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REPORTS > KEYWORD > BARRIERS:
Reports tagged with barriers:
TR16-040 | 16th March 2016
Baris Aydinlioglu, Eric Bach

#### Affine Relativization: Unifying the Algebrization and Relativization Barriers

Revisions: 3

We strengthen existing evidence for the so-called "algebrization barrier". Algebrization --- short for algebraic relativization --- was introduced by Aaronson and Wigderson (AW) in order to characterize proofs involving arithmetization, simulation, and other "current techniques". However, unlike relativization, eligible statements under this notion do not seem to have basic closure ... more >>>

TR17-007 | 19th January 2017
Michael Forbes, Amir Shpilka, Ben Lee Volk

#### Succinct Hitting Sets and Barriers to Proving Algebraic Circuits Lower Bounds

Revisions: 1

We formalize a framework of algebraically natural lower bounds for algebraic circuits. Just as with the natural proofs notion of Razborov and Rudich for boolean circuit lower bounds, our notion of algebraically natural lower bounds captures nearly all lower bound techniques known. However, unlike the boolean setting, there has been ... more >>>

TR17-009 | 19th January 2017
Joshua Grochow, Mrinal Kumar, Michael Saks, Shubhangi Saraf

#### Towards an algebraic natural proofs barrier via polynomial identity testing

We observe that a certain kind of algebraic proof - which covers essentially all known algebraic circuit lower bounds to date - cannot be used to prove lower bounds against VP if and only if what we call succinct hitting sets exist for VP. This is analogous to the Razborov-Rudich ... more >>>

TR17-162 | 26th October 2017
Klim Efremenko, Ankit Garg, Rafael Mendes de Oliveira, Avi Wigderson

#### Barriers for Rank Methods in Arithmetic Complexity

Arithmetic complexity, the study of the cost of computing polynomials via additions and multiplications, is considered (for many good reasons) simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic complexity than ... more >>>

TR20-030 | 9th March 2020
Matthias Christandl, François Le Gall, Vladimir Lysikov, Jeroen Zuiddam

#### Barriers for Rectangular Matrix Multiplication

We study the algorithmic problem of multiplying large matrices that are rectangular. We prove that the method that has been used to construct the fastest algorithms for rectangular matrix multiplication cannot give optimal algorithms. In fact, we prove a precise numerical barrier for this method. Our barrier improves the previously ... more >>>

TR21-159 | 15th November 2021
Lijie Chen, Ce Jin, Rahul Santhanam, Ryan Williams

#### Constructive Separations and Their Consequences

For a complexity class \$C\$ and language \$L\$, a constructive separation of \$L \notin C\$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every \$C\$-algorithm attempting to decide \$L\$. We study the questions: Which lower bounds can be made constructive? What are the consequences ... more >>>

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