Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems, especially those employed in safety-critical environments, should be able to operate properly even in the presence of software faults. Monitoring the execution of a distributed system, and, on detecting a fault, initiating the appropriate corrective action is an important way to tolerate such faults. This gives rise to the predicate detection problem which requires finding a consistent cut of a given computation that satisfies a given global predicate, if it exists. Detecting a predicate in a computation is, however, an NP-complete problem. To ameliorate the associated combinatorial explosion problem, we introduce the notion of computation slice. Formally, the slice of a computation with respect to a predicate is a (sub)computation with the least number of consistent cuts that contains all consistent cuts of the computation satisfying the predicate. To detect a predicate, rather than searching the state-space of the computation, it is much more efficient to search the state-space of the slice. We prove that the slice exists and is uniquely defined for all predicates. We present efficient slicing algorithms for several useful classes of predicates. We develop efficient heuristic algorithms for computing an approximate slice for predicates for which computing the slice is otherwise provably intractable. Our experimental results show that slicing can lead to an exponential improvement over existing techniques for predicate detection in terms of time and space.