Arthur-Merlin games in Boolean decision trees

  title={Arthur-Merlin games in Boolean decision trees},
  author={Ran Raz and G{\'a}bor Tardos and Oleg Verbitsky and Nikolai K. Vereshchagin},
  journal={Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247)},
  • R. Raz, G. Tardos, N. Vereshchagin
  • Published 15 June 1998
  • Computer Science
  • Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247)
It is well known that probabilistic boolean decision trees cannot be much more powerful than deterministic ones. Motivated by a question if randomization can significantly speed up a nondeterministic computation via a boolean decision tree, we address structural properties of Arthur-Merlin games in this model and prove some lower bounds. We consider two cases of interest, the first when the length of communication between the players is limited and the second if it is not. While in the first… 

Quadratic Simulations of Merlin–Arthur Games

It is proved that this quadratic overhead is necessary for black-box simulations for 2-sided-error Merlin–Arthur games and that there is an oracle relative to which MA ⊈ NPBPP holds.

A Hierarchy Theorem for Interactive Proofs of Proximity

The hierarchy theorem for IPPs shows that the round reduction technique of Babai and Moran is (almost) optimal among all blackbox transformations, and a connection to the algebrization framework of Aaronson and Wigderson is shown.

Limits on Efficient Computation in the Physical World

This thesis attacks the common belief that quantum computing resembles classical exponential parallelism, by showing that quantum computers would face serious limitations on a wider range of problems than was previously known, and studies the relationship of the quantum computing model to physical reality.

An Exponential Separation Between MA and AM Proofs of Proximity

This work considers two natural minimally interactive variants of interactive proofs of proximity, in which the prover only sends a single message, referred to as the proof, and exhibits an explicit and natural property that admits an with complexity $$O(\log n)$$ O ( log n ) , whereas any for Π has complexity $$\tilde{\Omega}(n^{1/4})$$.

Quadratic Simulations of Merlin-Arthur Games

  • Thomas Watson
  • Computer Science, Mathematics
    Electron. Colloquium Comput. Complex.
  • 2017
It is proved that this quadratic overhead is necessary for black-box simulations and obtained an oracle relative to which \(\textsf {MA}\subseteq \textsf{NP}^\ textsf {BPP}\) (which was previously known to hold by a proof using generics).

Quantum certificate complexity

  • S. Aaronson
  • Computer Science
    18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.
  • 2003
Using Ambainis' adversary method, QC(f) is exactly characterized as the square root of RC(f), which is used to prove the new relation R/sub 0/(f)=O(Q/sub 2/(f)/sup 2/Q/ sub 0/( f)log n) for total f.



Query complexity, or why is it difficult to separateNPA∩coNPA fromPA by random oraclesA?

  • G. Tardos
  • Computer Science, Mathematics
  • 1989
It is conjecture that the analogues of these classes actually coincide in the query complexity model, thus indicating an answer to the question in the title, and proves the following result, where polynomial bounds refer to query complexity.

Generic oracles and oracle classes

  • M. BlumR. Impagliazzo
  • Computer Science, Mathematics
    28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
  • 1987
In this paper, we examine various complexity issues relative to an oracle for a generic set in order to determine which are the more "natural" conjectures for these issues. Generic oracle results


Starting with the paper of Baker, Gill, and Solovay [BGS 75] in complexity theory, many results have been proved that separate certain relativized complexity classes or show that they have no

Neither Reading Few Bits Twice Nor Reading Illegally Helps Much

Private coins versus public coins in interactive proof systems

The probabilistic, nondeterministic, polynomial time Turing machine is defined and shown to be equivalent in power to the interactive proof system and to BPP much as BPP is the Probabilistic analog to P.

Probabilistic computations: Toward a unified measure of complexity

  • A. Yao
  • Mathematics
    18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
  • 1977
Two approaches to the study of expected running time of algoritruns lead naturally to two different definitions of intrinsic complexity of a problem, which are the distributional complexity and the randomized complexity, respectively.

CREW PRAMS and decision trees

  • N. Nisan
  • Computer Science, Mathematics
    STOC '89
  • 1989
The results imply that changes in the instruction set of the processors or in the capacity of the shared memory cells do not change by more than a constant factor the time required by a CREW PRAM to compute any Boolean function.

The knowledge complexity of interactive proof-systems

A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.

Robust Machines Accept Easy Sets