@MISC{Valiant92whyis, author = {L.G. Valiant}, title = {Why is Boolean Complexity Theory Difficult?}, year = {1992} }

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Abstract

this paper we shall assume that S is a commutative ring with identity. Then each instruction f i can be identified with the polynomial that is computed at f i , if\Omega and \Phi are interpreted as the ring operations in the polynomial ring S[x 1 ; \Delta \Delta \Delta ; x n ]. Among natural multivariate polynomials whose complexity in this model is of interest are Hamiltonian circuits (HC), the permanent (PERM) and the determinant (DET). These are defined over a matrix X of indeterminates fx 11 ; \Delta \Delta \Delta ; x nn g where x ij