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    The next step of the word problem over monoids
    (ELSEVIER SCIENCE INC, 2011) Karpuz, E. Guzel; Ates, Firat; Cevik, A. Sinan; Cangul, I. Naci; Maden (Gungor), A. Dilek
    It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spherical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable "generalized identity problem'' that can be thought as the next step (or one-dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications. (C) 2011 Elsevier Inc. All rights reserved.