Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster Carry Bit Computation for Adder Circuits with Prescribed Arrival
  Times   We consider the fundamental problem of constructing fast circuits for the
carry bit computation in binary addition. Up to a small additive constant, the
carry bit computation reduces to computing an \aop, i.e., a formula of type
$t_0 \land (t_1 \lor (t_2 \land ( \dots t_{m-1}) \dots )$ or $t_0 \lor (t_1
\land (t_2 \lor ( \dots t_{m-1}) \dots )$. We present an algorithm that
computes the fastest known Boolean circuit for an \aop~ with given arrival
times $a(t_0), \dotsc, a(t_{m-1})$ for the input signals. Our objective
function is delay, a natural generalization of depth with respect to arrival
times. The maximum delay of the circuit we compute is $\log_2 W + \log_2 \log_2
m + \log_2 \log_2 \log_2 m + 4.3$, where $W := \sum_{i = 0}^{m-1} 2^{a(t_i)}$.
Note that $\lceil \log_2 W \rceil$ is a lower bound on the delay of any circuit
depending on inputs $t_0, \dotsc, t_{m-1}$ with prescribed arrival times. Our
method yields the fastest circuits for \aop s, carry bit computation and adders
in terms of delay known so far.

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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas