Vector groups and the equality problem for vector addition systems
Author:
Michael Anshel
Journal:
Math. Comp. 32 (1978), 614616
MSC:
Primary 20F10; Secondary 03D40, 20E06
MathSciNet review:
482272
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Abstract: Our purpose is to demonstrate that results concerning the equality problem for vector addition systems, may be uséd to establish the decidability and undecidability of decision problems associated with the class of HNN extensions of the infinite cyclic group. We call these groups 'vector groups.'
 [1]
Michael
Anshel, Conjugate powers in HNN
groups, Proc. Amer. Math. Soc. 54 (1976), 19–23. MR 0393249
(52 #14059), http://dx.doi.org/10.1090/S00029939197603932494
 [2]
Michael
Anshel, Decision problems for HNN groups and
vector addition systems, Math. Comput.
30 (1976), no. 133, 154–156. MR 0396766
(53 #626), http://dx.doi.org/10.1090/S00255718197603967664
 [3]
Michael
Anshel, The conjugacy problem for HNN groups
and the word problem for commutative semigroups, Proc. Amer. Math. Soc. 61 (1976), no. 2, 223–224. MR 0422457
(54 #10446), http://dx.doi.org/10.1090/S00029939197604224579
 [4]
E. W. CARDOZA, Computational Complexity of the Word Problem for Commutative Semigroups, MAC Technical Memo 67, Project MAC, M.I.T., Cambridge, Mass., October 1975.
 [5]
Seymour
Ginsburg, The mathematical theory of contextfree languages,
McGrawHill Book Co., New YorkLondonSydney, 1966. MR 0211815
(35 #2692)
 [6]
M. HACK, The Equality Problem for Vector Addition Systems, CSG Memo 121, Project MAC, M.I.T., Cambridge, Mass., April 1975. (Also to appear in J. Theoret. Comput. Sci.)
 [7]
J. HOPCROFT & J. J. PANSIOT, Decidability of SelfDual Vector Addition Systems, Dept. of Comput. Sci., Cornell Univ., Ithaca, N. Y.
 [1]
 M. ANSHEL, "Conjugate powers in HNN groups," Proc. Amer. Math. Soc., v. 54, 1976, pp. 1923. MR 0393249 (52:14059)
 [2]
 M. ANSHEL, "Decision problems for HNN groups and vector addition systems," Math. Comp., v. 30, 1976, pp. 154156. MR 0396766 (53:626)
 [3]
 M. ANSHEL, "The conjugacy problem for HNN groups and the word problem for commutative semigroups," Proc. Amer. Math. Soc., v. 61, 1976, pp. 223224. MR 0422457 (54:10446)
 [4]
 E. W. CARDOZA, Computational Complexity of the Word Problem for Commutative Semigroups, MAC Technical Memo 67, Project MAC, M.I.T., Cambridge, Mass., October 1975.
 [5]
 S. GINSBURG, The Mathematical Theory of ContextFree Languages, McGrawHill, New York, 1966. MR 0211815 (35:2692)
 [6]
 M. HACK, The Equality Problem for Vector Addition Systems, CSG Memo 121, Project MAC, M.I.T., Cambridge, Mass., April 1975. (Also to appear in J. Theoret. Comput. Sci.)
 [7]
 J. HOPCROFT & J. J. PANSIOT, Decidability of SelfDual Vector Addition Systems, Dept. of Comput. Sci., Cornell Univ., Ithaca, N. Y.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804822727
PII:
S 00255718(1978)04822727
Article copyright:
© Copyright 1978
American Mathematical Society
