All reports by Author Yogesh Dahiya:

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TR23-132
| 12th September 2023
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Yogesh Dahiya, Meena Mahajan, Sasank Mouli#### New lower bounds for Polynomial Calculus over non-Boolean bases

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TR23-039
| 28th March 2023
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Arkadev Chattopadhyay, Yogesh Dahiya, Meena Mahajan#### Query Complexity of Search Problems

Revisions: 1

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TR23-012
| 16th February 2023
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Yogesh Dahiya, Vignesh K, Meena Mahajan, Karteek Sreenivasaiah#### Linear threshold functions in decision lists, decision trees, and depth-2 circuits

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TR22-185
| 29th December 2022
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Arkadev Chattopadhyay, Yogesh Dahiya, Nikhil Mande, Jaikumar Radhakrishnan, Swagato Sanyal#### Randomized versus Deterministic Decision Tree Size

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TR22-001
| 28th December 2021
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Yogesh Dahiya, Meena Mahajan#### On (Simple) Decision Tree Rank

Revisions: 1

Yogesh Dahiya, Meena Mahajan, Sasank Mouli

In this paper, we obtain new size lower bounds for proofs in the

Polynomial Calculus (PC) proof system, in two different settings.

1. When the Boolean variables are encoded using $\pm 1$ (as opposed

to $0,1$): We establish a lifting theorem using an asymmetric gadget

$G$, showing ...
more >>>

Arkadev Chattopadhyay, Yogesh Dahiya, Meena Mahajan

We relate various complexity measures like sensitivity, block sensitivity, certificate complexity for multi-output functions to the query complexities of such functions. Using these relations, we improve upon the known relationship between pseudo-deterministic query complexity and deterministic query complexity for total search problems: We show that pseudo-deterministic query complexity is at ... more >>>

Yogesh Dahiya, Vignesh K, Meena Mahajan, Karteek Sreenivasaiah

We show that polynomial-size constant-rank linear decision trees (LDTs) can be converted to polynomial-size depth-2 threshold circuits LTF$\circ$LTF. An intermediate construct is polynomial-size decision lists that query a conjunction of a constant number of linear threshold functions (LTFs); we show that these are equivalent to polynomial-size exact linear decision lists ... more >>>

Arkadev Chattopadhyay, Yogesh Dahiya, Nikhil Mande, Jaikumar Radhakrishnan, Swagato Sanyal

A classic result of Nisan [SICOMP '91] states that the deterministic decision tree depth complexity of every total Boolean function is at most the cube of its randomized decision tree depth complexity. The question whether randomness helps in significantly reducing the size of decision trees appears not to have been ... more >>>

Yogesh Dahiya, Meena Mahajan

In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to several non-computational complexity measures of functions such as certificate complexity. The size measure ... more >>>