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INTERPRETING GRAPH COLORABILITY IN FINITE SEMIGROUPS

2006
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International journal of algebra and computation
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We show that a number of natural membership problems for classes associated with finite semigroups are computationally difficult. In particular, we construct a 55-element semigroup S such that the finite membership problem for the variety of semigroups generated by S interprets the graph 3-colorability problem. Recall that the term-equivalence problem for an algebra A is the problem of deciding for two terms s, t in the signature of A, if A |= s ≈ t. This problem is known to be in co-NP and

doi:10.1142/s0218196706002846
fatcat:tl2xcqfsnvcxvg62nwxycksepq