computational complexity

, Volume 5, Issue 2, pp 155–166 | Cite as

A note on logspace optimization

  • Carme Àlvarez
  • Birgit Jenner


We show that computing iterated multiplication of word matrices over {0,1}*, using the operations maximum and concatenation, is complete for the class optL of logspace optimization functions. The same problem for word matrices over {1}* is complete for the class FNL of nondeterministic logspace functions. Improving previously obtained results, we furthermore place the class optL in AC1, and characterize FNL by restricted logspace optimization functions.

Key words

Complexity classes nondeterministic logspace optimization iterated multiplication 

Subject classifications

68Q15 68Q25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. E. Allender, D. Bruschi, andG. Pighizzini, The complexity of computing maximal word functions.Comput complexity 3 (1993), 368–391.Google Scholar
  2. C. Àlvarez andB. Jenner, A very hard log-space counting class.Theoret. Comput. Sci. 107:1 (1993), 3–30.Google Scholar
  3. C. Àlvarez, J.L. Balcázar, andB. Jenner, Adaptive logspace reducibility and parallel time.Math. Systems Theory 28 (1995), 117–140.Google Scholar
  4. D.A. Barrington, Bounded-width polynomial-size branching programs recognize exactly those languages in NC1.J. Comput. System Sci. 38 (1989), 150–164.Google Scholar
  5. M. Beaudry and P. McKenzie, Circuits, matrices, and nonassociative computation.Proc. 7th Ann. IEEE Conf. Structure in Complexity Theory, 1992, 94–106.Google Scholar
  6. M. Ben-Or andR. Cleve, Computing algebraic formulas using a constant number of registers.SIAM J. Comput. 21 (1992), 54–58.Google Scholar
  7. D. Bruschi andG. Pighizzini, The complexity of computing maximal word functions.Proc. 8th FCT Conf., Lecture Notes in Computer Science529. Springer Verlag, Berlin, 1991, 157–167.Google Scholar
  8. A.K. Chandra, L. Stockmeyer, andU. Vishkin, Constant depth reducibility.SIAM J. Comput. 13:2 (1984), 423–439.Google Scholar
  9. S.A. Cook, A taxonomy of problems with fast parallel algorithms.Inform. and Control 64 (1985), 2–22.Google Scholar
  10. S. A. Cook andP. McKenzie, Problems complete for deterministic logarithmic space.J. Algorithms 8 (1987), 385–394.Google Scholar
  11. C. Damm, DET=L#L?Informatik Preprint 8, Fachbereich Informatik der Humboldt-Universität zu Berlin, 1991.Google Scholar
  12. N. Immerman, Nondeterministic space is closed under complement.SIAM J. Comput. 17:5 (1988), 935–938.Google Scholar
  13. N. Immerman andS. Landau, The complexity of iterated multiplication.Inform. and Comput. 116 (1995), 103–116.Google Scholar
  14. A., Selman, X. Mei-rui, andR. Book, Positive relativizations of complexity classes.SIAM J. Comput. 12 (1983), 565–579.Google Scholar
  15. R. Szelepcsényi, The method of forced enumeration for nondeterministic automata.Acta Infor. 26 (1988), 279–284.Google Scholar
  16. S. Toda, Counting problems computationally equivalent to computing the determinant.Technical Report CSIM 91-07, Dept. Comp. Sci. and Info. Math., Univ. of Electro-Communications, Tokyo, May 1991.Google Scholar
  17. V. Vinay, Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits.Proc. 6th Ann. IEEE Conf. Structure in Complexity Theory, 1991, 270–284.Google Scholar

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Carme Àlvarez
    • 1
  • Birgit Jenner
    • 2
  1. 1.Dept. Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Fakultät für InformatikUniversität TübingenTübingenGermany

Personalised recommendations