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On renamable Horn and generalized Horn functions

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Abstract

A Boolean function in disjunctive normal form (DNF) is aHorn function if each of its elementary conjunctions involves at most one complemented variable. Ageneralized Horn function is constructed from a Horn function by disjuncting a nested set of complemented variables to it. The satisfiability problem is solvable in polynomial time for both Horn and generalized Horn functions. A Boolean function in DNF is said to berenamable Horn if it is Horn after complementation of some variables. Succinct mathematical characterizations and linear-time algorithms for recognizing renamable Horn and generalized Horn functions are given in this paper. The algorithm for recognizing renamable Horn functions gives a new method to test 2-SAT. Some computational results are also given.

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Authors and Affiliations

  1. School of Industrial Engineering, Purdue University, 47907, West Lafayette, IN, USA

    Vijaya Chandru, Collette R. Coullard & Miguel Montañez

  2. RUTCOR-Rutgers Center for Operations Research, Rutgers University, 08903, New Brunswick, NJ, USA

    Peter L. Hammer & Xiaorong Sun

Authors
  1. Vijaya Chandru
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  2. Collette R. Coullard
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  3. Peter L. Hammer
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  4. Miguel Montañez
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  5. Xiaorong Sun
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Additional information

The authors were supported in part by the Office of Naval Research under University Research Initiative grant number N00014-86-K-0689. Chandru was also supported by NSF grant number DMC 88-07550.

The authors gratefully acknowledge the partial support of NSF (Grant DMS 89-06870) and AFOSR (Grant 89-0066 and 89-0512).

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Chandru, V., Coullard, C.R., Hammer, P.L. et al. On renamable Horn and generalized Horn functions. Ann Math Artif Intell 1, 33–47 (1990). https://doi.org/10.1007/BF01531069

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