Language and Automata Theory and Applications

In this paper we briefly survey the history of the Dichotomy Conjecture for the Constraint Satisfaction problem, that was posed 25 years ago by Feder and Vardi. We outline some of the approaches to this conjecture, and then describe an algorithm that yields an answer to the conjecture. 1 Constraint Satisfaction Problem We begin with definitions, examples and brief historical remarks on the Constraint Satisfaction Problem.

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