Abstract
For a finite weakly confluent monadic string-rewriting system R presenting a group the set of valid linear sentences is decidable. Thus, many decision problems for R can be solved in a uniform way. Here we show that this is no longer true in general if R is a finite weakly confluent monadic string-rewriting system that does not present a group. In fact, we construct a system R of this form that has an undecidable word problem. Some additional undecidability results as well as some decidability results for finite weakly confluent monadic string-rewriting systems are also presented.
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© 1991 Springer-Verlag Berlin Heidelberg
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Otto, F. (1991). Some undecidability results for weakly confluent monadic string-rewriting systems. In: Mattson, H.F., Mora, T., Rao, T.R.N. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1991. Lecture Notes in Computer Science, vol 539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54522-0_118
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DOI: https://doi.org/10.1007/3-540-54522-0_118
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