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Electronic Colloquium on Computational Complexity

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TR21-151 | 8th November 2021
Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, Shahar Mozes

Locally Testable Codes with constant rate, distance, and locality

Revisions: 1

A locally testable code (LTC) is an error correcting code that has a property-tester. The tester reads $q$ bits that are randomly chosen, and rejects words with probability proportional to their distance from the code. The parameter $q$ is called the locality of the tester.

LTCs were initially studied as ... more >>>


TR21-150 | 7th November 2021
Eldon Chung, Maciej Obremski, Divesh Aggarwal

Extractors: Low Entropy Requirements Colliding With Non-Malleability

The known constructions of negligible error (non-malleable) two-source extractors can be broadly classified in three categories:

(1) Constructions where one source has min-entropy rate about $1/2$, the other source can have small min-entropy rate, but the extractor doesn't guarantee non-malleability.
(2) Constructions where one source is uniform, and the other ... more >>>


TR21-149 | 5th November 2021
Sevag Gharibian, Dorian Rudolph

On polynomially many queries to NP or QMA oracles

We study the complexity of problems solvable in deterministic polynomial time with access to an NP or Quantum Merlin-Arthur (QMA)-oracle, such as $P^{NP}$ and $P^{QMA}$, respectively.
The former allows one to classify problems more finely than the Polynomial-Time Hierarchy (PH), whereas the latter characterizes physically motivated problems such as Approximate ... more >>>



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