• Corpus ID: 241035631

Effective guessing has unlikely consequences

  title={Effective guessing has unlikely consequences},
  author={Andr{\'a}s Z. Salamon and Michael Wehar},
A classic result of Paul, Pippenger, Szemer\'edi and Trotter states that DTIME(n) is strictly contained in NTIME(n). The natural question then arises: could DTIME(t(n)) be contained in NTIME(n) for some superlinear time-constructible function t(n)? If such a function t(n) does exist, then there also exist effective nondeterministic guessing strategies to speed up deterministic computations. In this work, we prove limitations on the effectiveness of nondeterministic guessing to speed up… 



New Non-Uniform Lower Bounds for Uniform Classes

The nondeterministic hierarchy theorem for non-deterministic polynomial time is strengthened to show that the lower bound holds against sub-linear advice, and a new lower bound for NP is derived against NP-uniform non-Deterministic circuits of size O(nk) for any fixed k.

On separators, segregators and time versus space

  • R. Santhanam
  • Computer Science, Mathematics
    Proceedings 16th Annual IEEE Conference on Computational Complexity
  • 2001
It is shown that nondeterministic time-bounded Turing machines can be simulated by /spl Sigma//sub 4/ machines with an asymptotically smaller time bound, under the assumption that the class of multi-pushdown graphs has sublinear separators.

P = BPP if E requires exponential circuits: derandomizing the XOR lemma

A pseudo-random generator which produces n instances of a problem for which the analog of the XOR lemma holds is given, and it is shown that if any problem in E = DTIAl E(2°t”j) has circuit complexity 2Q(”), then P = BPP.

The complexity of theorem-proving procedures

  • S. Cook
  • Mathematics, Computer Science
  • 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

Hierarchies for semantic classes

It is shown that for any constant a, ZPP/b(n) strictly contains ZPTIME(na)/b( n), and a similar statement for NP is proved by building on Zák's proof of the nondeterministic time hierarchy.

Two-Tape Simulation of Multitape Turing Machines

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.

Non-uniform ACC Circuit Lower Bounds

  • Ryan Williams
  • Computer Science
    2011 IEEE 26th Annual Conference on Computational Complexity
  • 2011
The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms can be applied to obtain the above lower bounds.

Computability and Complexity Theory

Conise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes.

A Turing Machine Time Hierarchy

  • S. Zák
  • Computer Science
    Theor. Comput. Sci.
  • 1983

Satisfiability Is Quasilinear Complete in NQL

Many of the "exhausUve search" type problems such as satlsflablhty and colorabdlty are complete in NQL with respect to reductions that take O(n(log n) k) steps.