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A Shortest 2-Basis for Boolean Algebra in Terms of the Sheffer Stroke

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Abstract

In this article, we present a short 2-basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2-basis can be shorter. We also prove that the new 2-basis is unique (for its length) up to applications of commutativity. Our proof of the 2-basis was found by using the method of proof sketches and relied on the use of an automated reasoning program.

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References

  1. McCharen, J., Overbeek, R. and Wos, L.: Complexity and related enhancements for automated theorem-proving programs, Comput. Math. Appl. 2 (1976), 1-16.

    MATH  Google Scholar 

  2. McCune, W.: OTTER 3.0 reference manual and guide, Technical Report ANL-94/6, Argonne National Laboratory, Argonne, Illinois, 1994.

    Google Scholar 

  3. McCune, W.: MACE 2.0 reference manual and guide, Technical Memorandum ANL/MCSTM-249, Argonne National Laboratory, Argonne, Illinois, 2001.

    Google Scholar 

  4. McCune, W., Veroff, R., Fitelson, B., Harris, K., Feist, A. and Wos, L.: Short single axioms for Boolean algebra, J. Automated Reasoning 29(1) (2002), 1-16.

    Article  MATH  MathSciNet  Google Scholar 

  5. McCune, W., Padmanabhan, R. and Veroff, R.: Yet another single law for lattices, Algebra Universalis, to appear.

  6. Meredith, C.: Equational postulates for the Sheffer stroke, Notre Dame J. Formal Logic 10(3) (1969), 266-270.

    Article  MATH  MathSciNet  Google Scholar 

  7. Sheffer, H.: A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Amer. Math. Soc. 14(4) (1913), 481-488.

    Article  MATH  MathSciNet  Google Scholar 

  8. Ulrich, D.: A legacy recalled and a tradition continued, J. Automated Reasoning 27(2) (2001), 97-122.

    Article  MATH  MathSciNet  Google Scholar 

  9. Veroff, R.: Using hints to increase the effectiveness of an automated reasoning program: Case studies, J. Automated Reasoning 16(3) (1996), 223-239.

    Article  MATH  MathSciNet  Google Scholar 

  10. Veroff, R.: Solving open questions and other challenge problems using proof sketches, J. Automated Reasoning 27(2) (2001), 157-174.

    Article  MATH  MathSciNet  Google Scholar 

  11. Veroff, R.: http://www.cs.unm.edu/~veroff/BA/candidates.html, 2001.

  12. Wolfram, S.: Correspondence by electronic mail, 2000.

  13. Wolfram, S.: A new kind of science, http://wolframscience.com, 2000.

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Authors and Affiliations

  1. University of New Mexico, Albuquerque, NM, 87131, USA

    Robert Veroff

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  1. Robert Veroff
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Veroff, R. A Shortest 2-Basis for Boolean Algebra in Terms of the Sheffer Stroke. Journal of Automated Reasoning 31, 1–9 (2003). https://doi.org/10.1023/A:1027322305654

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