THE PROPERTY FDT IS UNDECIDABLE FOR FINITELY PRESENTED MONOIDS THAT HAVE POLYNOMIAL-TIME DECIDABLE WORD PROBLEMS
Friedrich Otto, Andrea Sattler-Klein · International Journal of Algebra and Computation · 2000
By exploiting a new technique for proving undecidability results developed by A. Sattler-Klein in her doctoral dissertation (1996) it is shown that it is undecidable in general whether or not a finitely presented monoid with a polynomial-time decidable word problem has finite derivation type (FDT). This improves upon the undecidability result of R. Cremanns and F. Otto (1996), which was based on the undecidability of the word problem for the finitely presented monoids considered.