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Electronic Colloquium on Computational Complexity

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All reports by Author Yogesh Dahiya:

TR23-132 | 12th September 2023
Yogesh Dahiya, Meena Mahajan, Sasank Mouli

New lower bounds for Polynomial Calculus over non-Boolean bases

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 >>>

TR23-039 | 28th March 2023
Arkadev Chattopadhyay, Yogesh Dahiya, Meena Mahajan

Query Complexity of Search Problems

Revisions: 1

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 >>>

TR23-012 | 16th February 2023
Yogesh Dahiya, Vignesh K, Meena Mahajan, Karteek Sreenivasaiah

Linear threshold functions in decision lists, decision trees, and depth-2 circuits

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 >>>

TR22-185 | 29th December 2022
Arkadev Chattopadhyay, Yogesh Dahiya, Nikhil Mande, Jaikumar Radhakrishnan, Swagato Sanyal

Randomized versus Deterministic Decision Tree Size

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 >>>

TR22-001 | 28th December 2021
Yogesh Dahiya, Meena Mahajan

On (Simple) Decision Tree Rank

Revisions: 1

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 >>>

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