On the power of random access machines

  • Arnold Schönhage
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)


We study the power of deterministic successor RAM's with extra instructions like +,*,⋎ and the associated classes of problems decidable in polynomial time. Our main results are NP ... PTIME (+,*,⋎) and PTIME(+,*) ... RP, where RP denotes the class of problems randomly decidable (by probabilistic TM's) in polynomial time.


Polynomial Time Conjunctive Normal Form Floating Point Arithmetic Polynomial Reducibility Straight Line Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Hartmanis and J. Simon, On the power of multiplication in random access machines. IEEE Conf. Rec. 15th Symp. Switching Automata Theory (1974) 13–23.Google Scholar
  2. [2]
    J. E. Hopcroft, W. J. Paul and L. G. Valiant, On time versus space and related problems. Proc. 16th Ann. IEEE Symp. Foundations Comp. Sci. Berkeley (1975) 57–64.Google Scholar
  3. [3]
    V. Pratt, L. Stockmeyer, M. O. Rabin, A characterization of the power of vector machines. Proc. 6th Ann. ACM Symp. Theor. Comp. (1974) 122–134.Google Scholar
  4. [4]
    A. Schönhage, Storage modification machines. Preprint, Universität Tübingen (1978), submitted to SIAM J. Comput.Google Scholar
  5. [5]
    J. Simon, On feasible numbers. Proc. 9th ACM Symp. Theor. Comp., Boulder (1977) 195–207.Google Scholar
  6. [6]
    R. Solovay, V. Strassen, A fast Monte-Carlo test for primality. SIAM J. Comput. 6 (1977), 84–85.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Arnold Schönhage
    • 1
  1. 1.Mathematisches Institut der Universität TübingenGermany

Personalised recommendations