Combinatorial systems defined over one- and two-letter alphabets |
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Authors: | Charles E Hughes W E Singletary |
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Institution: | 1. Computer Science Department, University of Tennessee, 37920, Knoxville, Tn. 2. Mathematics Department, Northern Illinois University, 60115, De Kalb, Illinois
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Abstract: | In this paper we shall investigate some families of decision problems associated with a number of combinatorial systems whose alphabets are restricted to one and two letters. Our purpose is to try to gain a better understanding of the boundaries between classes of combinatorial systems whose decision problems are solvable and those whose decision problems are of any prescribed r.e. many-one degree of unsolvability. We show that, for one-letter alphabets, the decision problems considered here for semi-Thue systems, Thue systems, Post normal systems, Markov algorithms and Post correspondence classes are each solvable. In contrast, for two-letter alphabets, each such family of decision problems represents every r.e. many-one degree of unsolvability. |
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