A minimal nonfinitely based semigroup whose variety is polynomially recognizable

We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.Comment: 16 pages, 3 figure

A Minimal Nonfinitely Based Semigroup Whose Variety is Polynomially Recognizable

We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm. © 2011 Springer Science+Business Media, Inc.Acknowledgement. The first and the second authors acknowledge support from the Federal Education Agency of Russia, project 2.1.1/3537, and from the Russian Foundation for Basic Research, grant 09-01-12142