The Robbins conjecture
Let be a commutative and associative binary operation and a unary operation on a set, satisfying Robbins's equation for all . Prove that the structure is a Boolean algebra, or find a counterexample.
History and references
Solved in 1996 by William McCune (with the EQP prover).
In 1933 Edward Huntington gave axioms for Boolean algebra consisting of commutativity, associativity and the equation . Herbert Robbins soon asked whether his own equation could replace Huntington's. Huntington, Robbins, Alfred Tarski and others worked on the question without finding a proof or a counterexample, and Steve Winker at Argonne later reduced it to simpler sufficient conditions. In 1996 William McCune's automated theorem prover EQP found a proof after about eight days of search, showing that every Robbins algebra is Boolean, and the result was published in 1997. The machine proof was later rewritten in a form people can follow.
References
Solutions 0
Sign in or create an account to publish a solution