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Parallelizable algebras

  • Matthias Ragaz
Article

Keywords

Mathematical Logic Parallelizable Algebra 
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References

  1. [1]
    Borodin, A., Munro, I.: The computational complexity of algebraic and numeric problems. New York 1975.Google Scholar
  2. [2]
    Brent, E., Kuck, D., Maruyama, K.: The parallel evaluation of arithmetic expressions without division. IEEE Transactions on Computers C-22 (1973) 532–534.Google Scholar
  3. [3]
    Fischer, M.J., Meyer, A.R., Paterson, M.S.: Ω(nlogn) lower bounds on length of Boolean formulas. SIAM J. Comput.11, 3 (1982) 416–427.CrossRefGoogle Scholar
  4. [4]
    Hodes, L.E., Specker, E.: Length of formulas and elimination of quantifiers I. Contributions to Mathematical Logic. Amsterdam 1968.Google Scholar
  5. [5]
    Krapchenko, V.M.: Complexity of the realization of a linear function in the class of II-circuits. Math. Notes Acad. Sci. USSR (1971) 21–23.Google Scholar
  6. [6]
    Lyndon, R.: Identities in two-valued calculi. Trans. Am. Math. Soc.71 (1951) 457–465.Google Scholar
  7. [7]
    Murskii, V.L.: The existence in three-valued logic of a closed class with finite basis, not having a finite complete system of identities. Sov. Math. Dokl.6 (1965) 1020–1024.Google Scholar
  8. [8]
    Nečiporuk, E.I.: A Boolean function. Sov. Math. Dokl.7 (1966) 999–1000.Google Scholar
  9. [9]
    Perkins, P.: Bases for equational theories of semigroups. J. Algebra11 (1969) 293–314.CrossRefGoogle Scholar
  10. [10]
    Post, E.L.: The two-valued iterative systems of mathematical logic. Annals of Mathematics Studies5, Princeton 1941; reprint New York 1965.Google Scholar
  11. [11]
    Pratt, V.R.: The effect of basis on size of Boolean expressions. Proc. Annual IEEE Symposium on Foundations of Computer Science16 (1975) 119–121.Google Scholar
  12. [12]
    Pudlak, P.: Bounds for Hodes-Specker theorem. In: Logic and machines: Decision problems and complexity. Proceedings. Lecture Notes in Computer Science 171. Berlin 1984.Google Scholar
  13. [13]
    Rautenberg, W.: 2-element matrices. Studia LogicaXL (1981) 315–353.CrossRefGoogle Scholar
  14. [14]
    Savage, J.E.: The complexity of Computing. New York 1976.Google Scholar
  15. [15]
    Spira, P.M.: On time-hardware complexity tradeoffs for Boolean functions. Proc. Fourth Hawaii International Symposium on System Sciences (1971) 525–527.Google Scholar
  16. [16]
    Subbotovskaya, B.A.: Realizations of linear functions by formulas using &, ∨,. Sov. Math. Dokl.2 (1961) 110–112.Google Scholar
  17. [17]
    Subbotovskaya, B.A.: Comparison of bases in the realization by formulas of functions of the algebra of logic. Sov. Math. Dokl.4 (1963) 478–481.Google Scholar

Copyright information

© Verlag W. Kohlhammer 1987

Authors and Affiliations

  • Matthias Ragaz
    • 1
  1. 1.ZürichSuisse

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