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About the decision of reachability for register machines

Published online by Cambridge University Press:  15 February 2003

Véronique Cortier
Véronique Cortier*
Affiliation:
Laboratoire Spécification et Vérification, École Normale Supérieure de Cachan, CNRS, 61 avenue du Président Wilson, 94230 Cachan, France; cortier@lsv.ens-cachan.fr.
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Abstract

We study the decidability of the following problem: given p affine functions ƒ1,...,ƒp over $\mathbb{N}^k$ and two vectors $v_1, v_2\in\mathbb{N}^k$, is v2 reachable from v1 by successive iterations of ƒ1,...,ƒp (in this given order)? We show that this question is decidable for p = 1, 2 and undecidable for some fixed p.

Keywords

Verificationinfinite state systems.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 4 , October 2002 , pp. 341 - 358
Copyright
© EDP Sciences, 2002

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