All reports by Author Krishnamoorthy Dinesh:

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TR18-153
| 22nd August 2018
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Krishnamoorthy Dinesh, Samir Otiv, Jayalal Sarma#### New Bounds for Energy Complexity of Boolean Functions

Revisions: 1

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TR18-152
| 30th August 2018
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Krishnamoorthy Dinesh, Jayalal Sarma#### Sensitivity, Affine Transforms and Quantum Communication Complexity

Revisions: 1

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TR17-192
| 15th December 2017
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Krishnamoorthy Dinesh, Jayalal Sarma#### Alternation, Sparsity and Sensitivity : Bounds and Exponential Gaps

Revisions: 1

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TR16-076
| 27th April 2016
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Krishnamoorthy Dinesh, Sajin Koroth, Jayalal Sarma#### Characterization and Lower Bounds for Branching Program Size using Projective Dimension

Revisions: 2

Krishnamoorthy Dinesh, Samir Otiv, Jayalal Sarma

For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a finite basis $\cal{B}$, the energy complexity of $C$ (denoted by $\mathbf{EC}_{{\cal B}}(C)$) is the maximum over all inputs $\{0,1\}^n$ the numbers of gates of the circuit $C$ (excluding the inputs) that output a one. Energy Complexity ... more >>>

Krishnamoorthy Dinesh, Jayalal Sarma

In this paper, we study the Boolean function parameters sensitivity ($\mathbf{s}$), block sensitivity ($\mathbf{bs}$), and alternation ($\mathbf{alt}$) under specially designed affine transforms and show several applications. For a function $f:\mathbb{F}_2^n \to \{0,1\}$, and $A = Mx+b$ for $M \in \mathbb{F}_2^{n \times n}$ and $b \in \mathbb{F}_2^n$, the result of the ... more >>>

Krishnamoorthy Dinesh, Jayalal Sarma

The well-known Sensitivity Conjecture regarding combinatorial complexity measures on Boolean functions states that for any Boolean function $f:\{0,1\}^n \to \{0,1\}$, block sensitivity of $f$ is polynomially related to sensitivity of $f$ (denoted by $\mathbf{sens}(f)$). From the complexity theory side, the XOR Log-Rank Conjecture states that for any Boolean function, $f:\{0,1\}^n ... more >>>

Krishnamoorthy Dinesh, Sajin Koroth, Jayalal Sarma

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 >>>