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Parallelization of a Hyper-Linking–Based Theorem Prover

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Abstract

We describe the parallelization of a first-order logic theorem prover that is based on the hyper-linking proof procedure (HLPP). Four parallel schemes – process level, clause level, literal level, and flow level – are developed for two types of sequential implementation of HLPP: list based and network based. The motivation for developing each parallel scheme is presented, and the architecture and implementation details of each scheme are described. Issues about parallel processing, such as serialization and synchronization, load balancing, and access conflicts, are examined. Speedups over sequential implementations are attained, and timing results for benchmark problems are provided.

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References

  1. Bonacina, M. P.: On the reconstruction of proofs in distributed theorem proving: A modified Clause-Diffusion method, J. Symbolic Comput. 21 (1996), 507-522.

    Google Scholar 

  2. Bonacina, M. P.: Experiments with subdivision of search in diftributed theorem proving, in Proceedings of the Second International Symposium on Parallel Symbolic Computation, 1997, pp. 88-100.

  3. Bonacina, M. P. and Hsiang, J.: Distributed deduction by clause-diffusion: Distributed contraction and the Aquarius prover, J. Symbolic Comput. 19 (1995), 245-267.

    Google Scholar 

  4. Bonacina, M. P. and Hsiang, J.: Parallelization of deduction strategies: An analytical study, J. Automated Reasoning 13 (1994), 1-33.

    Google Scholar 

  5. Bonacina, M. P. and McCune, W.: Distributed theorem proving by Peers, in Proceedings of the 12th International Conference on Automated Deduction, 1994, pp. 841-845.

  6. Bose, S., Clarke, E. M., Long, D. E. and Michaylon, S.: PARTHENON: A parallel theorem prover for non-Horn clauses, J. Automated Reasoning 8(2) (1992), 153-182.

    Google Scholar 

  7. Brownston, L., Farrel, R., Kant, E. and Martin, N.: Programming Expert Systems in OPS5: An Introduction to Rule-Based Programming, Addison-Wesley, Reading, MA, 1985.

    Google Scholar 

  8. Cachera, D. and Utard, G.: Proving data-parallel programs: A unifying approach, Parallel Process. Lett. 6 (1996), 491-506.

    Google Scholar 

  9. Chang, C. L. and Lee, R. C. T.: Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.

    Google Scholar 

  10. Conry, S. E., MacIntosh, D. J. and Meyer, R. A.: DARES: A distributed automated resolution system, in Proceedings of the 11th National Conference on Artificial Intelligence, 1990, pp. 78-85.

  11. Davis, M. and Putnam, H.: A computing procedure for quantification theory, J. ACM 7(3) (1960), 201-215.

    Google Scholar 

  12. Deitel, H. M.: Operating Systems, Addison-Wesley, Reading, MA, 1990.

    Google Scholar 

  13. de Kleer, J.: An assumption-based TMS, Artif. Intell. 28 (1986), 127-162.

    Google Scholar 

  14. Denzinger, J. and Schulz, S.: Recording and analyzing knowledge-based distributed deduction processes, J. Symbolic Comput. 21 (1996), 523-541.

    Google Scholar 

  15. Forgy, C. L.: Rete: A fast algorithm for the many pattern/many object pattern match problem, Artif. Intell. 19 (1982), 17-37.

    Google Scholar 

  16. Goubault, J.: Proving with BDDs and control of information, in Proceedings of the 12th International Conference on Automated Deduction, 1994, pp. 499-513.

  17. Graf, P.: Extended path-indexing, in Proceedings of the 12th International Conference on Automated Deduction, 1994, pp. 514-528.

  18. Gutpa, A.: Parallelism in production systems, Ph.D. Thesis, Department of Computer Science, Carnegie-Mellon University, 1986.

  19. Gupta, A., Forgy, C., Newell, A. and Wedig, R.: Parallel algorithms and architectures for rule-based systems, in Proceedings of the 13th Annual International Symposium on Computer Architecture, 1986.

  20. Hasegawa, R. and Koshimura, M.: An AND parallelization method for MGTP and its evaluation, in Proceedings of the First International Symposium on Parallel Symbolic Computation, 1994.

  21. Hong, H.: Special issue on parallel symbolic computation: Foreword of the guest editor, J. Symbolic Comput. 21(4) (1996), 376-377.

    Google Scholar 

  22. Konrad, K.: HOT: A concurrent automated theorem prover based on higher-order tableaux, in Lecture Notes in Comput. Sci. 1479, Springer, 1998, pp. 245-262.

  23. Laird, J. E. and Newell, A.: A universal weak method, Technical Report CMU-CS-83-141, Department of Computer Science, Carnegie-Mellon University, 1983.

  24. Lee, S.-J. and Plaisted, D.: Eliminating duplication with hyper-linking strategy, J. Automated Reasoning 9(1) (1992), 25-42.

    Google Scholar 

  25. Lee, S.-J. and Wu, C.-H.: Improving the efficiency of a hyper-linking based theorem prover by incremental evaluation with network structures, J. Automated Reasoning 12 (1994), 359-388.

    Google Scholar 

  26. Lusk, E. L. and McCune, W. W.: Experiments with ROO: A parallel automated deduction system, Parallelization in Inference Systems 590 (1992), 139-162.

    Google Scholar 

  27. McCune, W. W.: Experiments with discrimination-tree indexing and path indexing for term retrieval, J. Automated Reasoning 9 (1992), 147-167.

    Google Scholar 

  28. McCune, W. W.: OTTER 3.0 Users' Guide, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, January 1994.

    Google Scholar 

  29. Moten, R.: Exploiting parallelism in interactive theorem provers, in Lecture Notes in Comput. Sci. 1479, Springer, 1998, pp. 315-330.

  30. Pelletier, F. J.: Seventy-five problems for testing automatic theorem provers, J. Automated Reasoning 2 (1986), 191-216.

    Google Scholar 

  31. Plaisted, D.: Non-Horn clause logic programming without contrapositives, J. Automated Reasoning 4 (1988), 287-325.

    Google Scholar 

  32. Schumann, J.: Delta-a bottom-up preprocessor for top-down theorem provers (system abstract), in Proceedings of the 12th International Conference on Automated Deduction, 1994, pp. 774-777.

  33. Singhal, A. and Yale, P.: Unification parallelism: How much can we exploit?, in Proceedings of the North American Conference on Logic Programming, 1989, pp. 1135-1147.

  34. Slaney, J. K. and Lusk, E. L.: Parallelizing the closure computation in automated deduction, in Proceedings of the 10th International Conference on Automated Deduction, 1990, pp. 28-39.

  35. Stickel, M. E.: A Prolog technology theorem prover: Implementation by an extended Prolog compiler, J. Automated Reasoning 4 (1988), 353-380.

    Google Scholar 

  36. Stolfo, S. J. and Shaw, D. E.: DADO: A tree-structured machine architecture for production systems, in Proceedings of the National Conference on Artificial Intelligence, August 1982, pp. 369-388.

  37. Stolfo, S. J. and Shaw, D. E.: Architecture and application of DADO: A large-scale parallel computer for artificial intelligence, in Proceedings of the International Joint Conference on Artificial Intelligence, 1983.

  38. Sturgill, D. B. and Segre, A.M.: A novel asynchronous parallelism scheme for first-order logic, in Proceedings of the 12th International Conference on Automated Deduction, 1994, pp. 484-498.

  39. Suttner, C. B.: SPTHEO-a PVM-based parallel theorem prover, in Lecture Notes in Comput. Sci. 1156, Springer, 1996, pp. 116-125.

  40. Suttner, C. B.: SPTHEO: A parallel theorem prover, J. Automated Reasoning 18 (1997), 253-258.

    Google Scholar 

  41. Suttner, C. B. and Schumann, J.: Parallel automated theorem proving, Parallel Process. Artif. Intell. 1 (1994), 209-257.

    Google Scholar 

  42. Suttner, C. B. and Sutcliffe, G.: The TPTP problem library, v2.2.0, Technical Report 99/02, Department of Computer Science, James Cook University, Australia, 1999.

    Google Scholar 

  43. Wielemaker, J.: SWI Prolog 3.1 Reference Manual, Dept. of Social Science Information (SWI), University of Amsterdam, Roeterstraat 15, 1018 WB Amsterdam, The Netherlands, 1998.

    Google Scholar 

  44. Wolf, A.: P-SETHEO: Strategy parallelism in automated theorem proving, in Lecture Notes in Comput. Sci. 1397, Springer, 1998, pp. 320-324.

  45. Zhang, H., Bonacina, M. P. and Hsiang, J.: PSATO: A distributed propositional prover and its application to quasigroup problems, J. Symbolic Comput. 21 (1996), 543-560.

    Google Scholar 

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Authors and Affiliations

  1. Department of Information Management, Shu-Te Institute of Technology, Kaohsiung, Taiwan, 824

    Chih-Hung Wu

  2. Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, 804

    Shie-Jue Lee

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  1. Chih-Hung Wu
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Wu, CH., Lee, SJ. Parallelization of a Hyper-Linking–Based Theorem Prover. Journal of Automated Reasoning 26, 67–106 (2001). https://doi.org/10.1023/A:1006469202251

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