Patent ID: 7440942

Claim:
A computer-implemented method to search a database for data satisfying a property specified by a query of a type “find element x that satisfies property P”, comprising: accessing a database containing data within an application domain and encoded in a group theory representation, the encoded data having one or more augmented database elements, where each augmented database element has a pair (c, G) including a database element c and an associated group G of group elements g acting on c and wherein each augmented database element has an associative binary operator acting on the group elements g such that the associative binary operator has an identity and each group element g has an inverse; formulating the query in terms of the group theory representation, the formulated query of a type “find database element c and element g of the associated group G, such that g(c) satisfies property P”; executing the formulated query on the encoded data in the database to identify one or more database elements and group elements in the group theory representation satisfying the query; and outputting the one or more database elements and group elements satisfying the query.