Abstract

Let C1 be the class of finitely presented monoids with word problem solvable in linear time. Let P be a Markov property of monoids related to class C1 in some sense. It is undecidable given a monoid in C1 whether it satisfies P. Let C and C′ be classes of finitely presented monoids with word problem solvable in some time-bounds. If C contains C1 and C′ properly contains C, then it is undecidable given a monoid in C′ whether it belongs to C.

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