Reducibilities among decision problems for HNN groups, vector addition systems and subsystems of Peano arithmetic
Authors:
Michael Anshel and Kenneth McAloon
Journal:
Proc. Amer. Math. Soc. 89 (1983), 425429
MSC:
Primary 03D80; Secondary 03F30, 20F05, 20F10, 68Q99
MathSciNet review:
715859
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Abstract: Our purpose is to exhibit reducibilities among decision problems for conjugate powers in HNN groups, reachability sets of vector addition systems and sentences in subsystems of Peano arithmetic, and show that although these problems are not primitive recursively decidable, they do admit decision procedures which are primitive recursive in the Ackermann function.
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 M. Anshel, Vector groups and the equality problem for vector addition systems, Math. Comp. 32 (1978), 614616. MR 482272 (81e:20042)
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 M. Hack, The equality problem for vector addition systems is undecidable, Theoret. Comput. Sci. 2 (1976), 7796. MR 0439610 (55:12496)
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 R. M. Karp and R. E. Miller, Parellel program schemata, J. Comput. System Sci. 3.(1969), 147195. MR 0246720 (39:8024)
 [4]
 L. Kirby and J. Paris, Initial segments of models of arithmetic, Set Theory and Hierarchy Theory V, Lecture Notes in Math., Vol. 619, SpringerVerlag, Berlin, 1977. MR 0491157 (58:10423)
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 R. C. Lyndon and P. E. Schupp, Combinatorial group theory, SpringerVerlag, Berlin, 1977. MR 0577064 (58:28182)
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 E. Mayr, The complexity of the finite containment problem for Petri nets, Laboratory for Computer Science, Technical Report No. 181, M.I.T., Cambridge, Mass., 1977.
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 K. McAloon, Petri nets and large finite sets, Theoret. Comput. Sci. (to appear). MR 761166 (86g:68130)
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 J. Paris, Hierarchy of cuts in models of arithmetic, Model Theory of Algebra and Arithmetic, Lecture Notes in Math., Vol. 834, SpringerVerlag, Berlin, 1980. MR 606791 (84e:03085)
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 C. Rackoff, The covering and boundedness problems for vector addition systems, Theoret. Comput. Sci. 6 (1978), 223231. MR 486584 (81e:68024)
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 G. Takeuti, Proof theory, NorthHolland, Amsterdam, 1975. MR 882549 (89a:03115)
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 A. Yashuhara, Recursive function theory and logic, Academic Press, New York, 1971. MR 0313027 (47:1582)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198307158598
PII:
S 00029939(1983)07158598
Article copyright:
© Copyright 1983 American Mathematical Society
