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Electronic Colloquium on Computational Complexity

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Reports tagged with Evaluation dimension:
TR14-158 | 26th November 2014
Rohit Gurjar, Arpita Korwar, Nitin Saxena, Thomas Thierauf

Deterministic Identity Testing for Sum of Read Once ABPs

Revisions: 2

A read once ABP is an arithmetic branching program with each variable occurring in at most one layer. We give the first polynomial time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial time complexity, i.e. ... more >>>

TR15-015 | 30th January 2015
Neeraj Kayal, Chandan Saha

Multi-$k$-ic depth three circuit lower bound

In a multi-$k$-ic depth three circuit every variable appears in at most $k$ of the linear polynomials in every product gate of the circuit. This model is a natural generalization of multilinear depth three circuits that allows the formal degree of the circuit to exceed the number of underlying variables ... more >>>

TR16-045 | 22nd March 2016
Michael Forbes, Mrinal Kumar, Ramprasad Saptharishi

Functional lower bounds for arithmetic circuits and connections to boolean circuit complexity

We say that a circuit $C$ over a field $F$ functionally computes an $n$-variate polynomial $P \in F[x_1, x_2, \ldots, x_n]$ if for every $x \in \{0,1\}^n$ we have that $C(x) = P(x)$. This is in contrast to {syntactically} computing $P$, when $C \equiv P$ as formal polynomials. In this ... more >>>

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