Vector groups and the equality problem for vector addition systems

Author:
Michael Anshel

Journal:
Math. Comp. **32** (1978), 614-616

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**, 10.1090/S0002-9939-1976-0393249-4**[2]**Michael Anshel,*Decision problems for HNN groups and vector addition systems*, Math. Comput.**30**(1976), no. 133, 154–156. MR**0396766**, 10.1090/S0025-5718-1976-0396766-4**[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**, 10.1090/S0002-9939-1976-0422457-9**[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 context-free languages*, McGraw-Hill Book Co., New York-London-Sydney, 1966. MR**0211815****[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 Self-Dual Vector Addition Systems*, Dept. of Comput. Sci., Cornell Univ., Ithaca, N. Y.

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1978-0482272-7

Article copyright:
© Copyright 1978
American Mathematical Society