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Monte Carlo circuits for the abelian permutation group intersection problem

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Summary

We show that the problem of computing a basis for an abelian transitive permutation group is in N C k and also we show that the problem of computing a basis for an abelian permutation group and the problem of computing the intersection of two abelian groups acting on n points, can be solved in depth (log n)k on a Monte Carlo Boolean circuit of polynomial size. Moreover the latter two problems are shown to be in N C k in the restricted case of bounded number of generators.

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References

  1. Ajtai, M., Kolmos, J., Szemeredi, E.: A O(n logn) sorting network. pp. 1–9. 15th. ACM Symposium on Theory of Computing. Boston, Mass 1983

  2. Beynon, W.M., Iliopoulos, C.S.: Computing a basis for a finite abelian p-group. Inf. Process. Lett. 20, 161–163 (1985)

    Google Scholar 

  3. Cook, S.A.: Towards a Complexity theory of synchronous parallel computation in L'enseignement mathematique. Serie II. Tome XXVII 1981

  4. Furst, M., Hopcroft, J., Luks, E.: Polynomial time algorithms for permutation groups. pp. 36–41. Proc. 21st IEEE Symposium on Foundations of Computer Science. Syracuse, NY 1980

  5. Hoffman, G.M.: Group-theoretic algorithms and graph isomorphism. Lect. Notes Comput. Sci. 136. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  6. Iliopoulos, C.S.: Worst-case complexity bounds on algorithms for computing the canonical structure of abelian groups and the Hermite and Smith normal forms of an integer matrix. (To appear in SIAM Comput.)

  7. McKenjie, P., Cook, S.A.: The parallel complexity of the abelian permutation group membership problem. pp. 154–161. 24th IEEE Symposium on Foundations of Computer Science. Tucson, Arizona 1983

  8. Pippinger, N.: On simultaneous resource bounds. Proc. 20th Symposium on Foundations of Computer Science. San Juan, Puerto Rico 1979

  9. Reif, J.: Logarithmic depth circuits for algebraic functions. 24th IEEE Symposium on Foundations of Computer Science. Tucson, Arizona 1983

  10. Reif, J.: Parallel algorithms for graph isomorphism. TR-14-83, Aiken Computation Laboratory, Harvard Univ., 1983

  11. Shiloach, Y., Viskin, U.: An O(n 2log n) parallel MAX-FLOW algorithm. J. Algorithms 3, 57–67 (1982)

    Google Scholar 

  12. Sims, C.C.: The influence of computers in algebra. Proc. Symp. Appl. Math. 20, 13–30 (1974)

    Google Scholar 

  13. Wielandt, H.: Finite permutation groups. New York: Academic Press 1964

    Google Scholar 

  14. Ofman, Y.: On the algorithmic complexity of Discrete functions. Sov. Phys. Dokl. 7, 589–591 (1963)

    Google Scholar 

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  1. Costas S. Iliopoulos

    Present address: Department of Computer Science, Purdue University, 47907, West Lafayette, IN, USA

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  1. Computer and Information Science Dept., New Jersey Institute of Technology, 07102, Newark, NJ, USA

    Costas S. Iliopoulos

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  1. Costas S. Iliopoulos
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Iliopoulos, C.S. Monte Carlo circuits for the abelian permutation group intersection problem. Acta Informatica 23, 697–705 (1986). https://doi.org/10.1007/BF00264315

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  • DOI: https://doi.org/10.1007/BF00264315

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