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Electronic Colloquium on Computational Complexity

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TR25-045 | 11th April 2025
Marco Carmosino, Stefan Grosser

Student-Teacher Constructive Separations and (Un)Provability in Bounded Arithmetic: Witnessing the Gap

Revisions: 1

Let $\mathcal{C}$ be a complexity class and $A$ be a language. The statement ``$A \not\in \mathcal{C}$'' is a separation of $A$ from $\mathcal{C}$. A separation is constructive if there is an efficient algorithm called a refuter that prints counterexamples to the statement ``$M$ decides $A$'' for every $\mathcal{C}$-algorithm $M$. Concretely, ... more >>>


TR25-044 | 10th April 2025
Somnath Bhattacharjee, Mrinal Kumar, Varun Ramanathan, Ramprasad Saptharishi, Shubhangi Saraf

Deterministic factorization of constant-depth algebraic circuits in subexponential time

While efficient randomized algorithms for factorization of polynomials given by algebraic circuits have been known for decades, obtaining an even slightly non-trivial deterministic algorithm for this problem has remained an open question of great interest. This is true even when the input algebraic circuit has additional structure, for instance, when ... more >>>


TR25-043 | 5th April 2025
Shlomi Dolev

Towards EXPTIME One Way Functions Bloom Filters, Succinct Graphs & Self Masking

Consider graphs of n nodes and use a Bloom filter of length 2 log3 n bits. An edge between nodes i and j, with i < j, turns on a certain bit of the Bloom filter according to a hash function on i and j. Pick a set of log ... more >>>



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