About the decision of reachability for register machines

Issue		RAIRO-Theor. Inf. Appl. Volume 36, Number 4, October-December 2002


Page(s)		341 - 358
DOI		10.1051/ita:2003001

Theoret. Informatics Appl. 36, 341-358 (2002)
DOI: 10.1051/ita:2003001

About the decision of reachability for register machines

Véronique Cortier

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

(Received May, 2001. Accepted October, 2002.)

Abstract
We study the decidability of the following problem: given p affine functions $f_1,\ldots, f_p$ over $\mathbb{N} ^k$ and two vectors $v_1, v_2\in\mathbb{N} ^k$ , is v₂ reachable from v₁ by successive iterations of $f_1,\ldots, f_p$ (in this given order)? We show that this question is decidable for p = 1, 2 and undecidable for some fixed p.

Mathematics Subject Classification. 68Q60

Key words: Verification -- infinite state systems.

© EDP Sciences 2002

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