1. A method for searching a database for data satisfying a property specified by a query, the database containing data within an application domain and encoded in a group theory representation, comprising: formulating the query in terms of the group theory representation; executing the query on the data in the database within the application domain and encoded in the group theory representation to identify zero or more database elements and group elements in the group theory representation satisfying the query; and outputting the zero or more database elements and group elements satisfying the query.