4 papers
From Liar Paradox to Incongruent Sets: A Normal Form for Self-Reference
Shalender Singh, Vishnu Priya Singh Parmar
We introduce incongruent normal form (INF), a structural representation for self-referential semantic sentences. An INF replaces a self-referential sentence with a finite family of…
An Algebraic Rigidity Framework for Order-Oblivious Deterministic Black-Box PIT of ROABPs
Shalender Singh, Vishnupriya Singh
Deterministic black-box polynomial identity testing (PIT) for read-once oblivious algebraic branching programs (ROABPs) is a central open problem in algebraic complexity, particula…
Inverse Falconer Distance Theorems over the Integer Residue Rings
Shalender Singh, Vishnupriya Singh
We establish an ideal-theoretic rigidity principle for quadratic distance images over integer residue rings. Specifically, we prove that near-extremal collapse of the distance set…
Inverse Theorems for Point-Sphere Incidences over Finite Fields
Shalender Singh, Vishnu Priya Singh
We prove unconditional inverse theorems for point-sphere incidences over , at the fixed-radius deviation scale. The full sphere system satisfies the cen…