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International Symposium on Mathematical Foundations of Computer Science

MFCS 2015: Mathematical Foundations of Computer Science 2015 pp 445–458Cite as

Parallel Identity Testing for Skew Circuits with Big Powers and Applications

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9235))

Abstract

Powerful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labelled with powers \(x^n\) for binary encoded numbers n. It is shown that polynomial identity testing for powerful skew arithmetic circuits belongs to \(\mathsf {coRNC}^2\), which generalizes a corresponding result for (standard) skew circuits. Two applications of this result are presented: (i) Equivalence of higher-dimensional straight-line programs can be tested in \(\mathsf {coRNC}^2\); this result is even new in the one-dimensional case, where the straight-line programs produce strings. (ii) The compressed word problem (or circuit evaluation problem) for certain wreath products belongs to \(\mathsf {coRNC}^2\). Full proofs can be found in the long version [13].

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References

  1. Agrawal, M., Biswas, S.: Primality and identity testing via Chinese remaindering. J. Assoc. Comput. Mach. 50(4), 429–443 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beaudry, M., McKenzie, P., Péladeau, P., Thérien, D.: Finite monoids: from word to circuit evaluation. SIAM J. Comput. 26(1), 138–152 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Berman, P., Karpinski, M., Larmore, L.L., Plandowski, W., Rytter, W.: On the complexity of pattern matching for highly compressed two-dimensional texts. J. Comput. Syst. Sci. 65(2), 332–350 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eberly, W.: Very fast parallel polynomial arithmetic. SIAM J. Comput. 18(5), 955–976 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fich, F.E., Tompa, M.: The parallel complexity of exponentiating polynomials over finite fields. J. Assoc. Comput. Mach. 35(3), 651–667 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Greenlaw, R., Hoover, H.J., Ruzzo, W.L.: Limits to Parallel Computation: \({P}\)-Completeness Theory. Oxford University Press, Oxford (1995)

    MATH  Google Scholar 

  7. Hesse, W., Allender, E., Barrington, D.A.M.: Uniform constant-depth threshold circuits for division and iterated multiplication. J. Comput. Syst. Sci. 65, 695–716 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hirshfeld, Y., Jerrum, M., Moller, F.: A polynomial algorithm for deciding bisimilarity of normed context-free processes. Theor. Comput. Sci. 158(1&2), 143–159 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ibarra, O.H., Moran, S.: Probabilistic algorithms for deciding equivalence of straight-line programs. J. Assoc. Comput. Mach. 30(1), 217–228 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  10. Impagliazzo, R., Wigderson, A.: P = BPP if E requires exponential circuits: Derandomizing the XOR lemma. In: Proceedings of the STOC 1997, pp. 220–229. ACM Press (1997)

    Google Scholar 

  11. Kabanets, V., Impagliazzo, R.: Derandomizing polynomial identity tests means proving circuit lower bounds. Comput. Complex. 13(1–2), 1–46 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. König, D., Lohrey, M.: Evaluating matrix circuits. In: Xu, D., Du, D., Du, D. (eds.) COCOON 2015. LNCS, vol. 9198, pp. 235–248. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  13. König, D., Lohrey, M.: Parallel identity testing for algebraic branching programs with big powers and applications. arXiv.org (2015). http://arxiv.org/abs/1502.04545

  14. Lohrey, M.: Word problems and membership problems on compressed words. SIAM J. Comput. 35(5), 1210–1240 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lohrey, M.: Algorithmics on SLP-compressed strings: asurvey. Groups Complex. Cryptol. 4(2), 241–299 (2012)

    MathSciNet  MATH  Google Scholar 

  16. Lohrey, M.: The Compressed Word Problem for Groups. SpringerBriefs in Mathematics. Springer, New York (2014)

    Book  MATH  Google Scholar 

  17. Lohrey, M., Steinberg, B., Zetzsche, G.: Rational subsets and submonoids of wreath products. Inf. Comput. 243, 191–204 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mehlhorn, K., Sundar, R., Uhrig, C.: Maintaining dynamic sequences under equality tests in polylogarithmic time. Algorithmica 17(2), 183–198 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. Novikov, P.S.: On the algorithmic unsolvability of the word problem in group theory. Amer. Math. Soc. Transl. Ser. 2(9), 1–122 (1958)

    MATH  Google Scholar 

  20. Plandowski, W.: Testing equivalence of morphisms on context-free languages. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 460–470. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  21. Vollmer, H.: Introduction to Circuit Complexity. Springer, New York (1999)

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Universität Siegen, Siegen, Germany

    Daniel König & Markus Lohrey

Authors
  1. Daniel König
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  2. Markus Lohrey
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Correspondence to Daniel König .

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Editors and Affiliations

  1. University of Rome "Tor Vergata", Rome, Italy

    Giuseppe F. Italiano

  2. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  3. University of Edinburgh, Edinburgh, United Kingdom

    Donald T. Sannella

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König, D., Lohrey, M. (2015). Parallel Identity Testing for Skew Circuits with Big Powers and Applications. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48054-0_37

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  • DOI: https://doi.org/10.1007/978-3-662-48054-0_37

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  • Print ISBN: 978-3-662-48053-3

  • Online ISBN: 978-3-662-48054-0

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