A lower bound for monotone arithmetic circuits computing O-l permanent

A Lower Bound for Boolean Permanent in Bijective Boolean Circuits and its Consequences

We identify a new restriction on Boolean circuits called bijectivity and prove that bijective Boolean circuits require exponential size to compute the Boolean permanent function. As consequences of this lower bound, we show exponential size lower bounds for: (a) computing the Boolean permanent using monotone multilinear circuits ; (b) computing the 0-1 permanent function using monotone arithmet...

A Lower Bound for Monotone Arithmetic Circuits Computing 0-1 Permanent

Arithmetic Circuit Size, Identity Testing, and Finite Automata

Let F〈x1, x2, · · · , xn〉 be the noncommutative polynomial ring over a field F, where the xi’s are free noncommuting formal variables. Given a finite automaton A with the xi’s as alphabet, we can define polynomials f(mod A) and f(div A) obtained by natural operations that we call intersecting and quotienting the polynomial f by A. Related to intersection, we also define the Hadamard product f ◦...

An exponential lower bound for homogeneous depth four arithmetic circuits with bounded bottom fanin

Agrawal and Vinay [AV08] have recently shown that an exponential lower bound for depth four homogeneous circuits with bottom layer of × gates having sublinear fanin translates to an exponential lower bound for a general arithmetic circuit computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via homogeneous depth four circuits with boun...

Lower Bounds for Perfect Matching in Restricted Boolean Circuits

We consider three restrictions on Boolean circuits: bijectivity, consistency and mul-tilinearity. Our main result is that Boolean circuits require exponential size to compute the bipartite perfect matching function when restricted to be (i) bijective or (ii) consistent and multilinear. As a consequence of the lower bound on bijec-tive circuits, we prove an exponential size lower bound for monot...