The Implication Problem of Computing Policies

A computing policy is a sequence of rules, where each rule consists of a predicate and an action, and where each action is either “accept” or “reject”. A policy P is said to accept (or reject, respectively) a request iff the action of the first rule in P , that is matched by the request is “accept” (or “reject”, respectively). A pair of policies (P , Q) is called an accept-implication pair iff every request that is accepted by policy P is also accepted by policy Q. The implication problem of policies is to design an efficient algorithm that can take as input any policy pair (P , Q) and determine whether (P , Q) is an accept-implication pair. Such an algorithm can support step-wise refinement methods for designing policies. In this paper, we present a polynomial algorithm that can take any policy pair (P , Q) and determine whether (P , Q) is an acceptimplication pair. The time complexity of this algorithm is O((m+n)t+2), where m is the number of rules in policy P , n is the number of rules in policy Q, and t is the number of attributes in P or in Q. This time complexity is polynomial when t is fixed, as is usually the case.