Abstract
This paper investigates decision problems of finite, special string-rewriting systems. There are two main results. The first one is that the word problem for a finite, special string-rewriting system T on alphabet A is reducible to its restricted version: given a word w, is w congruent to any fixed element z on A? Another is a Markov type theorem: a property P is undecidable for finite, special string-rewriting systems if P implies any fixed Markov property of finitely presented special monoids and there exists a finite, special string-rewriting system R on alphabet C with the property that a finite, special string-rewriting system T on A has P whenever M(A;T) is isomorphic to M(C;R).
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