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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > ALGEBRAIC CIRCUIT COMPLEXITY:
Reports tagged with algebraic circuit complexity:
TR14-052 | 14th April 2014
Joshua Grochow, Toniann Pitassi

Circuit complexity, proof complexity, and polynomial identity testing

We introduce a new and very natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomial-size algebraic circuits ($VNP \neq VP$). As a ... more >>>


TR17-007 | 19th January 2017
Michael Forbes, Amir Shpilka, Ben Lee Volk

Succinct Hitting Sets and Barriers to Proving Algebraic Circuits Lower Bounds

Revisions: 1

We formalize a framework of algebraically natural lower bounds for algebraic circuits. Just as with the natural proofs notion of Razborov and Rudich for boolean circuit lower bounds, our notion of algebraically natural lower bounds captures nearly all lower bound techniques known. However, unlike the boolean setting, there has been ... more >>>


TR17-009 | 19th January 2017
Joshua Grochow, Mrinal Kumar, Michael Saks, Shubhangi Saraf

Towards an algebraic natural proofs barrier via polynomial identity testing

We observe that a certain kind of algebraic proof - which covers essentially all known algebraic circuit lower bounds to date - cannot be used to prove lower bounds against VP if and only if what we call succinct hitting sets exist for VP. This is analogous to the Razborov-Rudich ... more >>>


TR18-135 | 31st July 2018
Prasad Chaugule, Nutan Limaye, Aditya Varre

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

We present polynomial families complete for the well-studied algebraic complexity classes VF, VBP, VP, and VNP. The polynomial families are based on the homomorphism polynomials studied in the recent works of Durand et al. (2014) and Mahajan et al. (2016). We consider three different variants of graph homomorphisms, namely injective ... more >>>


TR18-184 | 5th November 2018
Iddo Tzameret, Stephen Cook

Uniform, Integral and Feasible Proofs for the Determinant Identities

Aiming to provide weak as possible axiomatic assumptions in which one can develop basic linear algebra, we give a uniform and integral version of the short propositional proofs for the determinant identities demonstrated over $GF(2)$ in Hrubes-Tzameret [SICOMP'15]. Specifically, we show that the multiplicativity of the determinant function and the ... more >>>




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