Time-space lower bounds for satisfiability

  • Authors:

  • Lance Fortnow;Richard Lipton;Dieter van Melkebeek;Anastasios Viglas

  • Affiliations:

  • University of Chicago, Chicago, Illinois;Georgia Institute of Technology, Atlanta, Georgia;University of Wisconsin, Madison, Wisconsin;University of Sydney, Sydney, Australia

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2005

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Abstract

We establish the first polynomial time-space lower bounds for satisfiability on general models of computation. We show that for any constant c less than the golden ratio there exists a positive constant d such that no deterministic random-access Turing machine can solve satisfiability in time nc and space nd, where d approaches 1 when c does. On conondeterministic instead of deterministic machines, we prove the same for any constant c less than &2radic;.Our lower bounds apply to nondeterministic linear time and almost all natural NP-complete problems known. In fact, they even apply to the class of languages that can be solved on a nondeterministic machine in linear time and space n1/c.Our proofs follow the paradigm of indirect diagonalization. We also use that paradigm to prove time-space lower bounds for languages higher up in the polynomial-time hierarchy.