Truth Maintenance Systems for Problem Solving

The thesis developed here is that reasoning programs which take care to record the logical justifications for program beliefs can apply several powerful, but simple, domain-independent algorithms to (1) maintain the consistency of program beliefs, (2) realize substantial search efficiencies, and (3) automatically summarize explanations of program beliefs. These algorithms are the recorded justifications to maintain the consistency and well founded basis of the set of beliefs. The set of beliefs can be efficiently updated in an incremental manner when hypotheses are retracted and when new information is discovered. The recorded justifications also enable the pinpointing of exactly whose assumptions which support any particular belief. The ability to pinpoint the underlying assumptions is the basis for an extremely powerful domain-independent backtracking method. This method, called Dependency-Directed Backtracking, offers vastly improved performance over traditional backtracking algorithms.

On-the-Fly Maintenance of Series-Parallel Relationships in Fork-Join Multithreaded Programs

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships "on the fly" for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient "English-Hebrew" labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T₁ time on a single processor can be checked on the fly for determinacy races in O(T₁) time. Corresponding improved bounds can also be obtained for more sophisticated data-race detectors, for example, those that use locks. By combining SP-order with Feng and Leiserson’s serial SP-bags algorithm, we obtain a parallel SP-maintenance algorithm, called SP-hybrid. Suppose that a fork-join program has n threads, T₁ work, and a critical-path length of T[subscript ∞]. When executed on P processors, we prove that SP-hybrid runs in O((T₁/P + PT[subscript ∞]) lg n) expected time. To understand this bound, consider that the original program obtains linear speed-up over a 1-processor execution when P = O(T₁/T[subscript ∞]). In contrast, SP-hybrid obtains linear speed-up when P = O(√T₁/T[subscript ∞]), but the work is increased by a factor of O(lg n).