Monoids and Computations

This contribution wishes to argue in favor of increased interaction between experts on finite monoids and specialists of theory of computation. Developing the algebraic approach to formal computations as well as the computational point of view on monoids will prove to be beneficial to both communities. We give examples of this two-way relationship coming from temporal logic, communication complexity and Boolean circuits. Although mostly expository in nature, our paper proves some new results along the way.

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