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An SE-tree-based prime implicant generation algorithm

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Abstract

Prime implicants/implicates (PIs) have been shown to be a useful tool in several problem domains. In model-based diagnosis (MBD), de Kleer et al. (Proc. AAAI-90) have used PIs to characterize diagnoses. We present a PI generation algorithm which, although based on thegeneral SE-tree-based search framework, is effectively an improvement of aparticular PI generation algorithm proposed by Slagle et al. (IEEE Trans. Comput. 19(4) (1970)). The improvement is achieved via adecomposition tactic which is boosted by the SE-tree-based framework. The new algorithm is also more flexible in a number of ways. We present empirical results comparing the new algorithm to the old one, as well as to current PI generation algorithms.

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References

  1. C. Berge,Graphs and Hypergraphs (North-Holland, 1973) chap. 18.

  2. W. Bibel, A comparative study of several proof procedures, Artificial Intelligence 18 (1982) 269–293.

    Google Scholar 

  3. J. de Kleer and B.C. Williams, Diagnosis with behavioral modes,Proc. IJCAI-89, Detroit, MI, 1989, pp. 1324–1330.

  4. J. de Kleer, Exploiting locality in a TMS,Proc. AAAI-90, Boston, MA, 1990, pp. 254–271.

  5. J. de Kleer, A.K. Mackworth and R. Reiter, Characterizing diagnoses.Proc. AAAI-90, Boston, MA, 1990, pp. 324–330.

  6. J. de Kleer, Focusing on probable diagnoses.Proc. AAAI-91, Anaheim, CA, 1991, pp. 842–848.

  7. J. de Kleer, An improved incremental algorithm for generating prime implicates,Proc. AAAI-92, San Jose, CA, 1992, pp. 780–785.

  8. K.D. Forbus and J. de Kleer, Focusing the ATMS,Proc. AAAI-88, Saint Paul, MN, 1988, pp. 193–198.

  9. M. Ginsberg, A circumscriptive theorem prover, Artificial Intelligence 39 (1989) 209–230.

    Google Scholar 

  10. R. Greiner, B.A. Smith and R.W. Wilkerson, A correction to the algorithm in Reiter's theory of diagnosis, Artificial Intelligence 41 (1989) 79–88.

    Google Scholar 

  11. L.J. Holzblatt, Diagnosing multiple failures using knowledge of component states,Proc. IEEE AI Applications, 1988, pp. 139–143.

  12. P. Jackson and J. Pais, Computing prime implicants,Proc. Conference on Automated Deduction, 1990, pp. 543–557.

  13. G. Karnaugh, The map method for synthesis of combinational logic circuits, AIEE Trans. Commun. Electron. 72 (1953) 593–599.

    Google Scholar 

  14. A. Kean and G. Tsiknis, An incremental method for generating prime implicants/implicates, J. Symbolic Comput. 9 (1990) 185–206.

    Google Scholar 

  15. R.E. Korf, Linear-space best-first search: Summary of results, in:Proc. AAAI-92, San Jose, CA, 1992.

  16. E. McCluskey, Minimization of Boolean functions, Bell Syst. Tech. J. 35 (1956) 1417–1444.

    Google Scholar 

  17. T. Ngair, Convex spaces as an order-theoretic basis for problem solving, Ph.D. Thesis, Department of Computer and Information Science, University of Pennsylvania (1992).

  18. J.O.W. Quine, The problem of simplifying truth functions, Am. Math. Monthly 59 (1952) 521–531.

    Google Scholar 

  19. O. Raiman and J. de Kleer, A minimality maintenance system, to appear inProc. KR-92, Cambridge MA, 1992.

  20. R. Reiter, A theory of diagnosis from first principles, Artificial Intelligence 32 (1987) 57–95.

    Google Scholar 

  21. S. Russell, Efficient memory-bounded search algorithms, in:Proc. ECAI-92, Vienna, Austria, 1992.

  22. R. Rymon, Search through systematic set enumeration, to appear inProc. KR-92, Cambridge, MA, 1992.

  23. C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379–623.

    Google Scholar 

  24. J.R. Slagle, C. Chang and R.C. Lee, A new algorithm for generating prime implicants, IEEE Trans. Comput. 19(4) (1970).

  25. P. Struss and O. Dressler, Physical negation — Integrating fault models into the general diagnostic engine,Proc. IJCAI-89, Detroit, MI, 1989, pp. 1318–1323.

  26. R. Tarjan, Data structures and network algorithms,Society for Industrial and Applied Mathematics, Philadelphia, PA (1983).

  27. P. Tison, Generalized consensus theory and application to the minimization of Boolean functions, IEEE Trans. Comput. 16(4) (1967) 446–456.

    Google Scholar 

  28. T.D. Wu, A problem decomposition method for efficient diagnosis and interpretation of multiple disorders;Proc. SCAMC-90, Washington, DC, 1990, pp. 86–92.

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Authors and Affiliations

  1. Department of Computer and Information Science, University of Pennsylvania, 19104, Philadelphia, PA, USA

    Ron Rymon

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  1. Ron Rymon
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Additional information

This research was supported in part by a graduate fellowship ARO Grant DAAL03-89-C0031PRI.

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Rymon, R. An SE-tree-based prime implicant generation algorithm. Ann Math Artif Intell 11, 351–365 (1994). https://doi.org/10.1007/BF01530750

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