White-Box vs. Black-Box Complexity of Search Problems: Ramsey and Graph Property Testing

@article{Komargodski2017WhiteBoxVB,
  title={White-Box vs. Black-Box Complexity of Search Problems: Ramsey and Graph Property Testing},
  author={Ilan Komargodski and Moni Naor and Eylon Yogev},
  journal={2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2017},
  pages={622-632}
}
Ramsey theory assures us that in any graph there is a clique or independent set of a certain size, roughly logarithmic in the graph size. But how difficult is it to find the clique or independent set? If the graph is given explicitly, then it is possible to do so while examining a linear number of edges. If the graph is given by a black-box, where to figure out whether a certain edge exists the box should be queried, then a large number of queries must be issued. But what if one is given a… Expand
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References

SHOWING 1-10 OF 60 REFERENCES
White-Box vs. Black-Box Complexity of Search Problems
TLDR
It is shown that under the assumption that collision-resistant hash function exists (which follows from the hardness of problems such as factoring, discrete-log, and learning with errors) the white-box Ramsey problem is hard and this is true even if one is looking for a much smaller clique or independent set than the theorem guarantees. Expand
The Journey from NP to TFNP Hardness
TLDR
This work shows that hard-on-average TFNP problems can be based on the weak assumption that there exists a hard- on-average language in NP, in particular, this includes the assumption of the existence of one-way functions. Expand
Hardness of Continuous Local Search: Query Complexity and Cryptographic Lower Bounds
TLDR
The first hardness results for CLS are shown, showing instances for which any (computationally unbounded) randomized algorithm must perform exponentially many queries in order to find a local optimum and hardness for computationally bounded algorithms under cryptographic assumptions. Expand
On the Cryptographic Hardness of Finding a Nash Equilibrium
We prove that finding a Nash equilibrium of a game is hard, assuming the existence of indistinguishability obfuscation and one-way functions with sub-exponential hardness. We do so by showing howExpand
On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence
We define several new complexity classes of search problems, ''between'' the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of searchExpand
On the (Im)possibility of Obfuscating Programs
TLDR
It is proved that obfuscation is impossible, by constructing a family of functions F that are inherently unobfuscatable in the following sense: there is a property π : F → {0, 1} such that given any program that computes a function f ∈ F, the value π(f) can be efficiently computed. Expand
Revisiting the Cryptographic Hardness of Finding a Nash Equilibrium
TLDR
The hardness of PPAD assuming the existence of quasi-polynomially hard indistinguishability obfuscation and sub-exponentially hard one- way functions is proved and hardness can be based on polynomially hard compact public key functional encryption and one-way permutations. Expand
A new upper bound for the bipartite Ramsey problem
TLDR
Here it is improved upon, showing that it is sufficient to take n ≥ (1 + o(1))2 log k, where the log is taken to the base 2. Expand
The relative complexity of NP search problems
TLDR
This work proves several separations which show that in a generic relativized world, the search classes are distinct and there is a standard search problem in each of them that is not computationally equivalent to any decision problem. Expand
Zero-Knowledge and Code Obfuscation
TLDR
The gap between auxiliary-input zero-knowledge (AIZK) and blackbox-simulation zero- knowledge (BSZK) is investigated and it is shown that it is impossible to securely obfuscate a code of a cheating verifier behaving as a pseudorandom function. Expand
...
1
2
3
4
5
...