Title:
Lower Bounds for Perfect Matching in Restricted Boolean Circuits
Lower Bounds for Perfect Matching in Restricted Boolean Circuits
Author(s)
Sengupta, Rimli
Venkateswaran, H.
Venkateswaran, H.
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Abstract
We consider three restrictions on Boolean circuits: bijectivity, consistency
and multilinearity. 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 bijective circuits, we prove an exponential
size lower bound for monotone arithmetic circuits that compute the 0-1
permanent function. We also define a notion of homogeneity for Boolean
circuits and show that consistent homogeneous circuits require exponential
size to compute the bipartite perfect matching function. Motivated by
consistent multilinear circuits, we consider certain restricted (⊕, ⋀) circuits and obtain an exponential lower bound for computing
bipartite perfect matching using such circuits. Finally, we show that the
lower bound arguments for the bipartite perfect matching function on all these
restricted models can be adapted to prove exponential lower bounds for the
Hamiltonian circuit problem in all these models.
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Date Issued
1993
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255769 bytes
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Text
Resource Subtype
Technical Report