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Uniform constant-depth threshold circuits for division and iterated multiplication

William Hesse, Eric Allender, David A. Mix Barrington
2002 Journal of computer and system sciences (Print)  
, the division problem lies in P-uniform TC 0 .  ...  Integer division has been the outstanding example of a natural problem known to be in a P-uniform circuit complexity class, but not known to be in its DLOGTIME-uniform version.  ...  We also thank Dieter van Melkebeek, Samir Datta, Michal Koucký, Rüdiger Reischuk, and Sambuddha Roy for helpful discussions.  ... 
doi:10.1016/s0022-0000(02)00025-9 fatcat:vwqdpnv7njghzi2326rxqprtca

Uniform circuits for division: consequences and problems

E. Allender, D.A. Mix Barrington, W. Hesse
Proceedings 16th Annual IEEE Conference on Computational Complexity  
Integer division has been known to lie in P-uniform TC 0 since the mid-1980's, and recently this was improved to L-uniform TC 0 .  ...  At the time that the results in this paper were proved and submitted for conference presentation, it was unknown whether division lay in DLOGTIME-uniform TC 0 (also known as FOM).  ...  We also thank Dieter van Melkebeek, Samir Datta, Michal Koucký, Rüdiger Reischuk, and Sambuddha Roy for helpful discussions.  ... 
doi:10.1109/ccc.2001.933882 dblp:conf/coco/AllenderBH01 fatcat:mipveh6qyjdxxjao4gl4x3jqbi

Optimal size integer division circuits

J. H. Reif
1989 Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89  
Division is a fundamental problem for arithmetic and algebraic computation.  ...  The results match the best-known depth bounds for logspace uniform circuits, and are optimal in size.  ...  Independent w ork on a polynomial time uniform circuit by Hastad and Leighton 6 resulted in an e cient circuit for Chinese remaindering which g a v e a division circuit of size On 1+ and depth O1= 2 log  ... 
doi:10.1145/73007.73032 dblp:conf/stoc/ReifT89 fatcat:qjooadtdljc7hkj7esut7sdy2q

Optimal Size Integer Division Circuits

John H. Reif, Stephen R. Tate
1990 SIAM journal on computing (Print)  
Division is a fundamental problem for arithmetic and algebraic computation.  ...  The results match the best-known depth bounds for logspace uniform circuits, and are optimal in size.  ...  Independent w ork on a polynomial time uniform circuit by Hastad and Leighton 6 resulted in an e cient circuit for Chinese remaindering which g a v e a division circuit of size On 1+ and depth O1= 2 log  ... 
doi:10.1137/0219064 fatcat:bvbi7f7zwbcj3glrycdjzegmqe

Log Depth Circuits for Division and Related Problems

Paul W. Beame, Stephen A. Cook, H. James Hoover
1986 SIAM journal on computing (Print)  
We present optimal depth Boolean circuits (depth O(log n)) for integer division, powering and multiple products We also show t h a t these three problems are of equivalent uniform depth and space complexity  ...  In addition, we describe an algorithm for testing drvisibility t h a t is optimal for both depth and space  ...  Divisibility Although the DIVISION problem has P-uniform O(1ogn) depth circuits, it is still unclear whether or not it has log-space uniform O ( 1 o g n ) depth circuits.  ... 
doi:10.1137/0215070 fatcat:pntuddlzzvgzngh6ianmnmpid4

Asynchronous spatial division multiplexing router

Wei Song, Doug Edwards
2011 Microprocessors and microsystems  
Virtual channel (VC) is the most utilized flow control method in asynchronous routers but spatial division multiplexing (SDM) achieves better throughput performance for best effort traffic than VC.  ...  Performance comparisons have been made with different configurations of payload size, communication distance, buffer size, port bandwidth, network size and number of VCs/virtual circuits.  ...  Area and latency estimation models for the wormhole, the virtual channel and the spatial division multiplexing flow control methods are provided.  ... 
doi:10.1016/j.micpro.2010.08.007 fatcat:kfhc24ph35gpxch7debnjtqsvy

On the Complexity of Linear Arithmetic with Divisibility

Antonia Lechner, Joel Ouaknine, James Worrell
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
The decision problem for existential sentences over Qp is an important component of the decision procedure for existential Presburger arithmetic with divisibility.  ...  that the decision problem for such sentences is in NEXPTIME.  ...  ACKNOWLEDGMENT The authors gratefully acknowledge the support of the Engineering and Physical Sciences Research Council (EPSRC).  ... 
doi:10.1109/lics.2015.67 dblp:conf/lics/LechnerOW15 fatcat:u6pplixewzdivlu4velsbbqjbu

Polynomial division and its computational complexity

Dario Bini, Victor Pan
1986 Journal of Complexity  
The algorithm exploits the reduction of the problem to integer division; the polynomial remainder and quotient are recovered from integer remainder and quotient via binary segmentation.  ...  i) First we show that all the known algorithms for polynomial division can be represented as algorithms for triangular Toeplitz matrix inversion.  ...  )'(') processors su$'ice under the P-uniform Boolean circuit model of Beam, Cook, and Hoover (1984) .  ... 
doi:10.1016/0885-064x(86)90001-4 fatcat:ixnugw7k35bbdo4b6rvi7rhhfm

The complexity of divisibility

Johannes Bausch, Toby Cubitt
2016 Linear Algebra and its Applications  
We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard.  ...  We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue  ...  Acknowledgements Johannes Bausch would like to thank the German National Academic Foundation and EPSRC (grant number 1600123) for financial support.  ... 
doi:10.1016/j.laa.2016.03.041 pmid:28626246 pmcid:PMC5465997 fatcat:u42ze2cfcrbe5h7avoapwplzty

Multiplication, division, and shift instructions in parallel random access machines

Jerry L. Trahan, Michael C. Loui, Vijaya Ramachandran
1992 Theoretical Computer Science  
We obtain simulations of uniform circuits by RAMS with enhanced instruction sets and use the enhanced RAMS to simulate PRAMS with enhanced instruction sets.  ...  Loui and V. Ramachandran, Multiplication, division and shift instructions in parallel random access machines, Theoretical Computer Science 100 (1992) l-44. J.L. Trahan, M.C. Loui, V.  ...  Acknowledgment We thank the anonymous referee for the detailed reading given to this paper and for the comments that improved the presentation of the paper.  ... 
doi:10.1016/0304-3975(92)90362-j fatcat:jcn5g32fxzd3ljpxwt2qu24fdy

Orthogonal Frequency-Division Multiplexed Quantum Key Distribution

Sima Bahrani, Mohsen Razavi, Jawad A. Salehi
2015 Journal of Lightwave Technology  
circuits.  ...  We propose orthogonal frequency division multiplexing (OFDM), as a spectrally efficient multiplexing technique, for quantum key distribution (QKD) at the core of trustednode quantum networks.  ...  Hence, the parameters p xtalk and η g are, respectively, given by (43) and (44) , multiplied by N. Fig. 5 : 5 (a) The passive ODFT circuit for N = 4.  ... 
doi:10.1109/jlt.2015.2476821 fatcat:ctb4biodrncw7hzzlx6wmvplxy

Frequency division multiplexing readout and simultaneous manipulation of an array of flux qubits

M. Jerger, S. Poletto, P. Macha, U. Hübner, E. Il'ichev, A. V. Ustinov
2012 Applied Physics Letters  
Consequently, scaling up superconducting qubit circuits is no longer limited by the readout apparatus.  ...  Parallel readout of 6 flux qubits using a frequency division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 qubits.  ...  This work was supported by the EU project SOLID, the Deutsche Forschungsgemeinschaft (DFG) and the State of Baden-Württemberg through the DFG-Center for Functional Nanostructures (CFN) within subproject  ... 
doi:10.1063/1.4739454 fatcat:j47g7r4mgfcqrk4tigk4oqpddm

High-radix division and square-root with speculation

J. Cortadella, T. Lang
1994 IEEE transactions on computers  
This results in operations with a shorter cycle time and a variable number of cycles. The scheme can be used in separate division and square-root units, or in a combined one.  ...  Several designs were d i e d and compared in terms of execution time and area. The fastest unit considered is a radix-512 divider with a partial advance of six bits.  ...  Block diagram of the digit-speculation circuit for radix-5 12 division. Fig. 14 . 14 Implementation of 43 logic block. Fig. 15 . 15 Unit for division and square-root.  ... 
doi:10.1109/12.295854 fatcat:jt73ccbgmbhkhm3ks7pycor2nq

Divisive Normalization in Olfactory Population Codes

Shawn R. Olsen, Vikas Bhandawat, Rachel I. Wilson
2010 Neuron  
We exploit the orderly anatomy of this circuit to independently manipulate feedforward and lateral input to second-order projection neurons (PNs).  ...  Strikingly, a model with just two variables (feedforward and total ORN activity) accurately predicts PN odor responses.  ...  Input gain control largely solves this problem ( Figure 6C ).  ... 
doi:10.1016/j.neuron.2010.04.009 pmid:20435004 pmcid:PMC2866644 fatcat:aoht55lztza3dnzjdht6wracja

Time Division Multiplexing Front-Ends for Multiantenna Integrated Wireless Receivers

Gautham Krishnamurthy, Kevin G Gard
2010 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
Manager responsible for the design and development of RF integrated circuits (RFICs) for code-division multiple-access (CDMA) wireless products.  ...  His research interests include the areas of novel integrated circuit solutions for wireless transceivers and analysis of nonlinear microwave circuits with digitally modulated signals.  ...  Lipa for assistance with wirebonding the chip onto the test board.  ... 
doi:10.1109/tcsi.2009.2031759 fatcat:ew2gdtaamvh6heizkc6um2zsha
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