• Publications
  • Influence
Checking computations in polylogarithmic time
TLDR
WJe show that every nondeterministic computational task S(Z, y), defined as a polynomial time relation between the instance x, representing the input and output combined, and the witness y can be modified to a task S such that each instance/witness pair becomes checkable in poly!ogariihmic Monte Carlo time. Expand
Non-deterministic exponential time has two-prover interactive protocols
TLDR
It is shown that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time and that to prove membership in languages inEXP, the honest provers need the power ofEXP only. Expand
Infeasibility of instance compression and succinct PCPs for NP
TLDR
A new strong derandomization hypothesis is introduced, the Oracle Derandomization Hypothesis, and how it relates to traditional derandomizing assumptions is discussed, and various results about and connections between these variants are shown. Expand
Algebraic methods for interactive proof systems
TLDR
This technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system and played a pivotal role in the recent proofs that IP = PSPACE and MIP = NEXP. Expand
Algebraic methods for interactive proof systems
TLDR
The technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system and has implications for program checking, verification, and self-correction. Expand
Complexity limitations on quantum computation
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantumExpand
Nondeterministic exponential time has two-prover interactive protocols
TLDR
It is shown that the class of languages having two-prover interactive proof systems is computable in nondeterministic exponential time (NEXP), which represents a further step demonstrating the unexpectedly immense power for randomization and interaction in efficient provability. Expand
Gap-definable counting classes
TLDR
It is shown that most previously studied counting classes are gap-definable, i.e., definable using the values of GapP functions alone, and there is a smallest gap- definable class, SPP, which is still large enough to contain Few. Expand
Random-Self-Reducibility of Complete Sets
TLDR
It is shown that sets that are complete for any level of the polynomial hierarchy are not nonadaptively random-self-reducible, unless the hierarchy collapses, and it is show that sets complete for the classes PP andMOD are random- Self-Reducible. Expand
Non-deterministic exponential time has two-prover interactive protocols
TLDR
It is shown that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time and that to prove membership in languages inEXP, the honest provers need the power ofEXP only. Expand
...
1
2
3
4
5
...