The Complexity of Membership Problems for Circuits over Sets of Integers

  title={The Complexity of Membership Problems for Circuits over Sets of Integers},
  author={Stephen D. Travers},
  • Stephen D. Travers
  • Published in MFCS 2004
  • Mathematics, Computer Science
  • We investigate the complexity of membership problems for \(\{\cup,\cap,\!\bar{\quad},+,\times\}\)-circuits computing sets of integers. These problems are a natural modification of the membership problems for circuits computing sets of natural numbers studied by McKenzie and Wagner (2003). We show that there are several membership problems for which the complexity in the case of integers differs significantly from the case of the natural numbers: Testing membership in the subset of integers… CONTINUE READING

    Topics from this paper.

    Equivalence Problems for Circuits over Sets of Natural Numbers
    • 16
    • PDF
    Representing Hyper-arithmetical Sets by Equations over Sets of Integers
    • 9
    • PDF
    Evaluation of Circuits Over Nilpotent and Polycyclic Groups
    • 9
    • Highly Influenced
    • PDF
    On equations over sets of integers
    • 5
    • PDF
    Emptiness Problems for Integer Circuits
    • 4
    • Highly Influenced
    • PDF
    Complexity of Equations over Sets of Natural Numbers
    • 30
    • PDF
    Balance Problems for Integer Circuits
    • T. Dose
    • Computer Science, Mathematics
    • 2018
    Functions Definable by Arithmetic Circuits
    • 11
    • PDF


    Publications referenced by this paper.
    The monotone and planar circuit value problems are log space complete for P
    • 219
    Integer circuit evaluation is PSPACE-complete
    • K. Yang
    • Mathematics, Computer Science
    • 2000
    • 19
    An Introduction to the Theory of Numbers
    • 4,826
    • PDF
    The complexity of algorithmic problems on succinct instances
    • 56
    Nondeterministic Space is Closed Under Complementation
    • 668
    • PDF
    The twenty-fourth Fermat number is composite
    • 22
    • PDF
    Maze Recognizing Automata and Nondeterministic Tape Complexity
    • 60