About the decision of reachability for register machines

Véronique Cortier

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 36, Issue: 4, page 341-358
  • ISSN: 0988-3754

Abstract

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We study the decidability of the following problem: given p affine functions ƒ1,...,ƒp over k and two vectors v 1 , v 2 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.

How to cite

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Cortier, Véronique. "About the decision of reachability for register machines." RAIRO - Theoretical Informatics and Applications 36.4 (2010): 341-358. <http://eudml.org/doc/92706>.

@article{Cortier2010,
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. },
author = {Cortier, Véronique},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Verification; infinite state systems.; verification; infinite state systems; decidability},
language = {eng},
month = {3},
number = {4},
pages = {341-358},
publisher = {EDP Sciences},
title = {About the decision of reachability for register machines},
url = {http://eudml.org/doc/92706},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Cortier, Véronique
TI - About the decision of reachability for register machines
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 4
SP - 341
EP - 358
AB - 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.
LA - eng
KW - Verification; infinite state systems.; verification; infinite state systems; decidability
UR - http://eudml.org/doc/92706
ER -

References

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  2. B. Boigelot, Symbolic Methods for Exploring Infinite Sate Spaces, Ph.D. Thesis. Université de Liège (1998) 225.  
  3. H. Comon and Y. Jurski, Multiple counters automata, safety analysis and Presburger arithmetic, in Proc. Computer Aided Verification. Springer Verlag, Lecture Notes in Comput. Sci.1427 (1998) 268-279.  
  4. V. Cortier, Vérification de systèmes à compteurs (in French), Master's Thesis. Université Paris 7 (1999)  URIhttp://www.lsv.ens-cachan.fr/cortier/memoire_dea.ps
  5. L.E. Dickson, Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Amer. J. Math.35 (1913) 413-422.  Zbl44.0220.02
  6. C. Dufourd, A. Finkel and Ph. Schnoebelen, Between decidability and undecidability, in Proc. ICALP 1998. Springer-Verlag, Lecture Notes in Comput. Sci.1448 (1998) 103-115.  
  7. A. Finkel, P. McKenzie and C. Picaronny, A well-structured framework for analysing Petri nets extensions. Technical Report, Research Report LSV-99-2 (1999)  Zbl1101.68696URIhttp://www.lsv.ens-cachan.fr/Publis/RAPPORTS_LSV/rr-lsv-1999-2.rr.ps
  8. M.Yu. Matijacevitch, M. David and J. Robinson, Hilbert's Tenth Problem, Chapter 3 (1976).  
  9. C. Rorres and H. Anton, Applications of Linear Algebra, Chapters 9 and 13 (1979).  Zbl0439.15001

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