Geodesic
Algorithms for the boundedness problem for Minsky counter machines
Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 4, pp. 42-55

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In the paper, the algorithms that can be applied to solving the boundedness problem for Minsky counter machines are discussed. We introduce a polinomial-time algorithm that solves the boundedness problem for one-counter machines using the memory commensurate with the memory required for a machine representation.
Keywords: Minsky counter machines, boundedness problem, algorithm of the search of a cycle in a periodic sequence, model verification. 
@article{MAIS_2008_15_4_a4,
     author = {E. V. Kuzmin and D. Ju. Chalyy},
     title = {Algorithms for the boundedness problem for {Minsky} counter machines},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {42--55},
     publisher = {mathdoc},
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     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2008_15_4_a4/}
}
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E. V. Kuzmin; D. Ju. Chalyy. Algorithms for the boundedness problem for Minsky counter machines. Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 4, pp. 42-55. http://geodesic.mathdoc.fr/item/MAIS_2008_15_4_a4/