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1. Full Text Computing Mathematical Functions using DNA via Fractional Coding
by Salehi, Sayed Ahmad and Liu, Xingyi and Riedel, Marc D and Parhi, Keshab K
Scientific Reports, ISSN 2045-2322, 12/2018, Volume 8, Issue 1, pp. 8312 - 14
This paper discusses the implementation of mathematical functions such as exponentials, trigonometric functions, the sigmoid function and the perceptron... 
CHEMICAL IMPLEMENTATION | NETWORKS | COMPUTATION | MULTIDISCIPLINARY SCIENCES | CONSTRUCTION | Mathematical functions | Deoxyribonucleic acid--DNA | Stochasticity
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2. Full Text Performing Stochastic Computation Deterministically
by Hassan Najafi, M and Jenson, Devon and Lilja, David J and Riedel, Marc D
IEEE Transactions on Very Large Scale Integration (VLSI) Systems, ISSN 1063-8210, 8/2019, Volume 27, Issue 12, pp. 1 - 14
Stochastic logic performs computation on data represented by random bit-streams. The representation allows complex arithmetic to be performed with very simple... 
Multiplexing | Conferences | fast-converging process | Probability | Very large scale integration | Encoding | low-discrepancy (LD) bit-streams | pseudorandomized bit-stream | unary bit-streams | Deterministic computing | Logic gates | stochastic computing | Clocks
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3. Full Text Low-Cost Sorting Network Circuits Using Unary Processing
by Najafi, M. Hassan and Lilja, David. J and Riedel, Marc D and Bazargan, Kia
IEEE Transactions on Very Large Scale Integration (VLSI) Systems, ISSN 1063-8210, 08/2018, Volume 26, Issue 8, pp. 1471 - 1480
Sorting is a common task in a wide range of applications from signal and image processing to switching systems. For applications that require high performance,... 
Multiplexing | Power demand | unary processing | Low cost design | Sorting | time-encoding data | Fault tolerance | median filtering | sorting networks | Fault tolerant systems | Logic gates | Hardware | stochastic computing | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ALGORITHM | SENSOR | ENGINEERING, ELECTRICAL & ELECTRONIC | VLSI IMPLEMENTATION | COMPUTATION | Networks | Filtration | Image processing | Switching theory | Gate arrays | Integrated circuits | Power consumption | Coding | Energy conservation | Low cost | Signal processing | Field programmable gate arrays
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4. Full Text An Overview of Time-Based Computing with Stochastic Constructs
by Najafi, M. Hassan and Jamali-Zavareh, Shiva and Lilja, David J and Riedel, Marc D and Bazargan, Kia and Harjani, Ramesh
IEEE Micro, ISSN 0272-1732, 11/2017, Volume 37, Issue 6, pp. 62 - 71
Computing on time-based data is a recent evolution of research in stochastic computing. As with stochastic computing, complex functions can be computed with... 
time-based computing | Pulse width modulation | Generators | stochastic computing (SC) | time-encoded values | mixed-signal design | Image coding | ultra-low-power processing | Logic gates | energy-efficient computing | Hardware | Sensors | Clocks | pulse width modulation | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTATION | Computing time | Coding | Computing costs
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5. Full Text A Study on Monotone Self-Dual Boolean Functions
by Mustafa ALTUN Marc D. RIEDEL
应用数学学报：英文版, ISSN 0168-9673, 2017, Volume 33, Issue 1, pp. 43 - 52
This paper shows that monotone self-dual Boolean functions in irredundant disjuntive normal form （IDNF） do not have more variables than disjuncts. Monotone... 
布尔函数 | 自对偶 | 单调 | 运行时间 | 对偶算法 | 析取 | 同数 | 05-XX: Combinatorics | Theoretical, Mathematical and Computational Physics | self-dual Boolean functions | duality problem | 03-XX: Mathematical logic and foundations | Mathematics | monotone Boolean functions | Applications of Mathematics | Math Applications in Computer Science | MATHEMATICS, APPLIED | COMPLEXITY | HYPERGRAPH | DUALIZATION | LOGIC | Algorithms
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6. Full Text Synthesizing cubes to satisfy a given intersection pattern
by Qian, Weikang and Riedel, Marc D and Rosenberg, Ivo
Discrete Applied Mathematics, ISSN 0166-218X, 10/2015, Volume 193, pp. 11 - 38
In two-level logic synthesis, the typical input specification is a set of minterms defining the set and a set of minterms defining the set of a Boolean... 
Boolean product | Two-level logic synthesis | Cube | Minterm | MATHEMATICS, APPLIED
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7. Full Text An Architecture for Fault-Tolerant Computation with Stochastic Logic
by Weikang Qian and Xin Li and Riedel, M D and Bazargan, K and Lilja, D J
IEEE Transactions on Computers, ISSN 0018-9340, 01/2011, Volume 60, Issue 1, pp. 93 - 105
Mounting concerns over variability, defects, and noise motivate a new approach for digital circuitry: stochastic logic, that is to say, logic that operates on... 
Multiplexing | Fault tolerance | Stochastic logic | fault-tolerant computation | Fault tolerant systems | Wires | Computer architecture | reconfigurable hardware | Probabilistic logic | Polynomials | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ENGINEERING, ELECTRICAL & ELECTRONIC | Fuzzy logic | Technology application | Usage | Image processing | Digital integrated circuits | Innovations | Fault location (Engineering) | Fuzzy algorithms | Methods | Fuzzy systems | Architecture | Errors | Soft errors | Probability theory | Probabilistic methods | Stochasticity | Logic
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8. Full Text Computation on Stochastic Bit Streams Digital Image Processing Case Studies
by Peng Li and Lilja, David J and Weikang Qian and Bazargan, Kia and Riedel, Marc D
IEEE Transactions on Very Large Scale Integration (VLSI) Systems, ISSN 1063-8210, 03/2014, Volume 22, Issue 3, pp. 449 - 462
Maintaining the reliability of integrated circuits as transistor sizes continue to shrink to nanoscale dimensions is a significant looming challenge for the... 
finite state machine (FSM) | fault tolerance | stochastic computing | Digital image processing | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ARCHITECTURE | ENGINEERING, ELECTRICAL & ELECTRONIC | Neural networks | Digital imaging | Image processing | Computation | Mathematical analysis | Very large scale integration | Digital | Mathematical models | Stochasticity | Streams
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9. Full Text The synthesis of robust polynomial arithmetic with stochastic logic
by Qian, Weikang and Riedel, Marc D
Proceedings - Design Automation Conference, ISSN 0738-100X, 2008, pp. 648 - 653
Stochastic logic | Polynomial arithmetic | Probabilistic logic
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10. Full Text Polysynchronous Clocking: Exploiting the Skew Tolerance of Stochastic Circuits
by Najafi, M. Hassan and Lilja, David J and Riedel, Marc D and Bazargan, Kia
IEEE Transactions on Computers, ISSN 0018-9340, 10/2017, Volume 66, Issue 10, pp. 1734 - 1746
In the paradigm of stochastic computing, arithmetic functions are computed on randomized bit streams. The method naturally and effectively tolerates very high... 
Uncertainty | clock distribution networks | Logic gates | multi-clock circuits | Generators | Registers | Delays | relaxed clocking | Synchronization | Polysynchronous clocking | stochastic computing | Clocks | BIT STREAMS | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | LOGIC | ENGINEERING, ELECTRICAL & ELECTRONIC | CMOS | LDPC CODES | COMPUTATION | Usage | Stochastic processes | Gates (Electronics) | Electric generators | Domains | Distribution management | Mathematical functions
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11. Full Text Logic Synthesis for Switching Lattices
by Altun, M and Riedel, M. D
IEEE Transactions on Computers, ISSN 0018-9340, 11/2012, Volume 61, Issue 11, pp. 1588 - 1600
This paper studies the implementation of Boolean functions by lattices of four-terminal switches. Each switch is controlled by a Boolean literal. If the... 
Algorithm design and analysis | Boolean functions | switching circuits | nanowire crossbar arrays | Lattices | Switches | CMOS integrated circuits | Voltage control | lattices | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Logic circuitry | Numerical analysis | Algebra, Boolean | Mathematical optimization | Innovations | Studies | Algorithms | Synthesis | Tasks | Circuits | Mathematical analysis
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12. Full Text Time-Encoded Values for Highly Efficient Stochastic Circuits
by Najafi, M. Hassan and Jamali-Zavareh, Shiva and Lilja, David J and Riedel, Marc D and Bazargan, Kia and Harjani, Ramesh
IEEE Transactions on Very Large Scale Integration (VLSI) Systems, ISSN 1063-8210, 05/2017, Volume 25, Issue 5, pp. 1644 - 1657
Stochastic computing (SC) is a promising technique for applications that require low area overhead and fault tolerance, but can tolerate relatively high... 
stochastic computing (SC) circuits | stochastic number generator (SNG) | Image processing | Stochastic processes | Pulse width modulation | Logic gates | Generators | Hardware | time-encoded values | mixed-signal design | Energy-efficient computing | Clocks | pulse width modulation | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Pulse duration | Fault tolerance | Energy consumption | Power consumption | Linear feedback shift registers | Circuits | Coding | Energy conservation | Energy dissipation | Pulse duration modulation
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13. Full Text IIR filters using stochastic arithmetic
by Saraf, Naman and Bazargan, Kia and Lilja, David J and Riedel, Marc D
Proceedings -Design, Automation and Test in Europe, DATE, ISSN 1530-1591, 2014
Sigma-delta modulation | Stochastic computing | Oversampling | Stochastic integrator | IIR filters
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14. Full Text Logical Computation on Stochastic Bit Streams with Linear Finite-State Machines
by Peng Li and Lilja, David J and Qian, Weikang and Riedel, Marc D and Bazargan, Kia
IEEE Transactions on Computers, ISSN 0018-9340, 06/2014, Volume 63, Issue 6, pp. 1474 - 1486
Most digital systems operate on a positional representation of data, such as binary radix. An alternative is to operate on random bit streams where the signal... 
finite-state machine (FSM) | Radiation detectors | Stochastic processes | Logic gates | Encoding | Polynomials | Stochastic computing | Approximation methods | stochastic bit streams | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Stochastic analysis | Analysis | Finite state automata | Mathematical logic | Binary-Coded Decimal | Functions, Exponential | Symbolic and mathematical logic
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15. Full Text Transforming Probabilities With Combinational Logic
by Weikang Qian and Riedel, Marc D and Hongchao Zhou and Bruck, Jehoshua
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, ISSN 0278-0070, 09/2011, Volume 30, Issue 9, pp. 1279 - 1292
Schemes for probabilistic computation can exploit physical sources to generate random values in the form of bit streams. Generally, each source has a fixed... 
Logic synthesis | random bit streams | Transforms | Logic gates | Probabilistic logic | Inverters | Generators | Polynomials | stochastic bit streams | Switching circuits | probabilistic signals | probabilistic logic | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Circuit design | Digital integrated circuits | Stochastic processes | Geometric probabilities | Design and construction | Methods | Probabilities | Combinatorial probabilities | Studies | Probability | Design engineering | Reproduction | Probability theory | Logic | Computer aided design | Optimization | Streams
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16. Full Text Chemical Reaction Networks for Computing Polynomials
by Salehi, Sayed Ahmad and Parhi, Keshab K and Riedel, Marc D
ACS Synthetic Biology, ISSN 2161-5063, 01/2017, Volume 6, Issue 1, pp. 76 - 83
Chemical reaction networks (CRNs) provide a fundamental model in the study of molecular systems. Widely used as formalism for the analysis of chemical and... 
mass-action kinetics | molecular computing | polynomials | DNA strand-displacement reaction | COMPUTATION | BIOCHEMICAL RESEARCH METHODS | DNA - chemistry | Synthetic Biology | Algorithms | Computers, Molecular | Models, Chemical | Computer Simulation | Kinetics
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17. Full Text Asynchronous discrete-time signal processing with molecular reactions
by Salehi, Sayed Ahmad and Riedel, Marc D and Parhi, Keshab K
2014 48th Asilomar Conference on Signals, Systems and Computers, ISSN 1058-6393, 11/2014, Volume 2015-, pp. 1767 - 1772
This paper presents a new methodology to synthesize molecular reactions for discrete-time signal processing (DSP) computations that produce time-varying... 
Decision support systems | Finite impulse response filters | Processor scheduling | Digital signal processing | IIR filters | Delays | Clocks | Phases | Computer simulation | Methodology | Computation | Signal processing | Mathematical models | Delay
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18. Full Text Cyclic Boolean circuits
by Riedel, Marc D and Bruck, Jehoshua
Discrete Applied Mathematics, ISSN 0166-218X, 09/2012, Volume 160, Issue 13-14, pp. 1877 - 1900
A Boolean circuit is a collection of gates and wires that performs a mapping from Boolean inputs to Boolean outputs. The accepted wisdom is that such circuits... 
Cycles | Boolean functions | Cyclic circuits | Feedback | Combinational circuits | DAG | Boolean circuits | Loops | MATHEMATICS, APPLIED | NECESSITY | COMPLEXITY THEORY | COMBINATIONAL-CIRCUITS | Circuit design | Analysis | Equivalence | Circuits | Mathematical models | Boolean algebra | Topology | Wire | Gates (circuits)
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19. Full Text The Synthesis of Cyclic Dependencies with Boolean Satisfiability
by Backes, John D and Riedel, Marc D
ACM Transactions on Design Automation of Electronic Systems (TODAES), ISSN 1084-4309, 10/2012, Volume 17, Issue 4, pp. 1 - 24
The accepted wisdom is that combinational circuits must have acyclic (i.e., feed-forward) topologies. Yet simple examples suggest that this is incorrect. In... 
logic synthesis | cyclic circuits | circuit verification | Boolean satisfiability | logic design | Circuit verification | Logic design | Cyclic circuits | Logic synthesis | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | MODEL CHECKING | Theory | Verification | INTERPOLATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Algorithms | COMBINATIONAL-CIRCUITS | Benchmarking
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20. Full Text Stochastic functions using sequential logic
by Saraf, Naman and Bazargan, Kia and Lilja, David J and Riedel, Marc D
2013 IEEE 31st International Conference on Computer Design (ICCD), ISSN 1063-6404, 10/2013, pp. 507 - 510
Stochastic computing is a novel approach to real arithmetic, offering better error tolerance and lower hardware costs over the conventional implementations.... 
Decision support systems | Ground penetrating radar | Reversible Markov chains | Geophysical measurement techniques | Rational functions | Taylor series | Stochastic computing | Finite state machines
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