On the construction of parallel computers from various bases of Boolean functions

The effects of bases of two-input boolean functions are characterised in terms of their impact on some questions in parallel computation. It is found that a certain set of bases (called the P-complete set) which are not necessarily complete in the classical sense, apparently makes the circuit value problem difficult, and renders extended Turing machines and conglomerates equal to general parallel computers. A class of problems called EP arises naturally from this study, relating to the parity of the number of solutions to a problem, in contrast to previously defined classes concerning the count of the number of solutions (#P) or the existence of solutions to a problem (NP). Tournament isomorphism is a member of EP