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Boolean circuits versus arithmetic circuits

Joachim von zur Gathen, Gadiel Seroussi
1991 Information and Computation  
Over Q and finite fields, 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.  ... 
doi:10.1016/0890-5401(91)90078-g fatcat:aydwnfiodfgy3bizzgauso2sei

Tractable Boolean and Arithmetic Circuits [article]

Adnan Darwiche
2022 arXiv   pre-print
Tractable 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.  ... 
arXiv:2202.02942v1 fatcat:fq33u2ct4vgwngxan3k7dojxam

Enhancing the quantum cost of Reed-Muller Based Boolean quantum circuits using genetic algorithms

M Shaban, A Younes, A Elsayed
2020 Journal of Physics, Conference Series  
There is a direct equivalence between 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] .  ... 
doi:10.1088/1742-6596/1447/1/012031 fatcat:ksew625bvre37kj5xm2uwcdfbq

Valiant's Model: From Exponential Sums to Exponential Products [chapter]

Pascal Koiran, Sylvain Perifel
2006 Lecture Notes in Computer Science  
Our main result relates this hypothesis to Blum, Shub and Smale's algebraic version of P 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.  ... 
doi:10.1007/11821069_52 fatcat:2ua2rt7v4baefnvn3ypbhapimy

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.  ... 

An arithmetic model of computation equivalent to threshold circuits

Joan Boyar, Gudmund Frandsen, Carl Sturtivant
1992 Theoretical Computer Science  
These 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.  ... 
doi:10.1016/0304-3975(92)90335-d fatcat:4wnb5esqmvcvvop3hlql3vb5py

The synthesis of robust polynomial arithmetic with stochastic logic

Weikang Qian, Marc D. Riedel
2008 Proceedings of the 45th annual conference on Design automation - DAC '08  
As integrated 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] .  ... 
doi:10.1145/1391469.1391636 dblp:conf/dac/QianR08 fatcat:jwvw2zesozai5bmiltca3c2p54

A new 6-T multiplexer based full-adder for low power and leakage current optimization

G. Ramana Murthy, C. Senthilpari, P. Velrajkumar, T. S. Lim
2012 IEICE Electronics Express  
The proposed full adder clearly outperforms other existing adders in its temperature sustainability behavior 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) .  ... 
doi:10.1587/elex.9.1434 fatcat:my2zgp2gmjcfrgjvvcbn3keara

Characterizing Valiant's algebraic complexity classes

Guillaume Malod, Natacha Portier
2008 Journal of Complexity  
The basic computation model used is the 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.  ... 
doi:10.1016/j.jco.2006.09.006 fatcat:j25vuys4czbtnghbzvto3sp35q

Equivalence Checking of Arithmetic Circuits on the Arithmetic Bit Level

D. Stoffel, W. Kunz
2004 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
W e propose a 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  ... 
doi:10.1109/tcad.2004.826548 fatcat:ryy6ingbrvg37p4ogwho6z2jd4

Coin Flipping in Dynamic Programming Is Almost Useless

Stasys Jukna
2020 ACM Transactions on Computation Theory  
In particular, such 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.  ... 
doi:10.1145/3397476 fatcat:wxtxlgv2qrfmhe6yxgw44ekhtu

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  ... 

Arithmetic circuits: The chasm at depth four gets wider

Pascal Koiran
2012 Theoretical Computer Science  
We also use our techniques to reprove two results on: -the existence of nontrivial 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.  ... 
doi:10.1016/j.tcs.2012.03.041 fatcat:huq2vfddqvdozprytlf5rrptyy

Performance Evaluation of Secure Multi-party Computation on Heterogeneous Nodes [article]

Zhou Ni, Rujia Wang
2020 arXiv   pre-print
The applications of MPC range from privacy-preserving voting, 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.  ... 
arXiv:2004.10926v1 fatcat:lbsjg6bdr5dirfjhfj3svrwtf4

Can Markets Compute Equilibria?

Hunter K. Monroe
2009 IMF Working Papers  
A given 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"?  ... 
doi:10.5089/9781451871715.001 fatcat:ikfgqbkh7zaitff4lrpo2inczy
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