Qasim Shirazi

A Randomness-Efficient Replacement for G(k) Gates and an Improved Lower-Bound Consequence for GCC^0(k) Circuits

We give a randomness-efficient probabilistic replacement for G(k) gates and derive an improved quantitative circuit lower-bound consequence for constant-depth GCC^0(k) circuits within the Williams algorithmic-method framework. For a G(k) gate of fan-in m and pointwise error \vare...

Residue-Class Pair-Capacity Inequalities for Restricted Difference Bases

This preprint develops exact residue-class pair-capacity inequalities for sets of integer marks. Reducing marks modulo m partitions unordered mark pairs into undirected residue-difference classes, yielding necessary quadratic inequalities in the residue occupancies for any prescr...

A Randomness-Efficient Replacement for G(k) Gates and an Improved Lower-Bound Consequence for GCC^0(k) Circuits

We give a randomness-efficient probabilistic replacement for G(k) gates and derive an improved quantitative circuit lower-bound consequence for constant-depth GCC^0(k) circuits within the Williams algorithmic-method framework. For a G(k) gate of fan-in m and pointwise error \vare...

Residue-Class Pair-Capacity Inequalities for Restricted Difference Bases

This preprint develops exact residue-class pair-capacity inequalities for sets of integer marks. Reducing marks modulo m partitions unordered mark pairs into undirected residue-difference classes, yielding necessary quadratic inequalities in the residue occupancies for any prescr...