 Noisebased logic

Noisebased logic (NBL)^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[8]} is a new class of multivalued deterministic logic schemes where the logic values and bits are represented by different realizations of a stochastic process. The scheme is inspired by the brain where the neural signals are stochastic spike sequences.
Contents
The noisebased logic space and hyperspace
The logic values are represented by multidimensional vectors (orthogonal functions) and their superposition, where the orthogonal basis vectors are independent noises. By the proper combination (products or settheoretical products) of basisnoises, which are called noisebit, a logic hyperspace can be constructed with D(N) = 2^{N} number of dimensions, where N is the number of noisebits. Thus N noisebits in a single wire correspond to a system of 2^{N} classical bits that can express 2^{2N} different logic values. Independent realizations of a stochastic process of zero mean have zero crosscorrelation with each other and with other stochastic processes of zero mean. Thus the basis noise vectors are orthogonal not only to each other but they and all the noisebased logic states (superpositions) are orthogonal also to any background noises in the hardware. Therefore, the noisebased logic concept is robust against background noises, which is a property that can potentially offer a high energyefficiency.
The types of signals used in noisebased logic
In the paper,^{[3]} where noisebased logic was first introduced, generic stochasticprocesses with zero mean were proposed and a system of orthogonal sinusoidal signals were also proposed as a deterministicsignal version of the logic system. The mathematical analysis about statistical errors and signal energy was limited to the cases of Gaussian noises and superpositions as logic signals in the basic logic space and their products and superpositions of their products in the logic hyperspace (see also.^{[4]} In the subsequent brain logic scheme,^{[5]} the logic signals were (similarly to neural signals) unipolar spike sequences generated by a Poisson process, and settheoretical unifications (superpositions) and intersections (products) of different spike sequences. Later, in the instantaneous noisebased logic schemes^{[6]}^{[7]} and computation works,^{[8]} random telegraph waves (periodic time, bipolar, with fixed absolute value of amplitude) were also utilized as one of the simplest stochastic processes available for NBL. With choosing unit amplitude and symmetric probabilities, the resulting randomtelegraph wave has 0.5 probability to be in the +1 or in the 1 state which is held over the whole clock period.
The noisebased logic gates
Noisebased logic gates can be classified according to the method the input identifies the logic value at the input. The first gates^{[3]}^{[4]} analyzed the statistical correlations between the input signal and the reference noises. The advantage of these is the robustness against background noise. The disadvantage is the slow speed and higher hardware complexity. The instantaneous logic gates^{[5]}^{[6]}^{[7]} are fast, they have low complexity but they are not robust against background noises. With either neural spike type signals or with bipolar randomtelegraph waves of unity absolute amplitude, and randomness only in the sign of the amplitude offer very simple instantaneous logic gates. Then linear or analog devices unnecessary and the scheme can operate in the digital domain. However, whenever instantaneous logic must be interfaced with classical logic schemes, the interface must use correlatorbased logic gates for an errorfree signal.^{[6]}
Universality of noisebased logic
All the noisebased logic schemes listed above are proven universal.^{[3]}^{[6]}^{[7]} The papers typically produce the NOT and the AND gates to prove universality, because having both of them is a satisfactory condition for the universality of a Boolean logic.
Computation by noisebased logic
The string verification work^{[8]} over a slow communication channel shows a powerful computing application where the methods is inherently based on calculating the hash function. The scheme is based on random telegraph waves and it is mentioned in the paper^{[8]} that the authors intuitively conclude that the intelligence of the brain is using similar operations to make a reasonably good decision based on a limited amount of information. It is also interesting to note that the superposition of the first D(N) = 2^{N} integer numbers can be produced with only 2N operations, which the authors call "Achilles ankle operation" in the paper.^{[4]}
Computer chip realization of noisebased logic
Preliminary schemes have already been published^{[8]} to utilize noisebased logic in practical computers. However, it is obvious from these papers that this young field has yet a long way to go to be seen in everyday applications.
References
 ^ David Boothroyd (22 February 2011). "Cover Story: What's this noise all about?". New Electronics. http://www.newelectronics.co.uk/electronicstechnology/coverstorywhatsallthisnoiseabout/31678/.
 ^ Justin Mullins (7 October 2010). "Breaking the Noise Barrier: Enter the phonon computer". New Scientist. http://amkon.net/showthread.php/29622BreakingthenoisebarrierEnterthephononcomputer.
 ^ ^{a} ^{b} ^{c} ^{d} Laszlo B. Kish (2009). "Noisebased logic: Binary, multivalued, or fuzzy, with optional superposition of logic states". Physics Letters A 373 (10): 911–918. arXiv:0808.3162. doi:10.1016/j.physleta.2008.12.068.
 ^ ^{a} ^{b} ^{c} ^{d} Laszlo B. Kish; Sunil Khatri; Swaminathan Sethuraman (2009). "Noisebased logic hyperspace with the superposition of 2^N states in a single wire". Physics Letters A 373 (22): 1928–1934. arXiv:0901.3947. doi:10.1016/j.physleta.2009.03.059.
 ^ ^{a} ^{b} ^{c} Sergey M. Bezrukov; Laszlo B. Kish (2009). "Deterministic multivalued logic scheme for information processing and routing in the brain". Physics Letters A 373 (27–28): 2338–2342. arXiv:0902.2033. doi:10.1016/j.physleta.2009.04.073.
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} Laszlo B. Kish; Sunil Khatri; Ferdinand Peper (2010). "Instantaneous noisebased logic". Fluctuation and Noise Letters 09 (4): 323–330. arXiv:1004.2652. doi:10.1142/S0219477510000253.
 ^ ^{a} ^{b} ^{c} ^{d} Peper, Ferdinand; Kish, Laszlo B. (2011). "Instantaneous, NonSqueezed, NoiseBased Logic". Fluctuation and Noise Letters 10 (2): 231. doi:10.1142/S0219477511000521. http://www.worldscinet.com/fnl/10/1002/openaccess/S0219477511000521.pdf.
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} Laszlo B. Kish; Sunil Khatri; Tamas Horvath (2010). "Computation using Noisebased Logic: Efficient String Verification over a Slow Communication Channel". The European Physical Journal B 79: 85–90. arXiv:1005.1560. doi:10.1140/epjb/e201010399x.
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