# A space optimal algorithm to solve a problem

1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Given a semi-decidable relation $R$, and a string $x$, deciding wether or not there is a witness $y$ such that $(x,y) \in R$ is a very hard problem. However, Leonid Levin has constructed a time optimal algorithm to solve the above question. The algorithms is not based on a brute-force search but on testing programs that generate witness. Following Levin's work, we define a space-efficient algorithm that solves the above question. Then, we discuss on the ability to improve Savitch's Theorem
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https://hal.inria.fr/inria-00099303
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 8:52:36 AM
Last modification on : Thursday, January 11, 2018 - 6:19:48 AM

### Identifiers

• HAL Id : inria-00099303, version 1

### Citation

Jérôme Besombes. A space optimal algorithm to solve a problem. [Intern report] A00-R-135 || besombes00a, 2000, 5 p. ⟨inria-00099303⟩

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