• Publications
  • Influence
The complexity of theorem-proving procedures
  • S. Cook
  • Mathematics, Computer Science
    STOC
  • 3 May 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a
The Relative Efficiency of Propositional Proof Systems
TLDR
All standard Hilbert type systems and natural deduction systems are equivalent, up to application of a polynomial, as far as minimum proof length goes, and extended Frege systems are introduced, which allow introduction of abbreviations for formulas.
A new recursion-theoretic characterization of the polytime functions
TLDR
A recursion-theoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds, and avoids the explicit size bounds on recursion of Cobham.
A Taxonomy of Problems with Fast Parallel Algorithms
  • S. Cook
  • Computer Science, Mathematics
    Inf. Control.
  • 1 March 1985
Characterizations of Pushdown Machines in Terms of Time-Bounded Computers
  • S. Cook
  • Computer Science
    J. ACM
  • 1 January 1971
TLDR
A class of machines called auxiliary pushdown machines is introduced, characterized in terms of time-bounded Turing machines, and corollaries are derived which answer some open questions in the field.
Soundness and Completeness of an Axiom System for Program Verification
  • S. Cook
  • Computer Science
    SIAM J. Comput.
  • 1 February 1978
TLDR
The main new results are the completeness theorem, and a careful treatment of the procedure call rules for procedures with global variables in their declarations.
Upper and Lower Time Bounds for Parallel Random Access Machines without Simultaneous Writes
TLDR
It is shown that even if the authors allow nonuniform algorithms, an arbitrary number of processors, and arbitrary instruction sets, $\Omega (\log n)$ is a lower bound on the time required to compute various simple functions, including sorting n keys and finding the logical “or” of n bits.
On the lengths of proofs in the propositional calculus (Preliminary Version)
TLDR
This paper studies the complexity of decision procedures for the propositional calculus, and the fundamental issue here is whether there exists any proof system, and a polynomial p( n) such that every valid formula has a proof of length not exceeding p(n), where n is the length of the formula.
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