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Electronic Colloquium on Computational Complexity

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TR21-089 | 25th June 2021
Hanlin Ren, Rahul Santhanam

A Relativization Perspective on Meta-Complexity

Meta-complexity studies the complexity of computational problems about complexity theory, such as the Minimum Circuit Size Problem (MCSP) and its variants. We show that a relativization barrier applies to many important open questions in meta-complexity. We give relativized worlds where:

* MCSP can be solved in deterministic polynomial time, but ... more >>>


TR21-088 | 23rd June 2021
Oded Goldreich

Open Problems in Property Testing of Graphs

Revisions: 1

We briefly discuss a few open problems in the study of various models of testing graph properties, focusing on the query complexity of the various tasks. In the dense graph model, we discuss several open problems, including:

* Determining the complexity of testing triangle-freeness.
* Characterizing the class of properties ... more >>>


TR21-087 | 22nd June 2021
Uma Girish, Ran Raz

Eliminating Intermediate Measurements using Pseudorandom Generators

Revisions: 1

We show that quantum algorithms of time T and space $S \ge \log T$ with intermediate measurements can be simulated by quantum algorithms of time $T\cdot \mathrm{poly}(S)$ and space $O(S\cdot \log T)$ without intermediate measurements. The best simulations prior to this work required either $\Omega(T)$ space (by the deferred measurement ... more >>>



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