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Boolean circuits versus arithmetic circuits

1991
*
Information and Computation
*

Over Q and finite fields,

doi:10.1016/0890-5401(91)90078-g
fatcat:aydwnfiodfgy3bizzgauso2sei
*Boolean**circuits*can simulate*arithmetic**circuits*efficiently with respect to size. ... We compare the two computational models of*Boolean**circuits*and*arithmetic**circuits*in cases where they both apply, namely the computation of polynomials over the rational numbers or over finite fields ... We note that*Boolean**circuits*can solve problems that*arithmetic**circuits*are not adapted to. ...##
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Tractable Boolean and Arithmetic Circuits
[article]

2022
*
arXiv
*
pre-print

Tractable

arXiv:2202.02942v1
fatcat:fq33u2ct4vgwngxan3k7dojxam
*Boolean*and*arithmetic**circuits*have been studied extensively in AI for over two decades now. ... In more recent years, the role of tractable*circuits*has significantly expanded as they became a computational and semantical backbone for some approaches that aim to integrate knowledge, reasoning and ...*Circuits*that Lookup Values*Versus**Circuits*that Reason The central question posed and treated in [24] is the following. ...##
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Enhancing the quantum cost of Reed-Muller Based Boolean quantum circuits using genetic algorithms

2020
*
Journal of Physics, Conference Series
*

There is a direct equivalence between

doi:10.1088/1742-6596/1447/1/012031
fatcat:ksew625bvre37kj5xm2uwcdfbq
*Boolean*functions represented in Reed-Muller logic and*Boolean*Quantum*Circuits*. ... Different polarity Reed-Muller expansions will give different*Boolean*quantum*circuits*with different cost for the same*Boolean*function. ... Eftakhar et al. used genetic programming with subtree mutation for evolving common RL*arithmetic**circuits*[9] . ...##
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Valiant's Model: From Exponential Sums to Exponential Products
[chapter]

2006
*
Lecture Notes in Computer Science
*

Our main result relates this hypothesis to Blum, Shub and Smale's algebraic version of P

doi:10.1007/11821069_52
fatcat:2ua2rt7v4baefnvn3ypbhapimy
*versus*NP. Let K be a field of characteristic 0. ... Lemma 1 Any*boolean**circuit*C can be simulated by an*arithmetic*one of size at most 3|C|, in the sense that on*boolean*inputs, both*circuits*output the same value. ...*Arithmetic**circuits*are at least as powerful as*boolean**circuits*in the sense that one can simulate the latter by the former. ...##
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Page 437 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

*circuits*

*versus*

*arithmetic*

*circuits*. ... Over Q and finite fields,

*Boolean*

*circuits*can simulate

*arithmetic*

*circuits*efficiently with respect to size. ...

##
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An arithmetic model of computation equivalent to threshold circuits

1992
*
Theoretical Computer Science
*

These

doi:10.1016/0304-3975(92)90335-d
fatcat:4wnb5esqmvcvvop3hlql3vb5py
*circuits*have only one input and one output. We show how they correspond naturally to*boolean*computations with n inputs and n outputs. ... We show that if*circuit*sizes are polynomially related, then the*arithmetic**circuit*depth and the threshold*circuit*depth to compute a given function differ by at most a constant factor. ... A*Boolean*majority function may be simulated on 0. 1 field values by a small*arithmetic**circuit*as shown in Lemma 4.2. ...##
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The synthesis of robust polynomial arithmetic with stochastic logic

2008
*
Proceedings of the 45th annual conference on Design automation - DAC '08
*

As integrated

doi:10.1145/1391469.1391636
dblp:conf/dac/QianR08
fatcat:jwvw2zesozai5bmiltca3c2p54
*circuit*technology plumbs ever greater depths in the scaling of feature sizes, maintaining the paradigm of deterministic*Boolean*computation is increasingly challenging. ... Experiments show that our method produces*circuits*that are highly tolerant of errors in the input stream, while the area-delay product of the*circuit*is comparable to that of deterministic implementations ... Stochastic logic has the advantage that basic*arithmetic*operations can be performed with simple logic*circuits*[3] . ...##
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A new 6-T multiplexer based full-adder for low power and leakage current optimization

2012
*
IEICE Electronics Express
*

The proposed full adder clearly outperforms other existing adders in its temperature sustainability behavior

doi:10.1587/elex.9.1434
fatcat:my2zgp2gmjcfrgjvvcbn3keara
*versus*power dissipation, leakage current parameters. ... An adder determines the overall performance of the*circuits*in most of those systems. In this paper a 1-bit full adder cell which uses only six transistors has been proposed. ... The*circuit*layout temperature*versus*power dissipation of the adder along with the existing adders is shown in Fig. 2 (a) . ...##
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Characterizing Valiant's algebraic complexity classes

2008
*
Journal of Complexity
*

The basic computation model used is the

doi:10.1016/j.jco.2006.09.006
fatcat:j25vuys4czbtnghbzvto3sp35q
*arithmetic**circuit*, which makes these classes very easy to define and open to combinatorial techniques. ... such as the equality of the classes VNP and VNP e or the completeness of the Determinant for VQP, and new results such as a characterization of the classes VQP and VP (which we can also apply to the*Boolean*...*Arithmetic**circuits*are also linked to*Boolean*complexity. ...##
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Equivalence Checking of Arithmetic Circuits on the Arithmetic Bit Level

2004
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

W e propose a

doi:10.1109/tcad.2004.826548
fatcat:ryy6ingbrvg37p4ogwho6z2jd4
*Boolean*mapping algorithm that extracts a network of half adders from the gate netlist of an addition*circuit*. ... Index T erms-*Arithmetic*bit lev el,*arithmetic**circuit*, datapath v erification, equiv alence checking, formal hardware v erification, multiplier. ... In the cases where a different encoding was used (Booth*versus*non-Booth), each of the*circuits*was checked against the reference*circuit*with the same encoding produced by the front end of the equivalence ...##
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Coin Flipping in Dynamic Programming Is Almost Useless

2020
*
ACM Transactions on Computation Theory
*

In particular, such

doi:10.1145/3397476
fatcat:wxtxlgv2qrfmhe6yxgw44ekhtu
*circuits*can use all*arithmetic*operations +, -, x, /, optimization operations min and max, conditional branching (if-then-else), and many more. ... A not much larger blow up in*circuit*size is also shown when derandomizing approximating*circuits*. ... So, ⊆ ∕poly holds for*Boolean**circuits*. ...##
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Page 2410 of Mathematical Reviews Vol. , Issue 96d
[page]

1996
*
Mathematical Reviews
*

This notion, introduced by Goode, encompasses

*Boolean**circuit*complexity,*arithmetic**circuit*complexity, and the Blum-Shub-Smale notion of complexity over the reals. ...*circuits*), Spira’s theorem (a size s*Boolean*formula is equivalent to an O(log s)-depth*Boolean*for- mula), and the Hoover-Klawe-Pippenger theorem (an arbitrary fan-out*Boolean**circuit*of fan-out m, size ...##
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Arithmetic circuits: The chasm at depth four gets wider

2012
*
Theoretical Computer Science
*

We also use our techniques to reprove two results on: -the existence of nontrivial

doi:10.1016/j.tcs.2012.03.041
fatcat:huq2vfddqvdozprytlf5rrptyy
*boolean**circuits*of constant depth for languages in LOGCFL; -reduction to polylogarithmic depth for*arithmetic**circuits*... In their paper on the "chasm at depth four", Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit*arithmetic**circuits*of size 2 o(m) also admit*arithmetic**circuits*of ... A discussion of depth reduction in the*boolean**versus**arithmetic*setting can already be found in [1] , but that paper did not actually provide any result of this type. ...##
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Performance Evaluation of Secure Multi-party Computation on Heterogeneous Nodes
[article]

2020
*
arXiv
*
pre-print

The applications of MPC range from privacy-preserving voting,

arXiv:2004.10926v1
fatcat:lbsjg6bdr5dirfjhfj3svrwtf4
*arithmetic*calculation, and large-scale data analysis. From the system perspective, each party in MPC can run on one compute node. ... The schemes used to split secrets can either use*Boolean**circuits*(XOR, AND, MUX) or*Arithmetic**circuits*(addition, multiplication). ... Although*Boolean*and*Arithmetic*sharing have a similar sharing semantics, the construction process of these two types of garble*circuits*is different. ...##
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Can Markets Compute Equilibria?

2009
*
IMF Working Papers
*

A given

doi:10.5089/9781451871715.001
fatcat:ikfgqbkh7zaitff4lrpo2inczy
*Boolean**circuit*has a fixed number of*Boolean*input variables, but there can be a different*Boolean**circuit*specified for each number of inputs, for instance, a different multiplication*circuit*...*Boolean**circuit*: Are at least two inputs "TRUE"? ...
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