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Electronic Colloquium on Computational Complexity

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TR22-068 | 5th May 2022
Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, Madhu Sudan, Santhoshini Velusamy

Sketching Approximability of (Weak) Monarchy Predicates

Revisions: 1

We analyze the sketching approximability of constraint satisfaction problems on Boolean domains, where the constraints are balanced linear threshold functions applied to literals. In particular, we explore the approximability of monarchy-like functions where the value of the function is determined by a weighted combination of the vote of the first ... more >>>


TR22-067 | 4th May 2022
Vikraman Arvind, Abhranil Chatterjee, Partha Mukhopadhyay

Black-box Identity Testing of Noncommutative Rational Formulas of Inversion Height Two in Deterministic Quasipolynomial-time

Hrube\v{s} and Wigderson (2015) initiated the complexity-theoretic study of noncommutative formulas with inverse gates. They introduced the Rational Identity Testing (RIT) problem which is to decide whether a noncommutative rational formula computes zero in the free skew field. In the white-box setting, deterministic polynomial-time algorithms are known for this problem ... more >>>


TR22-066 | 4th May 2022
Joanna Boyland, Michael Hwang, Tarun Prasad, Noah Singer, Santhoshini Velusamy

On sketching approximations for symmetric Boolean CSPs

A Boolean maximum constraint satisfaction problem, Max-CSP\((f)\), is specified by a predicate \(f:\{-1,1\}^k\to\{0,1\}\). An \(n\)-variable instance of Max-CSP\((f)\) consists of a list of constraints, each of which applies \(f\) to \(k\) distinct literals drawn from the \(n\) variables. For \(k=2\), Chou, Golovnev, and Velusamy [CGV20, FOCS 2020] obtained explicit ratios ... more >>>



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