About the decision of reachability for register machines

Cortier, Véronique

doi:10.1051/ita:2003001

Cortier, Véronique

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 341-358.

Résumé

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

MR Zbl

DOI : 10.1051/ita:2003001

Classification : 68Q60
Mots-clés : verification, infinite state systems

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     author = {Cortier, V\'eronique},
     title = {About the decision of reachability for register machines},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {341--358},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     doi = {10.1051/ita:2003001},
     mrnumber = {1965421},
     zbl = {1034.68057},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2003001/}
}

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Cortier, Véronique. About the decision of reachability for register machines. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 341-358. doi : 10.1051/ita:2003001. http://archive.numdam.org/articles/10.1051/ita:2003001/

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