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Electronic Colloquium on Computational Complexity

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TR25-035 | 25th March 2025
Abhibhav Garg, Rafael Mendes de Oliveira, Nitin Saxena

Primes via Zeros: Interactive Proofs for Testing Primality of Natural Classes of Ideals

A central question in mathematics and computer science is the question of determining whether a given ideal $I$ is prime, which geometrically corresponds to the zero set of $I$, denoted $Z(I)$, being irreducible. The case of principal ideals (i.e., $m=1$) corresponds to the more familiar absolute irreducibility testing of polynomials, ... more >>>


TR25-034 | 20th March 2025
Neha Kuntewar, Jayalal Sarma

Range Avoidance in Boolean Circuits via Turan-type Bounds

Given a circuit $C : \{0,1\}^n \to \{0,1\}^m$ from a circuit class $F$, with $m > n$, finding a $y \in \{0,1\}^m$ such that $\forall x \in \{0,1\}^n$, $C(x) \ne y$, is the range avoidance problem (denoted by $F$-AVOID). It is known that deterministic polynomial time algorithms (even with access ... more >>>


TR25-033 | 18th March 2025
Bruno Pasqualotto Cavalar, Igor Oliveira

Boolean Circuit Complexity and Two-Dimensional Cover Problems

We reduce the problem of proving deterministic and nondeterministic Boolean circuit size lower bounds to the analysis of certain two-dimensional combinatorial cover problems. This is obtained by combining results of Razborov (1989), Karchmer (1993), and Wigderson (1993) in the context of the fusion method for circuit lower bounds with the ... more >>>



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