1. A computer-implemented method for verifying membership in one or more sets that are subsets of a global set, wherein a d-dimensional data structure is utilized to represent the global set, where one or more vertices of the d-dimensional data structure are respectively mapped to one or more members of the global set, the method comprising: representing a subset C of the global set based on a Boolean clause assignment C=y 1 z 1 or y 2 z 2 or. .. or y i z i , wherein y i and z i represent a first word and a second word of respective Boolean clauses the conjunction of which defines the subset C; determining that a code x i is a member of C if: 
 (( x i XOR z i )AND y i )=0.