A Distributed Logical Filter for Connected Row Convex Constraints

Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. Popular filtering techniques like Kalman and particle filters maintain compact representations of the belief state at all times. However, these techniques cannot be applied to situations where the world is described using constraints instead of stochastic models. In such cases, the belief state is a logical formula describing all possible world states. In this paper, we first review a logical filtering algorithm for connected row convex (CRC) constraints. CRC constraints are representationally very powerful; and the filtering algorithm for CRC constraints is a logical equivalent of the Kalman filter. We later study the CRC filtering algorithm in distributed settings where nodes of a network are interested in different subsets of variables from a larger system. We deduce its reducibility to the problem of distributed path consistency (PC) and prove the compactness of the belief state representations maintained at each node at all times.