Undecidable properties of monoids with word problem solvable in linear time

Authors:
Masashi Katsura;Yuji Kobayashi
Affiliations:
Department of Mathematics, Kyoto-Sangyo University, Kyoto 603-8555, Japan;Department of Information Science, Toho University, Funabashi 274-8510, Japan
Venue:
Theoretical Computer Science
Year:
2003

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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.