A fine-grained parallel completion procedure

Abstract

We present a parallel Knuth-Bendiz completion algorithm where the inner loop, deriving the consequences of adding a new rule to the system, is multi-threaded. The selection of the best new rule in the outer loop, and hence the completion strategy, is exactly the same as for the sequential algorithm. Our implementation, which is within the PARSA C-2 parallel symbolic computation system, exhibits good parallel speed-UPS on a standard multi-processor workstation.

Multi-Completion with Termination Tools

“…In the following paragraphs we summarize results obtained for the whole test set, and illustrate our conclusions with selected examples from that database. For this purpose, systems with prefix TPTP refer to theories underlying unit equality problems in TPTP 3.6.0 [27], prefix SK90 refers to [25,Section 3], WSW06 refers to the Slothrop [32] distribution, and BGK94 and C89 indicate systems stemming from [5] and [6], respectively. The whole testbench as well as the full experimental data can be obtained from the website.…”

“…In a section on implementation details, besides the basic control loop we present optimizations such as term indexing techniques and selection strategies and explain how various options can be controlled by the user. Recent optimizations led to the completion of novel systems such as CGE 5 . By conducting thorough benchmark tests on a considerably extended database we assessed the different enhancements.…”

Strategy-Accurate Parallel Buchberger Algorithms

“…Adhering to a strategy which imposes an ordering seems to restrict parallelism; this antinomy is solved through a "process manager", which subdivides the whole computation in many independent tasks, and has the responsibility of "pasting" the different parallel activities into the proper sequence, sometimes even discarding intermediate results not complying with the strategy. The same type of concern has been raised in Bündgen et al (1994) for the Knuth-Bendix completion procedure. In order to validate our approach, we performed both a theoretical analysis and some experiments with an implementation of the algorithm.…”

Parallel Term Rewriting with Paredux

“…Our PaReDuX system (Bündgen et al, 1996b;Bündgen et al, 1995;Bünd-gen et al, 1994c;Bündgen et al, 1994b) is the parallel form of ReDuX (Bündgen, 1993). The origins of ReDuX go back to the early eighties (Küch-lin, 1982), and it was originally developed within the framework of the ALDES/SAC-2 computer algebra library (Collins, 1980), using the list processing and symbol packages of SAC-2.…”