Title:
A Lower Bound for Boolean Permanent in Bijective Boolean Circuits and Its Consequences
A Lower Bound for Boolean Permanent in Bijective Boolean Circuits and Its Consequences
Authors
Sengupta, Rimli
Venkateswaran, H.
Venkateswaran, H.
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Abstract
We identify a new and non-trivial restriction called bijectivity on Boolean
circuits and prove an exponential size lower bound for computing the Boolean
permanent matching function in this model. 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 arithmetic circuits; and (c) computing the lexicographically
first bipartite perfect matching function using circuits over (min, concat).
The lower bound arguments for the Boolean permanent function are adapted to
prove an exponential lower bound for computing the Hamiltonian cycle function
using bijective circuits.
We identify a class of monotone functions such that if their counting version
is #P-hard, then there are no polynomial size bijective circuits
for such functions unless PH collapses.
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Date Issued
1994
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239631 bytes
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Text
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Technical Report