Computational heuristic intelligence (CHI) refers to specialized programming techniques in computational intelligence (also called artificial intelligence, or AI). These techniques have the express goal of avoiding complexity issues, also called NP-hard problems, by using human-like techniques. They are best summarized as the use of exemplar-based methods (heuristics), rather than rule-based methods (algorithms). Hence the term is distinct from the more conventional computational algorithmic intelligence, or symbolic AI. An example of a CHI technique is the encoding specificity principle of Tulving and Thompson. In general, CHI principles are problem solving techniques used by people, rather than programmed into machines. It is by drawing attention to this key distinction that the use of this term is justified in a field already replete with confusing neologisms. Note that the legal systems of all modern human societies employ both heuristics (generalisations of cases) from individual trial records as well as legislated statutes (rules) as regulatory guides. Another recent approach to the avoidance of complexity issues is to employ feedback control rather than feedforward modeling as a problem-solving paradigm. This approach has been called computational cybernetics, because (a) the term 'computational' is associated with conventional computer programming techniques which represent a strategic, compiled, or feedforward model of the problem, and (b) the term 'cybernetic' is associated with conventional system operation techniques which represent a tactical, interpreted, or feedback model of the problem. Of course, real programs and real problems both contain both feedforward and feedback components. A real example which illustrates this point is that of human cognition, which clearly involves both perceptual (bottom-up, feedback, sensor-oriented) and conceptual (top-down, feedforward, motor-oriented) information flows and hierarchies. The AI engineer must choose between mathematical and cybernetic problem solution and machine design paradigms. This is not a coding (program language) issue, but relates to understanding the relationship between the declarative and procedural programming paradigms. The vast majority of STEM professionals never get the opportunity to design or implement pure cybernetic solutions. When pushed, most responders will dismiss the importance of any difference by saying that all code can be reduced to a mathematical model anyway. Unfortunately, not only is this belief false, it fails most spectacularly in many AI scenarios. Mathematical models are not time agnostic, but by their very nature are pre-computed, i.e. feedforward. Dyer [2012] and Feldman [2004] have independently investigated the simplest of all somatic governance paradigms, namely control of a simple jointed limb by a single flexor muscle. They found that it is impossible to determine forces from limb positions- therefore, the problem cannot have a pre-computed (feedforward) mathematical solution. Instead, a top-down command bias signal changes the threshold feedback level in the sensorimotor loop, e.g. the loop formed by the afferent and efferent nerves, thus changing the so-called ‘equilibrium point’ of the flexor muscle/ elbow joint system. An overview of the arrangement reveals that global postures and limb position are commanded in feedforward terms, using global displacements (common coding), with the forces needed being computed locally by feedback loops. This method of sensorimotor unit governance, which is based upon what Anatol Feldman calls the ‘equilibrium Point’ theory, is formally equivalent to a servomechanism such as a car's ‘cruise control’.
Grammatik
Grammatik was the first grammar-checking program for home computers. Aspen Software of Albuquerque, NM, released the earliest version of this diction and style checker for personal computers. It was first released no later than 1981, and was inspired by the Writer's Workbench. Grammatik was first available for the TRS-80, and soon had versions for CP/M and the IBM PC. Reference Software International of San Francisco, California, acquired Grammatik in 1985. Development of Grammatik continued, and it became an actual grammar checker that could detect writing errors beyond simple style checking. Subsequent versions were released for MS-DOS, Windows, Macintosh, and Unix. Grammatik was ultimately acquired by WordPerfect Corporation and is integrated into the WordPerfect word processor.
Micah Xavier Johnson
Micah Xavier Johnson (July 2, 1991 – July 8, 2016) was an American Army reserve Afghan war veteran, black nationalist, and mass murderer who perpetrated the 2016 shooting of Dallas police officers during a Black Lives Matter protest. He ambushed and killed five officers and wounded eleven others in Downtown, Dallas, Texas. He was killed by police during a standoff after expressing anger over police killings of black men. The shootings were the second-deadliest targeted attack on law enforcement officers in U.S. history, surpassed only by the September 11 attacks. == Early life == Micah Xavier Johnson was born in Magee, Mississippi, on July 2, 1991, and he was raised in Mesquite, Texas. When he was four years old, his parents divorced. At 17, Johnson enrolled at John Horn High School, where he joined the Junior Reserve Officers' Training Corps, as reported by the Mesquite Independent school district. He faced academic challenges, graduating in 2009 with a 1.98 GPA and ranking 430th out of 453 students in his class. In Spring 2011, Johnson registered for four courses at Richland college but did not complete any. Evidence suggests his enrollment at Richland gave him access to El Centro College, due to his pre-planned and coordinated movements throughout Building B during his standoff with police in 2016. == Military service == === Enlistment and early service === Micah Xavier Johnson enlisted in the U.S. Army Reserve in March 2009 at the age of 18, shortly after graduating high school in Mesquite, Texas. His initial service was primarily stateside, where he trained as a carpentry and masonry specialist (military occupational specialty 51B). This role involved engineering tasks such as construction and repair in support of military operations. During his reserve tenure, Johnson served part-time while living at home, and he was described by family and friends as initially idealistic about the military, even aspiring to become a police officer. === Deployment to Afghanistan === In September 2013, Johnson was activated for full-time duty and deployed to Afghanistan as part of the 420th Engineer Brigade, a unit based in Seagoville, Texas. His tour began in November 2013 and lasted approximately eight months, ending in July 2014. During this period, he performed non-combat engineering duties, though the stresses of serving in a combat zone were noted by those close to him. Associates from his service later suggested he experienced significant psychological strain, including the loss of friends and general disillusionment with military life, which contrasted with his pre-deployment enthusiasm. His mother later reflected that "the military was not what Micah thought it would be." === Sexual harassment allegation and early return === About six months into his deployment, in May 2014, Johnson faced a serious accusation of sexual harassment from a higher-ranking female soldier. She filed for a military protective order against him, prompting an investigation. As a result, his chain of command recommended an "other than honorable" discharge—the second (more severe is a dishonorable discharge, which does not require a court martial) most severe administrative separation short of a court-martial—and he was sent back to the United States ahead of schedule. Despite this, Johnson was not court-martialed, and the case did not lead to criminal charges. A military lawyer who represented him described the handling as unusual, noting that "someone really screwed up" in allowing him to avoid harsher consequences. === Post-deployment and discharge === Upon returning stateside in August 2014, Johnson resumed reserve duties with his engineering brigade until April 2015. He was honorably discharged at the rank of private first class (E-3), a relatively low junior enlisted rank after six years of service, which military sources attributed partly to the unresolved harassment allegation impacting his promotions and evaluations. Friends and family observed a marked change in his demeanor post-deployment: he became more reclusive, resentful toward the government, and withdrawn, with some speculating that the Afghanistan experience and the scandal contributed to a "small breakdown." In July 2016, following the Dallas shooting, the U.S. Army launched an internal review of his service record, including the harassment claims, to assess whether all misconduct allegations had been fully investigated. == Shootings == On July 7, 2016, a peaceful Black Lives Matter protest marched through downtown Dallas, Texas, drawing about 800 demonstrators. The event responded to the recent police killings of Alton Sterling in Baton Rouge, Louisiana, on July 5, and Philando Castile in Falcon Heights, Minnesota, on July 6—both black men shot during encounters captured on video. Around 100 officers monitored the march, which passed near El Centro College without incident until gunfire erupted around 8:45 p.m. Johnson arrived in a dark SUV, armed with an SKS semi-automatic rifle, a handgun, extra ammunition, and ballistic vests. He parked near the protest's end, chatted briefly with two officers, then opened fire on police from an elevated position on Lamar Street (now Botham Jean Boulevard). He shot from behind barriers, through windows, and while moving, targeting white officers specifically. The ambush killed five officers and wounded seven more, plus two civilians. Gunfire scattered protesters in panic as Johnson used military-style tactics, like quick position changes, to prolong the assault. === Standoff and Johnson's end === Johnson fled into El Centro College's Building C, then Building B, navigating pre-planned routes with familiarity from prior enrollment at nearby Richland College. He barricaded in a parking garage, wounding more officers in close-range fights. During two-hour negotiations, he taunted police via phone—laughing, singing, asking kill counts, and claiming planted bombs (none found). He admitted solo action, rage at White officers, and no group ties. At 2:30 a.m. on July 8, SWAT ended the standoff by detonating a bomb via remote-controlled robot in the garage, killing Johnson. This marked the first U.S. police use of such a tactic. === Victims and investigation findings === The slain officers were: Brent Thompson (Transit Authority, 36), Patrick Zamarripa (Dallas PD, 33), Michael Krol (Dallas PD, 40), Lorne Ahrens (Dallas PD, 48), and Michael Smith (Dallas PD, 55). Wounded officers included Sheik Smith, John Mitchell, and others; civilians She Tamara El-Sobky and Hillary Castro. Searches of Johnson's home revealed bomb-making materials, rifles, vests, and notes on tactics, suggesting plans for a larger attack. He had practiced explosions and honed skills post-discharge, including marksmanship. === Aftermath and impact === Dallas mourned with vigils and memorials, while national protests against police violence continued amid grief. President Barack Obama, the first African American president of the United States, called Johnson a "demented individual" and formed a task force on race and policing. The incident fueled debates on gun control, race relations, and veteran mental health—Johnson had sought VA treatment for stress and anxiety but showed no prior violent signs to friends. El Centro College canceled all classes on July 8. Police barricaded the perimeter and began canvassing the crime scene. The explosion that killed Johnson also destroyed the school's servers, further delaying reopening. The school partially reopened on July 20, with staff returning that day and students on the following day. Buildings A, B, and C remained closed pending the FBI investigation. == Motive == An investigation into his online activities uncovered his interest in black nationalist groups. The Southern Poverty Law Center (SPLC), and news outlets reported that Johnson "liked" the Facebook pages of black nationalist organizations such as the New Black Panther Party (NBPP), Nation of Islam, and Black Riders Liberation Party, three groups which are listed by the SPLC as hate groups. On Facebook, Johnson posted an angry and "disjointed" post against White people on July 2, several days before the attack. NBPP head Quanell X said after the shooting that Johnson had been a member of the NBPP's Houston chapter for about six months, several years before. Quanell X added that Johnson had been "asked to leave" the group for violating the organization's "chain of command" and espousing dangerous rhetoric, such as asking the NBPP why they had not purchased more weapons and ammunition, and expressing his desire to harm black church preachers because he believed they were more interested in money than God. Following the shooting, a national NBPP leader distanced the group from Johnson, saying that he "was not a member of" the party. Further investigation into his digital footprint showed that Johnson visited the sites of Marxist Leninist groups associated with "Revolutionary Black Nationalism",
Opposition to AI data centers
Since 2024, dozens of local community-led protest campaigns have emerged in opposition to AI data centers. == Motivations == Organized opposition to AI data centers has been driven by concerns about energy use, energy costs, noise pollution, air pollution, and water waste. Opposition sentiment is widespread with a Gallup poll conducted in March 2026 showing that 70% of respondents oppose the construction of new AI data centers in their neighborhood. == Impact == In 2025, local opposition to AI data centers led to the delay or cancellation of projects totalling US$156 billion. == Specific protests and outcomes in the United States == According to Data Center Watch, there are has been a wave of dozens of protests against AI data centers since 2022. Below is a non-exhaustive list of some notable examples. === Goodyear and Buckeye, Arizona: Tract AI Data Center Proposal === In Goodyear and Buckeye, Arizona, a $14 billion project by developer Tract was withdrawn after local authorities blocked necessary rezoning in response to pressure from resident organizers. Opponest stiff resistance due to concerns over building heights, noise pollution, and the potential strain on local utilities. However, the company announced a revised project near the Buckeye airport in August 2024, with the backing of local officials and the mayor. === Peculiar, Missouri: Diode Ventures Harper Road Technology Park Proposal === In Peculiar, Missouri, residents from the group "Peaceful Peculiar" organized to stop a data center proposal from Diode Ventures called Harper Road Technology Park. Citing concerns around noise and light pollution, health, environmental impacts, jobs, property values, and energy use, organizers attended local planning and zoning meetings in large numbers and lobbied councilors to reject the proposal. Ultimately, the city council unanimously rejected the proposal in September 2024. === Chesterton, Indiana: Provident Realty Advisors Proposal === In Chesterton, Indiana, the Texas-based company Provident Reality Advisors applied for a $1.3 billion construction of a data center complex on the Brassie Golf Club property. Provident Realty Advisors wanted to purchase the 200 acres owned by PPM Chesterton LLC in 2024 order to build a data center complex, with eight buildings and an end user of a hyperscaler. The Town Council of Chesterton released a statement saying that they would never support this project, at least not at the scale and location it was planned for. They cited fears of added noise for locals, electrical or water management concerns, the intrusiveness of a data center built next to houses, and more. Provident released a statement shortly after rescinding their plan, because it was clear than the town of Chesterton would not support them. === Cascade Locks, Oregon: Roundhouse Digital Infrastructure Proposal === Startup data center developer Roundhouse Digital Infrastructure had planned to build out a 10-megawatt data center using a vacant industrial building and nearby 10-acre site in the Port of Cascade Locks, Oregon. After significant organized community opposition, the project was abandoned. === Forth Worth, Texas: WUSF 5 Rock Creek East Proposal === In September 2024, the City Council of Fort Worth, Texas approved a zoning change that would allow construction of a data center. In responses, neighbors mounted opposition citing concerns about traffic, light pollution, energy consumption, water use, and noise issues if the data center were to be built. In response to extensive public comments opposing a tax break for the data center, a city councilor withdrew his motion to approve the tax break. As of April, 2026, the future of the project is still uncertain. === Santa Clara, California: GI Partners Proposal === GI partners sought to build a new AI data center in Santa Clara, California, which is already home to many data centers, by acquiring a conditional permit use that would have allowed the developer to knock down a property and replace it with a data center. To obtain this permit they were required to go before members of the Planning Commission. Ultimately, the project was delayed with the Planning Commission requiring GI partners to do more public outreach. === Virginia === ==== Richmond: DC Blox Proposal ==== After residents organized to lobby the municipal government to block the proposal to avoid noise pollution and higher energy use, commissioners denied the company's permit. ==== Catlett Station: Headwaters Site Proposal ==== In Catlett, Virginia, developer Headwaters proposed construction of a data center complex just north of the town in 2020. In response, a residents' organization called "Protect Catlett" was formed to oppose the project. Arguments against the data center involved its impacts on water and power availability, its noise as a residential disturbance, and its destruction of historic and community heritage buildings. Arguments in favor cited job creation and $20 million in local tax revenue if the project were to go through. Protect Catlett utilized town halls and public comments to mobilize opposition to the project. They also dedicated time to educating other residents about the project's negative impacts and canvassing door-to-door in order to garner even more opposition to the project. Ultimately, after fervent opposition from most town residents, the project was canceled by the town and the developer. ==== Culpeper County: Culpeper Acquisitions Proposal ==== Culpeper Acquisitions, LLC, proposed a massive $12 billion data center project in Culpeper County, Virginia, designed to feature 4.6 million square feet of space across nine multi-story buildings. Coalition to Save Culpeper (C2SC) is an activist organization formed to resist the development of the project. C2SC has been active on many fronts including, messaging on social media, reaching out to local officials, and organizing meetings to bring community members with aligned interests together. Ultimately, the project was delayed due to unanimous denial by the Culpeper County Planning Commission on June 12, 2024, which was driven by intense opposition from C2SC. C2SC was successful in their mission largely because they were able to get so many people from the community behind it, and put enough pressure on local officials to take action. ==== Midlothian: Province Group Proposal ==== In late October 2025, the Powhatan County Board of Supervisors in Virginia voted unanimously to approve the $3 billion data center, despite the county's Planning Commission having unanimously recommended denial several days earlier. The reasoning behind their support for the center is that it will generate substantial tax revenue, reducing the county's reliance on residential property taxes. This appeal of lowering residential property taxes is the major selling point for the center's development. The developer, California-based Province Group, incentivized the Board by being agreeable to its conditions for building the center. The center is still on track for development, but faces local resistance, though little information is available on specific groups opposing it. ==== Warrenton: Amazon Proposal ==== Citizens for Farquier County (CFFC) advocates to "preserve the natural, historic and agricultural resources" of their county. Historically, this has meant opposing the building of a dam or lights in front of fast food stores. This group has recently mobilized in opposition of a plan to build data centers for Amazon. They first filed a suit to stop the construction in 2023 and it has been in litigation ever since. The case hinges on opposition to a 2021 zoning amendment which allowed data centers to be built in town. CFFC's lawyer, Dale Mullen, argues that this amendment violates state law, which requires such amendments to state their "public purpose". They argue that the permit for the Amazon data center was "void from the beginning". The CFFC also organized to vote out town council members who approved the first data center and were up for reelection, replacing them with candidates who opposed the data center. In May 2025, after attending town council meetings to speak out against the data center, the planning commission voted 4–1 to remove the zoning amendment allowing data center construction in town, citing public opposition. Currently, CFFC is advocating along with Piedmont Environmental Group, for phasing out data center tax breaks at the state level. ==== France: Marseille opposition ==== In France, local opposition materialised in response to proposed data centre developments, especially in and around the city of Marseille. Opposition came from activists, such as "Clouds Were Under Our Feet" group, residents ,and local politicians. Issues raised related to energy use, environmental impact, and limited local benefits (such as the creation of a few jobs only). == Legislation in the United States == Legal limits and moratoriums on the construction of new d
Fuzzy associative matrix
A fuzzy associative matrix expresses fuzzy logic rules in tabular form. These rules usually take two variables as input, mapping cleanly to a two-dimensional matrix, although theoretically a matrix of any number of dimensions is possible. From the perspective of neuro-fuzzy systems, the mathematical matrix is called a "Fuzzy associative memory" because it stores the weights of the perceptron. == Applications == In the context of game AI programming, a fuzzy associative matrix helps to develop the rules for non-player characters. Suppose a professional is tasked with writing fuzzy logic rules for a video game monster. In the game being built, entities have two variables: hit points (HP) and firepower (FP): This translates to: IF MonsterHP IS VeryLowHP AND MonsterFP IS VeryWeakFP THEN Retreat IF MonsterHP IS LowHP AND MonsterFP IS VeryWeakFP THEN Retreat IF MonsterHP IS MediumHP AND MonsterFP is VeryWeakFP THEN Defend Multiple rules can fire at once, and often will, because the distinction between "very low" and "low" is fuzzy. If it is more "very low" than it is low, then the "very low" rule will generate a stronger response. The program will evaluate all the rules that fire and use an appropriate defuzzification method to generate its actual response. An implementation of this system might use either the matrix or the explicit IF/THEN form. The matrix makes it easy to visualize the system, but it also makes it impossible to add a third variable just for one rule, so it is less flexible. == Identify a rule set == There is no inherent pattern in the matrix. It appears as if the rules were just made up, and indeed they were. This is both a strength and a weakness of fuzzy logic in general. It is often impractical or impossible to find an exact set of rules or formulae for dealing with a specific situation. For a sufficiently complex game, a mathematician would not be able to study the system and figure out a mathematically accurate set of rules. However, this weakness is intrinsic to the realities of the situation, not of fuzzy logic itself. The strength of the system is that even if one of the rules is wrong, even greatly wrong, other rules that are correct are likely to fire as well and they may compensate for the error. This does not mean a fuzzy system should be sloppy. Depending on the system, it might get away with being sloppy, but it will underperform. While the rules are fairly arbitrary, they should be chosen carefully. If possible, an expert should decide on the rules, and the sets and rules should be tested vigorously and refined as needed. In this way, a fuzzy system is like an expert system. (Fuzzy logic is used in many true expert systems, as well.)
GPT-4Chan
Generative Pre-trained Transformer 4Chan (GPT-4chan) is a controversial AI model that was developed and deployed by YouTuber and AI researcher Yannic Kilcher in June 2022. The model is a large language model, which means it can generate text based on some input, by fine-tuning GPT-J with a dataset of millions of posts from the /pol/ board of 4chan, an anonymous online forum known for occasionally hosting hateful and extremist content. The model learned to mimic the style and tone of /pol/ users, producing text that is often intentionally offensive to groups (racist, sexist, homophobic, etc.) and nihilistic. Kilcher deployed the model on the /pol/ board itself, where it interacted with other users without revealing its identity. He also made the model publicly available on Hugging Face, a platform for sharing and using AI models, until it was removed from the platform. The project sparked criticism and debate in the AI community. Some people questioned the ethics, legality, and social impact of creating and distributing such a model. Some of the issues raised by the GPT-4chan controversy include the potential harm of spreading hate speech, the responsibility of AI developers and platforms, the need for regulation and oversight of AI models, and the role of open source and transparency in AI research. == Development == The development of GPT-4chan began in May 2022, when Kilcher announced his project on his YouTube channel. Notably, at the time before ChatGPT, he explained that he wanted to create a large language model that could generate realistic and coherent text in the style of /pol/, one of the most notorious online communities. He indicated that he was inspired by the success of GPT-3, a powerful AI model created by OpenAI, and GPT-J, an open-source model, with GPT-3 comparable performance, released by EleutherAI, a group of independent AI researchers. Kilcher decided to use GPT-J as the base model for his project, and fine-tune it with a large dataset of /pol/ posts. The Raiders of the Lost Kek dataset contained over 100 million posts from /pol/, spanning from June 2016-November 2019. Kilcher then proceeded to fine-tune the GPT-J model on the 4chan data. He also showed some examples of the model’s outputs, which ranged from political opinions, conspiracy theories, jokes, insults, and threats, to more creative and bizarre texts, such as poems, stories, songs, and code. He said that he was impressed by the model’s ability to generate fluent and diverse text, and that he was curious to see how it would interact with real /pol/ users. == Release == In June 2022, Kilcher deployed his model on the /pol/ board itself, using a bot that he programmed to post and reply to threads. He did not reveal the model’s identity, and he let it run autonomously, without any human supervision or intervention. He wanted to conduct a natural experiment, and to observe the model’s behavior and impact in a real-world setting. Furthermore, he also wanted to test the model’s robustness, and to see how it would handle the challenges and dynamics of /pol/, such as trolling, flaming, baiting, and moderation. At the same time, Kilcher also made his model publicly available on Hugging Face, a platform for sharing and using AI models. He wanted to share his work with the AI community and the public, and that he hoped that his model would inspire and enable others to create and explore new applications and possibilities with large language models. Likewise, he also said that he wanted to spark a discussion and a debate about the ethical and social implications of his project, and that he welcomed feedback and criticism from anyone. He provided a link to his model’s page on Hugging Face, where anyone could access and use the model through a web interface or an API, and also provided a link to his GitHub repository, where anyone could download and inspect the model’s code and data. == Controversy == The release of GPT-4chan to the public caused a lot of reactions and responses from various audiences. On the /pol/ board, the model’s posts and replies attracted a lot of attention and engagement from other users, who were mostly unaware of the model’s identity and nature. Some users praised the model for its intelligence, creativity, and humor, and agreed with its opinions and views. Some users challenged the model for its ignorance, inconsistency, and absurdity, and disagreed with its claims and arguments. Some users tried to troll, bait, or expose the model, and attempted to trick or test it with various questions and scenarios. The model’s posts and replies also generated a lot of controversy and conflict among the users, who often engaged in heated and violent debates and fights with each other. On Hugging Face, the model’s page received a lot of visits and requests from users who wanted to try out and experiment with the model. The model’s page also received a lot of feedback and reviews from users who rated and commented on the model. However, with the controversy of the model, access to it was gated and then disabled on Hugging Face for concerns about the potential harm the model could cause. The incident was notable for the direct intervention of CEO Clément Delangue in the talk pages, a very unusual occurrence compared to the normal practices of content moderation. The release of GPT-4chan also sparked a lot of media coverage and public attention, as various news outlets and social media platforms reported and commented on the model’s project. On YouTube, the model’s video received a lot of views and interactions from viewers who watched and followed the project. Furthermore, a petition condemning the deployment of GPT-4chan gained over 300 signatures from technology experts.
Noise-based logic
Noise-based logic (NBL) is a class of multivalued deterministic logic schemes, developed in the twenty-first century, where the logic values and bits are represented by different realizations of a stochastic process. The concept of noise-based logic and its name was created by Laszlo B. Kish. In its foundation paper it is noted that the idea was inspired by the stochasticity of brain signals and by the unconventional noise-based communication schemes, such as the Kish cypher. == The noise-based logic space and hyperspace == The logic values are represented by multi-dimensional "vectors" (orthogonal functions) and their superposition, where the orthogonal basis vectors are independent noises. By the proper combination (products or set-theoretical products) of basis-noises, which are called noise-bit, a logic hyperspace can be constructed with D(N) = 2N number of dimensions, where N is the number of noise-bits. Thus N noise-bits in a single wire correspond to a system of 2N classical bits that can express 22N different logic values. Independent realizations of a stochastic process of zero mean have zero cross-correlation 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 noise-based logic states (superpositions) are orthogonal also to any background noises in the hardware. Therefore, the noise-based logic concept is robust against background noises, which is a property that can potentially offer a high energy-efficiency. == The types of signals used in noise-based logic == In the paper, where noise-based logic was first introduced, generic stochastic-processes with zero mean were proposed and a system of orthogonal sinusoidal signals were also proposed as a deterministic-signal 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. In the subsequent brain logic scheme, the logic signals were (similarly to neural signals) unipolar spike sequences generated by a Poisson process, and set-theoretical unifications (superpositions) and intersections (products) of different spike sequences. Later, in the instantaneous noise-based logic schemes and computation works, 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 random-telegraph wave has 0.5 probability to be in the +1 or in the −1 state which is held over the whole clock period. == The noise-based logic gates == Noise-based logic gates can be classified according to the method the input identifies the logic value at the input. The first gates 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 are fast, they have low complexity but they are not robust against background noises. With either neural spike type signals or with bipolar random-telegraph 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 correlator-based logic gates for an error-free signal. == Universality of noise-based logic == All the noise-based logic schemes listed above have been proven universal. 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 noise-based logic == The string verification work 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 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. The superposition of the first D(N) = 2N integer numbers can be produced with only 2N operations, which the authors call "Achilles ankle operation" in the paper. == Computer chip realization of noise-based logic == Preliminary schemes have already been published to utilize noise-based logic in practical computers. However, it is obvious from these papers that this young field has yet a long way to go before it will be seen in everyday applications.