A hierarchy for nondeterministic time complexity

@article{Cook1973AHF,
  title={A hierarchy for nondeterministic time complexity},
  author={Stephen A. Cook},
  journal={Proceedings of the fourth annual ACM symposium on Theory of computing},
  year={1973}
}
  • S. Cook
  • Published 1 May 1972
  • Computer Science
  • Proceedings of the fourth annual ACM symposium on Theory of computing
The purpose of this paper is to prove the following result: Theorem 1 For any real numbers r1, r2, 1 ≤ r1 < r2, there is a set A of strings which has nondeterministic time complexity nr2 but not nondeterministic time complexity nr1 The computing devices are non-deterministic multitape Turing machines. 

Tables from this paper

Almost-Everywhere Complexity Hierarchies for Nondeterministic Time
Nondeterministic Separations
TLDR
Results include separating NEXP from NP with limited advice, a new proof of the nondeterministic time hierarchy and a surprising relativized world where NP is as powerful as NEXP infinitely.
Complexity classes and theories of finite models
  • J. Lynch
  • Mathematics
    Mathematical systems theory
  • 2005
TLDR
If L is accepted in nondeterministic timend, d a natural number, then there is a sentence whose relational symbols are d-ary or less, whose finite spectrum is L.
Diagonalizing Against Polynomial-Time Bounded Turing Machines Via Nondeterministic Turing Machine
TLDR
This work enumerates all polynomial-time deterministic Turing machines and diagonalize over all of them by an universal nondeterministic Turing machine, and obtains a proof that P and NP differs.
On the Complexity of SAT ( Revised )
We show1 that non-deterministic time NTIME(n) is not contained in deterministic time n √ 2− and polylogarithmic space, for any > 0. This implies that (infinitely often) satisfiability cannot be
Structure in Average Case Complexity
TLDR
A characterization of Levin's notion of functions, that are polynomial on average, gives a very smooth translation from worst case complexity to average case complexity of the notions for time and space complexity.
Diagonalization of Polynomial-Time Turing Machines Via Nondeterministic Turing Machine
TLDR
It is obtained that there is a language L d not accepted by any polynomial-time deterministic Turing machines but accepted by a nondeterministic Turing machine working within O ( n k ) for any k ∈ N 1 .
Hardness and hierarchy theorems for probabilistic quasi-polynomial time
We prove tight hierarchy theorems for bounded error probabilistic quasi-polynomial time classes, under se”era1 hardness assumptions. We show that if either (1) the Permanent does not have a
Probabilistic computation and linear time
TLDR
An oracle under which BPP is equal to probabilistic linear time is given, an unusual collapse of a complexity time hierarchy, implying that there are languages solvable by interactive proof systems that can not be solved in probabilism linear time.
Word problems requiring exponential time(Preliminary Report)
TLDR
A number of similar decidable word problems from automata theory and logic whose inherent computational complexity can be precisely characterized in terms of time or space requirements on deterministic or nondeterministic Turing machines are considered.
...
...

References

SHOWING 1-10 OF 16 REFERENCES
Relationships Between Nondeterministic and Deterministic Tape Complexities
  • W. Savitch
  • Computer Science
    J. Comput. Syst. Sci.
  • 1970
The complexity of theorem-proving procedures
  • S. Cook
  • Mathematics, Computer Science
    STOC
  • 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
A Note Concerning Nondeterministic Tape Complexities
A set of sufficient condit ions on tape funct ions Ll(n) and L2(n) is presented t h a t guarantees the existence of a set accepted by an Ll (n) tape bounded nondeterminis t ic Turing machine, bu t
Two-Tape Simulation of Multitape Turing Machines
TLDR
The trade-off relation between number of tapes and speed of computation can be used in a diagonalization argument to show that, if a given function requires computation time T for a k-tape realization, then it requires at most computation time log T log log log for a two-Tape realization.
Reducibility among combinatorial problems" in complexity of computer computations
TLDR
In his 1972 paper, Reducibility Among Combinatorial Problems, Richard Karp used Stephen Cooks 1971 theorem that the boolean satisfiability problem is.
Translational methods and computational complexity
This paper investigates the computational complexity of binary sequences as measured by the rapidity of their generation by multitape Turing machines. A "translational" method which escapes some of
Reducibility Among Combinatorial Problems
  • R. Karp
  • Computer Science
    50 Years of Integer Programming
  • 1972
TLDR
Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
J. Computer and em Sciences
  • J. Computer and em Sciences
STEARNS, Two-tape simulation of multi-tape Turing machines
  • J. Assoc. for Computing Machinery
  • 1966
FISCHEa, Multi-tape simulation of multi-head Turing machines
  • IEEE Conference Record of 1967 Eighth Annual Symposium on Switching and Automata
  • 1967
...
...