8 papers
Bounds for Hardness Condensation in the Query Model
Chandrima Kayal, Rajat Mittal, Sai Soumya Nalli +4
For any Boolean function with a complexity measure having value , is it possible to restrict the function to variables while keeping…
Spectral Norm, Economical Sieve, and Linear Invariance Testing of Boolean Functions
Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal +2
Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(…
Spectral Shadows: When Communication Complexity Meets Linear Invariance Testing
Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal +2
In this short note, we initiate the study of the Linear Isomorphism Testing Problem in the setting of communication complexity, a natural linear algebraic generalization of the cla…
Separations between Combinatorial Measures for Transitive Functions
Sourav Chakraborty, Chandrima Kayal, Manaswi Paraashar
The role of symmetry in Boolean functions has been extensively studied in complexity theory. For example, symmetric functions, that is, functions that are…
Testing Isomorphism of Boolean Functions over Finite Abelian Groups
Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal +2
Let and be Boolean functions over a finite Abelian group , where is fully known, and we have {\em query access} to , that is, given any $x \in \mathcal{…
Approximate Degree Composition for Recursive Functions
Sourav Chakraborty, Chandrima Kayal, Rajat Mittal +2
Determining the approximate degree composition for Boolean functions remains a significant unsolved problem in Boolean function complexity. In recent decades, researchers have conc…