The Implication Problem of Computing Policies

Abstract

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 accept-implication pair. The time complexity of this algorithm is $\mathcal {O}$(($m + n$)$^{t+2}$), 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.