Computational Complexity of the Word Problem for Commutative Semigroups
Name
MIT-LCS-TM-067.pdf
Size
11 MB
Format
Adobe PDF
Checksum (MD5)
6b39de7d3d23a723baf20c8330aeceff
Author(s)
Cardoza, Edward W.
Advisor(s)
Meyer, Albert R.
Date Issued
October 1975
Series/Report no.
MIT-LCS-TM-067
MAC-TM-067
Abstract
We analyze the computational complexity of some decision problems for commutative semigroups in terms of time and space on a Turing machine. The main result we present is that any decision procedure for the word problemm for commutative semigroups requires storage space at least proportional to n/logn on a multitape Turing machine. This implies that the word problem is polynomia space hard (and in particular that it is at least NP-hard). We comment on the close relation of commutative semigroups to vector addition systems and Petri nets. We also show that the lower bound of space n/logn can be extended to certain other natural algorithmic problems for commutative semigroups. Finally we show that for several other algorithmic problems for commutative semigroups there exist polynomial time algorithms.
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