And-Or Parallelism on Shared-Memory Multiprocessors

Abstract This paper presents an extended and—or tree and an extended WAM (Warren Abstract Machine) for efficiently supporting both and-parallel and or-parallel execution of logic programs on shared-memory multiprocessors. Our approach for exploiting both and- and or-parallelism is based on the binding-arrays method for or-parallelism and the RAP (Restricted And-Parallelism) method for and-parallelism, two succesful methods for implementing or-parallelism and and-parallelism, respectively. Our combined and—or model avoids redundant computations when goals exhibit both and- and or-parallelism, by representing the cross product of the solutions from the and—or parallel goals rather than recomputing them. We extend the classical and—or tree with two new nodes: a “sequential” node (for RAPs sequencial goals), and a “cross-product” node (for the cross product of solutions from and—or parallel goals). The paper also presents an extension of the WAM, called AO—WAM, which is used to compile logic programs for and—or parallel execution based on the extended and—or tree. The AO—WAM incorporates a number of novel features: (i) inclusion of a base array with each processor's binding array for constant-time access to variables in the presence of and-parallelism, (ii) inclusion of new stack frames and instructions to express solution sharing , and (iii) novel optimizations which minimize the cost of binding-array updates in the presence of and-parallelism.