Noise-based deterministic logic and computing: a brief survey
---
paper_title: End of Moore's law: thermal (noise) death of integration in micro and nano electronics

paper_content:

The exponential growth of memory size and clock frequency in computers has a great impact on everyday life. The growth is empirically described by Moore’s law of miniaturization. Physical limitations of this growth would have a serious impact on technology and economy. A thermodynamical effect, the increasing thermal noise voltage (Johnson–Nyquist noise) on decreasing characteristic capacitances, together with the constrain of using lower supply voltages to keep power dissipation manageable on the contrary of increasing clock frequency, has the potential to break abruptly Moore’s law within 6–8 years, or earlier.  2002 Elsevier Science B.V. All rights reserved.
---
paper_title: ENERGY BARRIERS, DEMONS, AND MINIMUM ENERGY OPERATION OF ELECTRONIC DEVICES

paper_content:

The presence of thermal noise dictates that an energy barrier is needed to preserve a binary state. Therefore, all electronic devices contain at least one energy barrier to control electron flow. The barrier properties determine the operating characteristics of electronic devices. Furthermore, changes in the barrier shape require changes in charge density. Operation of all charge transport devices includes charging/discharging capacitances to change barrier height. We analyze energy dissipation for several schemes of charging capacitors. A basic assumption of Reversible Computing is that the computing system is completely isolated from the thermal bath. An isolated system is a mathematical abstraction never perfectly realized in practice. Errors due to thermal excitations are equivalent to information erasure, and thus computation dissipates energy. Another source of energy dissipation is due to the need of measurement and control. To analyze this side of the problem, the Maxwell's Demon is a useful abstraction. We hold that apparent "energy savings" in models of adiabatic circuits result from neglecting the total energy needed by other parts of the system to implement the circuit.
---
paper_title: EDA for IC Implementation, Circuit Design, and Process Technology

paper_content:

Design Flows. Logic Synthesis. Power Analysis and Optimization from Circuit to Register Transfer Levels. Equivalence checking. Digital Layout - Placement. Static Timing Analysis. Structured Digital Design. Routing. Exploring Challenges of Libraries for Electronic Design. Design Closure. Tools for Chip-Package Codesign. Design Databases. FPGA Synthesis and Physical Design. Simulation of Analog and Radio Frequency Circuits and Systems. Simulation and Modeling for Analog and Mixed-Signal Integrated Circuits. Layout Tools for Analog ICs and Mixed-Signal SoCs. Design Rule Checking. Resolution Enhancement Technology and Mask Data Preparation. Design for Manufacturability in the Nanometer Era. Power Supply Network Design and Analysis. Noise Considerations in Digital ICs. Layout Extraction. Mixed-Signal Noise Coupling in System-on-Chip Design: Modeling, Analysis and Validation. Process Simulation. Device Modeling: From Physics to Electrical Parameter Extraction. High-Accuracy Parasitic Extraction.
---
paper_title: Comparison of Energy Requirements for Classical and Quantum Information Processing

paper_content:

By considering the energy requirements of quantum and classical computers we propose a criterion to separate the classical from the quantum regime and show that the classical scaling laws are much more favorable for conventional, general purpose computation.
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paper_title: Energy, Performance, and Probability Tradeoffs for Energy-Efficient Probabilistic CMOS Circuits

paper_content:

The scaling trend of semiconductor devices has raised several issues such as energy consumption and heat dissipation, as well as the increasing probabilistic behavior of devices. Motivated by the necessity to consider probabilistic approaches to future designs, probabilistic CMOS (PCMOS) based computing has been proposed. PCMOS devices are inherently probabilistic devices that compute correctly with a probability p. This paper investigates the tradeoffs between the energy, speed (or performance), and probability of correctness (p) of PCMOS circuits. For given constraints on p, performance, and energy delay product (EDP), and using analytical models of energy, delay, and p, the optimum values of EDP and probability are found for PCMOS circuits. The analytical models are validated using circuit simulations for PCMOS circuits designed in a 0.13-mum process. The results show that, to minimize EDP, it is preferable to operate PCMOS circuits at lower supply voltages. On the other hand, to maximize p, the highest possible supply voltage under the given constraints is preferable. Our analysis makes it possible to achieve an optimal circuit design that satisfies the p , performance, and EDP requirements for a given application. An analysis of the impact of variations in temperature, threshold voltage, and supply voltage on optimal EDP and probability values is also included.
---
paper_title: End of Moore's law: thermal (noise) death of integration in micro and nano electronics

paper_content:

The exponential growth of memory size and clock frequency in computers has a great impact on everyday life. The growth is empirically described by Moore’s law of miniaturization. Physical limitations of this growth would have a serious impact on technology and economy. A thermodynamical effect, the increasing thermal noise voltage (Johnson–Nyquist noise) on decreasing characteristic capacitances, together with the constrain of using lower supply voltages to keep power dissipation manageable on the contrary of increasing clock frequency, has the potential to break abruptly Moore’s law within 6–8 years, or earlier.  2002 Elsevier Science B.V. All rights reserved.
---
paper_title: Future Directions in Electronic Computing and Information Processing

paper_content:

We are facing a slowing down of the evolution of microprocessor performance. This is part of a more general slowing down which is indicated by, among others, the fact that IBM has recently given up its PC market. By applying the principles of physics, we discuss some characteristic features of the current situation and consider if some exotic new technologies such as nanoelectronics or quantum computing would be able to save us from this slowdown.
---
paper_title: A short review of nanoelectronic architectures

paper_content:

In nanoelectronics the search for a successor to CMOS technology has so far mainly been concentrated on nanodevices that could eventually be made much smaller than CMOS transistors, perhaps even brought down to the ultimate limit of the molecular scale. Much less effort has been invested in examining the architectural problems that will also have to be solved. These problems range from the device level up to the full circuit level, and they involve many different factors. The question of how much extra performance will be gained by going to new nanoscale devices is fundamentally linked to these architectural issues. This short review concentrates on recent work that has been done on architectures in nanoelectronics and includes topics such as the system dependent relation between performance and power dissipation, the applicability of concepts of parallelism and fault tolerance, and the design and fabrication of large circuits.
---
paper_title: ENERGY BARRIERS, DEMONS, AND MINIMUM ENERGY OPERATION OF ELECTRONIC DEVICES

paper_content:

The presence of thermal noise dictates that an energy barrier is needed to preserve a binary state. Therefore, all electronic devices contain at least one energy barrier to control electron flow. The barrier properties determine the operating characteristics of electronic devices. Furthermore, changes in the barrier shape require changes in charge density. Operation of all charge transport devices includes charging/discharging capacitances to change barrier height. We analyze energy dissipation for several schemes of charging capacitors. A basic assumption of Reversible Computing is that the computing system is completely isolated from the thermal bath. An isolated system is a mathematical abstraction never perfectly realized in practice. Errors due to thermal excitations are equivalent to information erasure, and thus computation dissipates energy. Another source of energy dissipation is due to the need of measurement and control. To analyze this side of the problem, the Maxwell's Demon is a useful abstraction. We hold that apparent "energy savings" in models of adiabatic circuits result from neglecting the total energy needed by other parts of the system to implement the circuit.
---
paper_title: EDA for IC Implementation, Circuit Design, and Process Technology

paper_content:

Design Flows. Logic Synthesis. Power Analysis and Optimization from Circuit to Register Transfer Levels. Equivalence checking. Digital Layout - Placement. Static Timing Analysis. Structured Digital Design. Routing. Exploring Challenges of Libraries for Electronic Design. Design Closure. Tools for Chip-Package Codesign. Design Databases. FPGA Synthesis and Physical Design. Simulation of Analog and Radio Frequency Circuits and Systems. Simulation and Modeling for Analog and Mixed-Signal Integrated Circuits. Layout Tools for Analog ICs and Mixed-Signal SoCs. Design Rule Checking. Resolution Enhancement Technology and Mask Data Preparation. Design for Manufacturability in the Nanometer Era. Power Supply Network Design and Analysis. Noise Considerations in Digital ICs. Layout Extraction. Mixed-Signal Noise Coupling in System-on-Chip Design: Modeling, Analysis and Validation. Process Simulation. Device Modeling: From Physics to Electrical Parameter Extraction. High-Accuracy Parasitic Extraction.
---
paper_title: Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states

paper_content:

Article history: A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case (N = 2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/ f , Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart. © 2009 Elsevier B.V. All rights reserved.
---
paper_title: How much power does neural signal propagation need?

paper_content:

Two well known, biologically inspired non-dynamical models of stochastic resonance, the threshold-crossing model and the fluctuating rate model, are analyzed in terms of channel information capacity and dissipation of energy necessary for small-signal transduction. Using analogies to spike propagation in neurons we postulate the average output pulse rate as a measure of dissipation. The dissipation increases monotonically with the input noise. We find that for small dissipation both models give a close to linear dependence of the channel information capacity on dissipation. In both models the channel information capacity, as a function of dissipation, has a maximum at input noise amplitude that is different from that in the standard signal-to-noise ratio versus input noise plot. Though a direct comparison is not straightforward, for small signals the threshold model gives appreciably higher density of information per dissipation than the exponential fluctuating rate model. We show that a formal introduction of cooperativity in the rate fluctuating model permits us to imitate the response function of the threshold model and to enhance performance. This finding may have direct relevance to real neural spike generation where, due to a strong positive feedback, the ion channel currents add up in a synchronized way.
---
paper_title: Thermal noise driven computing

paper_content:

A new type of computing, where thermal noise is the information carrier and the clock in a computer, is proposed. The energy requirement/dissipation is studied in a simple digital system with zero threshold voltage when the thermal noise is equal to or greater than the digital signal. In a simple realization of a thermal noise driven gate, the lower limit of energy needed to generate the digital signal is ≈1.1kT∕bit. The arrangement has potentially improved energy efficiency and it is free of leakage current, cross-talk, and ground plane electromagnetic interference problems. Disadvantage is the larger number of required elements.
---
paper_title: Deterministic multivalued logic scheme for information processing and routing in the brain

paper_content:

Driven by analogies with state vectors of quantum informatics and noise-based logic, we propose a general scheme and elements of neural circuitry for processing and addressing information in the brain. Specifically, we consider random (e.g., Poissonian) trains of finite-duration spikes, and, using the idealized concepts of excitatory and inhibitory synapses, offer a procedure for generating 2^N-1 orthogonal vectors out of N partially overlapping trains ("neuro-bits"). We then show that these vectors can be used to construct 2^(2^N-1)-1 different superpositions which represent the same number of logic values when carrying or routing information. In quantum informatics the above numbers are the same, however, the present logic scheme is more advantageous because it is deterministic in the sense that the presence of a vector in the spike train is detected by an appropriate coincidence circuit. For this reason it does not require time averaging or repeated measurements of the kind used in standard cross-correlation analysis or in quantum computing.
---
paper_title: Implementing digital logic with sinusoidal supplies

paper_content:

In this paper, a new type of combinational logic circuit realization is presented. Logic values are implemented as sinusoidal signals. Sinusoidal signals of the same frequency are phase shifted by π to destructively interfere with each other, and represent the logic 0 and 1 values of Boolean Logic. These properties of sinusoids can be used to identify a signal without ambiguity. Thus, representing logic values as sinusoidal signals yields a realizable system of logic. The paper presents a logic gate family that can operate using the sinusoidal signals for logic 0 and logic 1 values. Due to orthogonality of sinusoid signals with different frequencies, multiple sinusoids could be transmitted on a single wire. This provides a natural way of implementing multilevel logic. Signals traveling long distances could take advantage of this fact and can share interconnect lines. Recent research in circuit design has made it possible to harvest sinusoidal signals of the same frequency and 180° phase difference from a single resonant clock ring in a distributed manner. Other advantage of such a logic family is its immunity from external additive noise. The experiments in this paper indicate that this paradigm, when used to implement binary valued logic, yields an improvement in switching (dynamic) power.
---
paper_title: Noise-based logic hyperspace with the superposition of 2N states in a single wire

paper_content:

Abstract In the introductory paper [L.B. Kish, Phys. Lett. A 373 (2009) 911], about noise-based logic, we showed how simple superpositions of single logic basis vectors can be achieved in a single wire. The superposition components were the N orthogonal logic basis vectors. Supposing that the different logic values have “on/off” states only, the resultant discrete superposition state represents a single number with N bit accuracy in a single wire, where N is the number of orthogonal logic vectors in the base. In the present Letter, we show that the logic hyperspace (product) vectors defined in the introductory paper can be generalized to provide the discrete superposition of 2 N orthogonal system states. This is equivalent to a multi-valued logic system with 2 2 N logic values per wire. This is a similar situation to quantum informatics with N qubits, and hence we introduce the notion of noise-bit. This system has major differences compared to quantum informatics. The noise-based logic system is deterministic and each superposition element is instantly accessible with the high digital accuracy, via a real hardware parallelism, without decoherence and error correction, and without the requirement of repeating the logic operation many times to extract the probabilistic information. Moreover, the states in noise-based logic do not have to be normalized, and non-unitary operations can also be used. As an example, we introduce a string search algorithm which is O ( M ) times faster than Grover's quantum algorithm (where M is the number of string entries), while it has the same hardware complexity class as the quantum algorithm.
---
paper_title: Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states

paper_content:

Article history: A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case (N = 2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/ f , Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart. © 2009 Elsevier B.V. All rights reserved.
---
paper_title: Deterministic multivalued logic scheme for information processing and routing in the brain

paper_content:

Driven by analogies with state vectors of quantum informatics and noise-based logic, we propose a general scheme and elements of neural circuitry for processing and addressing information in the brain. Specifically, we consider random (e.g., Poissonian) trains of finite-duration spikes, and, using the idealized concepts of excitatory and inhibitory synapses, offer a procedure for generating 2^N-1 orthogonal vectors out of N partially overlapping trains ("neuro-bits"). We then show that these vectors can be used to construct 2^(2^N-1)-1 different superpositions which represent the same number of logic values when carrying or routing information. In quantum informatics the above numbers are the same, however, the present logic scheme is more advantageous because it is deterministic in the sense that the presence of a vector in the spike train is detected by an appropriate coincidence circuit. For this reason it does not require time averaging or repeated measurements of the kind used in standard cross-correlation analysis or in quantum computing.
---
paper_title: Noise-based logic hyperspace with the superposition of 2N states in a single wire

paper_content:

Abstract In the introductory paper [L.B. Kish, Phys. Lett. A 373 (2009) 911], about noise-based logic, we showed how simple superpositions of single logic basis vectors can be achieved in a single wire. The superposition components were the N orthogonal logic basis vectors. Supposing that the different logic values have “on/off” states only, the resultant discrete superposition state represents a single number with N bit accuracy in a single wire, where N is the number of orthogonal logic vectors in the base. In the present Letter, we show that the logic hyperspace (product) vectors defined in the introductory paper can be generalized to provide the discrete superposition of 2 N orthogonal system states. This is equivalent to a multi-valued logic system with 2 2 N logic values per wire. This is a similar situation to quantum informatics with N qubits, and hence we introduce the notion of noise-bit. This system has major differences compared to quantum informatics. The noise-based logic system is deterministic and each superposition element is instantly accessible with the high digital accuracy, via a real hardware parallelism, without decoherence and error correction, and without the requirement of repeating the logic operation many times to extract the probabilistic information. Moreover, the states in noise-based logic do not have to be normalized, and non-unitary operations can also be used. As an example, we introduce a string search algorithm which is O ( M ) times faster than Grover's quantum algorithm (where M is the number of string entries), while it has the same hardware complexity class as the quantum algorithm.
---
paper_title: Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states

paper_content:

Article history: A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case (N = 2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/ f , Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart. © 2009 Elsevier B.V. All rights reserved.
---
paper_title: Noise-based logic hyperspace with the superposition of 2N states in a single wire

paper_content:

Abstract In the introductory paper [L.B. Kish, Phys. Lett. A 373 (2009) 911], about noise-based logic, we showed how simple superpositions of single logic basis vectors can be achieved in a single wire. The superposition components were the N orthogonal logic basis vectors. Supposing that the different logic values have “on/off” states only, the resultant discrete superposition state represents a single number with N bit accuracy in a single wire, where N is the number of orthogonal logic vectors in the base. In the present Letter, we show that the logic hyperspace (product) vectors defined in the introductory paper can be generalized to provide the discrete superposition of 2 N orthogonal system states. This is equivalent to a multi-valued logic system with 2 2 N logic values per wire. This is a similar situation to quantum informatics with N qubits, and hence we introduce the notion of noise-bit. This system has major differences compared to quantum informatics. The noise-based logic system is deterministic and each superposition element is instantly accessible with the high digital accuracy, via a real hardware parallelism, without decoherence and error correction, and without the requirement of repeating the logic operation many times to extract the probabilistic information. Moreover, the states in noise-based logic do not have to be normalized, and non-unitary operations can also be used. As an example, we introduce a string search algorithm which is O ( M ) times faster than Grover's quantum algorithm (where M is the number of string entries), while it has the same hardware complexity class as the quantum algorithm.
---
paper_title: Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states

paper_content:

Article history: A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case (N = 2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/ f , Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart. © 2009 Elsevier B.V. All rights reserved.
---
paper_title: Implementing digital logic with sinusoidal supplies

paper_content:

In this paper, a new type of combinational logic circuit realization is presented. Logic values are implemented as sinusoidal signals. Sinusoidal signals of the same frequency are phase shifted by π to destructively interfere with each other, and represent the logic 0 and 1 values of Boolean Logic. These properties of sinusoids can be used to identify a signal without ambiguity. Thus, representing logic values as sinusoidal signals yields a realizable system of logic. The paper presents a logic gate family that can operate using the sinusoidal signals for logic 0 and logic 1 values. Due to orthogonality of sinusoid signals with different frequencies, multiple sinusoids could be transmitted on a single wire. This provides a natural way of implementing multilevel logic. Signals traveling long distances could take advantage of this fact and can share interconnect lines. Recent research in circuit design has made it possible to harvest sinusoidal signals of the same frequency and 180° phase difference from a single resonant clock ring in a distributed manner. Other advantage of such a logic family is its immunity from external additive noise. The experiments in this paper indicate that this paradigm, when used to implement binary valued logic, yields an improvement in switching (dynamic) power.
---
paper_title: Noise-based logic hyperspace with the superposition of 2N states in a single wire

paper_content:

Abstract In the introductory paper [L.B. Kish, Phys. Lett. A 373 (2009) 911], about noise-based logic, we showed how simple superpositions of single logic basis vectors can be achieved in a single wire. The superposition components were the N orthogonal logic basis vectors. Supposing that the different logic values have “on/off” states only, the resultant discrete superposition state represents a single number with N bit accuracy in a single wire, where N is the number of orthogonal logic vectors in the base. In the present Letter, we show that the logic hyperspace (product) vectors defined in the introductory paper can be generalized to provide the discrete superposition of 2 N orthogonal system states. This is equivalent to a multi-valued logic system with 2 2 N logic values per wire. This is a similar situation to quantum informatics with N qubits, and hence we introduce the notion of noise-bit. This system has major differences compared to quantum informatics. The noise-based logic system is deterministic and each superposition element is instantly accessible with the high digital accuracy, via a real hardware parallelism, without decoherence and error correction, and without the requirement of repeating the logic operation many times to extract the probabilistic information. Moreover, the states in noise-based logic do not have to be normalized, and non-unitary operations can also be used. As an example, we introduce a string search algorithm which is O ( M ) times faster than Grover's quantum algorithm (where M is the number of string entries), while it has the same hardware complexity class as the quantum algorithm.
---
paper_title: Decorrelated Neuronal Firing in Cortical Microcircuits

paper_content:

Correlated trial-to-trial variability in the activity of cortical neurons is thought to reflect the functional connectivity of the circuit. Many cortical areas are organized into functional columns, in which neurons are believed to be densely connected and to share common input. Numerous studies report a high degree of correlated variability between nearby cells. We developed chronically implanted multitetrode arrays offering unprecedented recording quality to reexamine this question in the primary visual cortex of awake macaques. We found that even nearby neurons with similar orientation tuning show virtually no correlated variability. Our findings suggest a refinement of current models of cortical microcircuit architecture and function: Either adjacent neurons share only a few percent of their inputs or, alternatively, their activity is actively decorrelated.
---
paper_title: Deterministic multivalued logic scheme for information processing and routing in the brain

paper_content:

Driven by analogies with state vectors of quantum informatics and noise-based logic, we propose a general scheme and elements of neural circuitry for processing and addressing information in the brain. Specifically, we consider random (e.g., Poissonian) trains of finite-duration spikes, and, using the idealized concepts of excitatory and inhibitory synapses, offer a procedure for generating 2^N-1 orthogonal vectors out of N partially overlapping trains ("neuro-bits"). We then show that these vectors can be used to construct 2^(2^N-1)-1 different superpositions which represent the same number of logic values when carrying or routing information. In quantum informatics the above numbers are the same, however, the present logic scheme is more advantageous because it is deterministic in the sense that the presence of a vector in the spike train is detected by an appropriate coincidence circuit. For this reason it does not require time averaging or repeated measurements of the kind used in standard cross-correlation analysis or in quantum computing.
---
paper_title: First spikes in ensembles of human tactile afferents code complex spatial fingertip events

paper_content:

It is generally assumed that primary sensory neurons transmit information by their firing rates. However, during natural object manipulations, tactile information from the fingertips is used faster than can be readily explained by rate codes. Here we show that the relative timing of the first impulses elicited in individual units of ensembles of afferents reliably conveys information about the direction of fingertip force and the shape of the surface contacting the fingertip. The sequence in which different afferents initially discharge in response to mechanical fingertip events provides information about these events faster than the fastest possible rate code and fast enough to account for the use of tactile signals in natural manipulation.
---
paper_title: Neurons Tune to the Earliest Spikes Through STDP

paper_content:

Spike timing-dependent plasticity (STDP) is a learning rule that modifies the strength of a neuron's synapses as a function of the precise temporal relations between input and output spikes. In many brains areas, temporal aspects of spike trains have been found to be highly reproducible. How will STDP affect a neuron's behavior when it is repeatedly presented with the same input spike pattern? We show in this theoretical study that repeated inputs systematically lead to a shaping of the neuron's selectivity, emphasizing its very first input spikes, while steadily decreasing the postsynaptic response latency. This was obtained under various conditions of background noise, and even under conditions where spiking latencies and firing rates, or synchrony, provided conflicting informations. The key role of first spikes demonstrated here provides further support for models using a single wave of spikes to implement rapid neural processing.
---
paper_title: Instantaneous noise-based logic

paper_content:

We show two universal, Boolean, deterministic logic schemes based on binary noise timefunctions that can be realized without time-averaging units. The first scheme is based on a new bipolar random telegraph wave scheme and the second one makes use of the recent noise-based logic which is conjectured to be the brain's method of logic operations [Physics Letters A 373 (2009) 2338-2342]. Error propagation and error removal issues are also addressed.
---
paper_title: Instantaneous noise-based logic

paper_content:

We show two universal, Boolean, deterministic logic schemes based on binary noise timefunctions that can be realized without time-averaging units. The first scheme is based on a new bipolar random telegraph wave scheme and the second one makes use of the recent noise-based logic which is conjectured to be the brain's method of logic operations [Physics Letters A 373 (2009) 2338-2342]. Error propagation and error removal issues are also addressed.
---
paper_title: Instantaneous noise-based logic

paper_content:

We show two universal, Boolean, deterministic logic schemes based on binary noise timefunctions that can be realized without time-averaging units. The first scheme is based on a new bipolar random telegraph wave scheme and the second one makes use of the recent noise-based logic which is conjectured to be the brain's method of logic operations [Physics Letters A 373 (2009) 2338-2342]. Error propagation and error removal issues are also addressed.
---
paper_title: Instantaneous noise-based logic

paper_content:

We show two universal, Boolean, deterministic logic schemes based on binary noise timefunctions that can be realized without time-averaging units. The first scheme is based on a new bipolar random telegraph wave scheme and the second one makes use of the recent noise-based logic which is conjectured to be the brain's method of logic operations [Physics Letters A 373 (2009) 2338-2342]. Error propagation and error removal issues are also addressed.
---
paper_title: Deterministic multivalued logic scheme for information processing and routing in the brain

paper_content:

Driven by analogies with state vectors of quantum informatics and noise-based logic, we propose a general scheme and elements of neural circuitry for processing and addressing information in the brain. Specifically, we consider random (e.g., Poissonian) trains of finite-duration spikes, and, using the idealized concepts of excitatory and inhibitory synapses, offer a procedure for generating 2^N-1 orthogonal vectors out of N partially overlapping trains ("neuro-bits"). We then show that these vectors can be used to construct 2^(2^N-1)-1 different superpositions which represent the same number of logic values when carrying or routing information. In quantum informatics the above numbers are the same, however, the present logic scheme is more advantageous because it is deterministic in the sense that the presence of a vector in the spike train is detected by an appropriate coincidence circuit. For this reason it does not require time averaging or repeated measurements of the kind used in standard cross-correlation analysis or in quantum computing.
---
paper_title: End of Moore's law: thermal (noise) death of integration in micro and nano electronics

paper_content:

The exponential growth of memory size and clock frequency in computers has a great impact on everyday life. The growth is empirically described by Moore’s law of miniaturization. Physical limitations of this growth would have a serious impact on technology and economy. A thermodynamical effect, the increasing thermal noise voltage (Johnson–Nyquist noise) on decreasing characteristic capacitances, together with the constrain of using lower supply voltages to keep power dissipation manageable on the contrary of increasing clock frequency, has the potential to break abruptly Moore’s law within 6–8 years, or earlier.  2002 Elsevier Science B.V. All rights reserved.
---
paper_title: Computation using Noise-based Logic: Efficient String Verification over a Slow Communication Channel

paper_content:

Utilizing the hyperspace of noise-based logic, we show two string verification methods with low communication complexity. One of them is based on continuum noise-based logic. The other one utilizes noise-based logic with random telegraph signals where a mathematical analysis of the error probability is also given. The last operation can also be interpreted as computing universal hash functions with noise-based logic and using them for string comparison. To find out with 10^-25 error probability that two strings with arbitrary length are different (this value is similar to the error probability of an idealistic gate in today's computer) Alice and Bob need to compare only 83 bits of the noise-based hyperspace.
---

Title: Noise-based deterministic logic and computing: a brief survey

Section 1: Introduction: Errors (noise), speed (bandwidth) and power dissipation in computers
Description 1: Provide a summary of the ongoing efforts in the development of noise-based deterministic multivalued logic schemes, emphasizing the problems with current microprocessors and the search for non-conventional computing alternatives.

Section 2: Inspiration of noise-based logic: the brain
Description 2: Discuss how biological systems, particularly the brain, utilize noise as an information carrier, and how this inspires the construction of deterministic high-performance logic schemes using noise.

Section 3: Noise-based logic with continuum noise
Description 3: Analyze the logic schemes utilizing continuum noise, including the design and advantages of such systems, and their relevance to nanoelectronics.

Section 4: Some of the advantages and disadvantages of continuum noise-based logic
Description 4: Enumerate the potential benefits and drawbacks of continuum noise-based logic, emphasizing aspects like energy consumption, robustness against errors, and potential for multivalued logic.

Section 5: Noise-based logic with random spikes
Description 5: Explore the deterministic logic schemes using random spike trains, conjectured to model brain logic, and examine how set-theoretical operations can create multidimensional Hilbert spaces.

Section 6: Instantaneous noise-based logic
Description 6: Detail Boolean logic schemes based on noise that do not require a time-averaging process, proving their universality and potential for fast, low power consumption operations in special-purpose engines.

Section 7: Instantaneous logic by random telegraph waves
Description 7: Discuss the implementation of instantaneous noise-based logic using random telegraph waves, illustrating the realization of AND and NOT gates.

Section 8: Instantaneous logic based on random spike sequences
Description 8: Describe the binary version of brain logic based on random spike sequences and how logic functions like AND and NOT gates can be implemented using orthon elements.

Section 9: Efficient string verification by instantaneous noise-based logic
Description 9: Explain two methods for string verification with low communication complexity based on noise-based hyperspace, and discuss how these methods compare to traditional digital gates.

Section 10: Final remarks
Description 10: Reflect on the potential applications of noise-based logic in hybrid computing engines, combining classical computing with noise-based logic for enhanced performance in intelligent systems.