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Electronic Colloquium on Computational Complexity

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All reports by Author Sajin Koroth:

TR20-144 | 7th September 2020
Mohammad Jahanara, Sajin Koroth, Igor Shinkar

Toward Probabilistic Checking against Non-Signaling Strategies with Constant Locality

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is ... more >>>

TR20-049 | 17th April 2020
Mika Göös, Sajin Koroth, Ian Mertz, Toniann Pitassi

Automating Cutting Planes is NP-Hard

We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula $F$,

(1) it is NP-hard to find a CP refutation of $F$ in time polynomial in the length of the shortest such refutation; and

(2) unless Gap-Hitting-Set admits a nontrivial algorithm, one cannot find a ... more >>>

TR20-018 | 18th February 2020
Valentine Kabanets, Sajin Koroth, Zhenjian Lu, Dimitrios Myrisiotis, Igor Oliveira

Algorithms and Lower Bounds for de Morgan Formulas of Low-Communication Leaf Gates

The class $FORMULA[s] \circ \mathcal{G}$ consists of Boolean functions computable by size-$s$ de Morgan formulas whose leaves are any Boolean functions from a class $\mathcal{G}$. We give lower bounds and (SAT, Learning, and PRG) algorithms for $FORMULA[n^{1.99}]\circ \mathcal{G}$, for classes $\mathcal{G}$ of functions with low communication complexity. Let $R^{(k)}(\mathcal{G})$ be ... more >>>

TR19-103 | 7th August 2019
Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi

Query-to-Communication Lifting Using Low-Discrepancy Gadgets

Revisions: 1

Lifting theorems are theorems that relate the query complexity of a function $f:\left\{ 0,1 \right\}^n\to \left\{ 0,1 \right\}$ to the communication complexity of the composed function $f\circ g^n$, for some “gadget” $g:\left\{ 0,1 \right\}^b\times \left\{ 0,1 \right\}^b\to \left\{ 0,1 \right\}$. Such theorems allow transferring lower bounds from query complexity to ... more >>>

TR16-076 | 27th April 2016
Krishnamoorthy Dinesh, Sajin Koroth, Jayalal Sarma

Characterization and Lower Bounds for Branching Program Size using Projective Dimension

Revisions: 2

We study projective dimension, a graph parameter (denoted by $pd(G)$ for a graph $G$), introduced by (Pudlak, Rodl 1992), who showed that proving lower bounds for $pd(G_f)$ for bipartite graphs $G_f$ associated with a Boolean function $f$ imply size lower bounds for branching programs computing $f$. Despite several attempts (Pudlak, ... more >>>

TR14-072 | 29th April 2014
Sajin Koroth, Jayalal Sarma

Depth Lower Bounds against Circuits with Sparse Orientation

Revisions: 1

We study depth lower bounds against non-monotone circuits, parametrized by a new measure of non-monotonicity: the orientation of a function $f$ is the characteristic vector of the minimum sized set of negated variables needed in any DeMorgan circuit computing $f$. We prove trade-off results between the depth and the weight/structure ... more >>>

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