma, A. (1999).
*Systems that learn*(2nd ed.). Cambridge, MA: MIT Press.Google Scholar - Jain, S., Kinber, E. B., Lange, S., Wiehagen, R., & Zeugmann, Th. (2000). Learning languages and functions by erasing.
*Theoretical Computer Science, 241*(1–2), 143–189.Google Scholar - Lange, S., Wiehagen, R., & Zeugmann, Th. (1996).
*Learning by erasing*(Tech. Rep. RIFIS-TR-CS-122). Fukuoka: Research Institute of Fundamental Information Science, Kyushu University.Google Scholar