The closure operator with the equality predicate branching on the set of partial Boolean functions

On the set $P_2^*$ of partial Boolean functions, we consider the closure operator with the equality predicate branching. We prove that each closed class with respect to this operator is generated in $P_2^*$ by the set of all its functions depending on at most two variables. In the paper, all maximal and submaximal classes in $P_2^*$ and all closed classes generated by one one-place or two-place function are presented.
This research was supported by the Russian Foundation for Basis Research, grant 06–01–00438.