Karen Hao (born in the United States c. 1993) is an American journalist and author. Currently a freelancer for publications like The Atlantic and previously a foreign correspondent based in Hong Kong for The Wall Street Journal and senior artificial intelligence editor at the MIT Technology Review, she is best known for her coverage on AI research, technology ethics and the social impact of AI. Hao also co-produced the podcast In Machines We Trust and wrote the newsletter The Algorithm. Previously, she worked at Quartz as a tech reporter and data scientist and was an application engineer at the first startup to spin out of X Development. Hao's writing has also appeared in Mother Jones, Sierra Magazine, The New Republic, and other publications. == Early life and education == Hao is the daughter of Chinese immigrant parents, and grew up in New Jersey. She is a native speaker of both English and Mandarin Chinese. She graduated from The Lawrenceville School in 2011. She then studied at the Massachusetts Institute of Technology (MIT), graduating with a B.S. in mechanical engineering and a minor in energy studies in 2015. == Career == Hao is known in the technology world for her coverage of new AI research findings and their societal and ethical impacts. Her writing has spanned research and issues regarding big tech data privacy, misinformation, deepfakes, facial recognition, and AI healthcare tools. In March 2021, Hao published a piece that uncovered previously unknown information about how attempts to combat misinformation by different teams at Facebook using machine learning were impeded and constantly at odds with Facebook's drive to grow user engagement. Upon its release, leaders at Facebook including Mike Schroepfer and Yann LeCun immediately criticized the piece through Twitter responses. AI researchers and AI ethics experts Timnit Gebru and Margaret Mitchell responded in support of Hao's writing and advocated for more change and improvement for all. Hao also co-produced the podcast In Machines We Trust, which discusses the rise of AI with people developing, researching, and using AI technologies. The podcast won the 2020 Front Page Award in investigative reporting. Hao has occasionally created data visualizations that have been featured in her work at the MIT Technology Review and elsewhere. In 2018, her "What is AI?" flowchart visualization was exhibited as an installation at the Museum of Applied Arts in Vienna. She has been an invited speaker at TEDxGateway, the United Nations Foundation, EmTech, WNPR, and many other conferences and podcasts. Her TEDx talk discussed the importance of democratizing how AI is built. In March 2022, she was hired by The Wall Street Journal to cover China technology and society, while being based in Hong Kong. She left the WSJ in 2023. In May 2025, Hao released the book Empire of AI: Dreams and Nightmares in Sam Altman's OpenAI. The book became a New York Times Bestseller and was named a Book of the Year by the Financial Times. In December 2025, after criticism from readers, Hao issued a correction to her book where she had previously overestimated the water consumption of a data center in Chile compared to the community's water consumption by factor of 1,000, due to an error in a government document. In April 2026 the book won the New York Public Library's Helen Bernstein Book Award for Excellence in Journalism. === Selected awards and honors === 2019 Webby Award nominee for best newsletter, as a writer of The Algorithm 2021 Front Page Award in investigative reporting, as a co-producer for In Machines We Trust 2021 Ambies Award nominee for best knowledge and science podcast, as a co-producer for In Machines We Trust 2021 Webby Award nominee for best technology podcast, as a co-producer for In Machines We Trust 2024 American Humanist Media Award 2025 TIME100 AI, named by TIME magazine as one of the 100 most influential people in artificial intelligence 2026 New York Public Library's Helen Bernstein Book Award for Excellence in Journalism 2026 Whiting Award in Non-fiction
Image translation
Image translation is the machine translation of images of printed text (posters, banners, menus, screenshots etc.). This is done by applying optical character recognition (OCR) technology to an image to extract any text contained in the image, and then have this text translated into a language of their choice, and the applying digital image processing on the original image to get the translated image with a new language. == General == Machine translation made available on the internet (web and mobile) is a notable advance in multilingual communication eliminating the need for an intermediary translator/interpreter, translating foreign texts still poses a problem to the user as they cannot be expected to be able to type the foreign text they wish to translate and understand. Manually entering the foreign text may prove to be a difficulty especially in cases where an unfamiliar alphabet is used from a script which user can't read, e.g. Cyrillic, Chinese, Japanese etc. for an English speaker or any speaker of a Latin-based language or vice versa. The technical advancements in OCR made it possible to recognize text from images. The possibility to use one's mobile device's camera to capture and extract printed text is also known as mobile OCR and was first introduced in Japanese manufactured mobile telephones in 2004. Using the handheld's camera one could take a picture of (a line of) text and have it extracted (digitalized) for further manipulation such as storing the information in their contacts list, as a web page address (URL) or text to use in an SMS/email message etc. Presently, mobile devices having a camera resolution of 2 megapixels or above with an auto-focus ability, often feature the text scanner service. Taking the text scanning facility one step further, image translation emerged, giving users the ability to capture text with their mobile phone's camera, extract the text, and have it translated in their own language. More and more applications emerged on this technology including Word Lens. After getting acquired by Google, it was made a part of Google Translate mobile app. Another simultaneous advancement in Image Processing, has also made it possible now to replace the text on the image with the translated text and create a new image altogether. == History == The development of the image translation service springs from the advances in OCR technology (miniaturization and reduction of memory resources consumed) enabling text scanning on mobile telephones. Among the first to announce mobile software capable of “reading” text using the mobile device's camera is International Wireless Inc. who in February 2003 released their “CheckPoint” and “WebPoint” applications. “CheckPoint” reads critical symbolic information on checks and is aimed at reducing losses that mobile merchants suffer from “bounced” checks by scanning the MICR number on the bottom of a check, while “WebPoint” enables the visual recognition and decoding of printed URL's, which are then opened by the device's web browser. The first commercial release of a mobile text scanner, however, took place in December 2004 when Vodafone and Sharp began selling the 902SH mobile which was the first to feature a 2 megapixel digital camera with optical zoom. Among the device's various multimedia features was the built-in text/bar code/QR code scanner. The text scanner function could handle up to 60 alphabetical characters simultaneously. The scanned text could be then sent as an email or SMS message, added as a dictionary entry or, in the case of scanned URLs, opened via the device's web browser. All subsequent Sharp mobiles feature the text scanner functionality. In September 2005, NEC Corporation and the Nara Institute of Science and Technology in Japan (NAIST) announced new software capable of transforming cameraphones into text scanners. The application differs substantially from similarly equipped mobile telephones in Japan (able to scan businesscards and small bits of text and use OCR to convert that to editable text or to URL addresses) by it ability to scan a whole page. The two companies, however, said they would not release the software commercially before the end of 2008. Combining the text scanner function with machine translation technology was first made by US company RantNetwork who in July 2007 started selling the Communilator, a machine translation application for mobile devices featuring the Image Translation functionality. Using the built-in camera, the mobile user could take a picture of some printed text, apply OCR to recognize the text and then translate it into any one of over 25 language available. In April 2008 Nokia showcased their Shoot-to-Translate application for the N73 model which is capable of taking a picture using the device's camera, extracting the text and then translating it. The application only offers Chinese to English translation, and does not handle large segments of text. Nokia said they are in the process of developing their Multiscanner product which, besides scanning text and business cards, would be able to translate between 52 languages. Again in April 2008, Korean company Unichal Inc. released their handheld Dixau text scanner capable of scanning and recognizing English text and then translating it into Korean using online translation tools such as Wikipedia or Google Translate. The device is connected to a PC or a laptop via the USB port. In February 2009, Bulgarian company Interlecta presented at the Mobile World Congress in Barcelona their mobile translator including image recognition and speech synthesis. The application handles all European languages along with Chinese, Japanese and Korean. The software connects to a server over the Internet to accomplish the image recognition and the translation. In May 2014, Google acquired Word Lens to improve the quality of visual and voice translation. It is able to scan text or picture with one's device and have it translated instantly. Since the OCR has been improving many companies or website started combining OCR and translation, to read the text from an image and show the translated text. In August 2018, an Indian company created ImageTranslate. It is able to read, translate and re-create the image in another language. As of late 2018, the tool added 13 new languages, including Arabic, Thai, Vietnamese, Hindi, and Bengali, significantly increasing its utility in Asia and the Middle East. This helps users translate photos already stored in their phone's gallery, not just live, real-time views. Currently, image translation is offered by the following companies: Google Translate app with camera ImageTranslate Yandex
Wang-Chiew Tan
Wang-Chiew Tan is a Singaporean computer scientist specializing in data management and natural language processing. Her work in data management includes data provenance (or data lineage) and data integration. She is currently a Research Scientist at Facebook AI, and was previously the Director of Research at Megagon Labs in Mountain View, California. At Megagon Labs, Tan was the lead researcher on a study with the University of Tokyo that concluded that the company of other people is more effective than pets at making people happy. == Education and career == Tan earned her bachelor's degree in computer science (first-class) at the National University of Singapore, and completed her Ph.D. at the University of Pennsylvania. Her 2002 dissertation, Data Annotations, Provenance, and Archiving, was jointly supervised by Peter Buneman and Sanjeev Khanna. Before working at Megagon, she has been a professor of computer science at the University of California, Santa Cruz beginning in 2002, and, from 2010 to 2012, was on leave from Santa Cruz as a researcher at IBM Research - Almaden. == Recognition == Tan was named a Fellow of the Association for Computing Machinery in 2015 "for contributions to data provenance and to the foundations of information integration".
Magnetic ink character recognition
Magnetic ink character recognition code, known in short as MICR code, is a character recognition technology used mainly by the banking industry to streamline the processing and clearance of cheques and other documents. MICR encoding, called the MICR line, is at the bottom of cheques and other vouchers and typically includes the document-type indicator, bank code, bank account number, cheque number, cheque amount (usually added after a cheque is presented for payment), and a control indicator. The format for the bank code and bank account number is country-specific. The technology allows MICR readers to scan and read the information directly into a data-collection device. Unlike barcode and similar technologies, MICR characters can be read easily by humans. MICR encoded documents can be processed much faster and more accurately than conventional OCR encoded documents. == Pre-Unicode standard representation == The ISO standard ISO 2033:1983, and the corresponding Japanese Industrial Standard JIS X 9010:1984 (originally JIS C 6229–1984), define character encodings for OCR-A, OCR-B and E-13B. == International spread == There are two major MICR fonts in use: E-13B and CMC-7. There is no particular international agreement on which countries use which font. In practice, this does not create particular problems as cheques and other vouchers do not usually flow out of a particular jurisdiction. The E-13B font has been adopted as an international standard in ISO 1004-1:2013, and is the standard in Australia, Canada, the United Kingdom, the United States, as well as Central America and much of Asia, besides other countries. The CMC-7 font has been adopted as an international standard in ISO 1004-2:2013, and is widely used in Europe, including France and Italy, Mexico, and South America, including Argentina, Brazil, Chile, besides other countries. Israel is the only country that can use both fonts simultaneously, though the practice makes the system significantly less efficient. This situation is the product of the Israelis adopting CMC-7, while the Palestinians opted for E-13B. == Fonts == === E-13B === E-13B is a 14-character set, comprising the 10 decimal digits, and the following symbols: ⑆ (transit: used to delimit a bank code); ⑈ (on-us: used to delimit a customer account number); ⑇ (amount: used to delimit a transaction amount); ⑉ (dash: used to delimit parts of numbers—e.g., routing numbers or account numbers). In the check printing and banking industries the E-13B MICR line is also commonly referred to as the TOAD line. This reference comes from the 4 characters: Transit, On-us, Amount, and Dash. Compared to CMC-7, some pairs of E-13B characters (notably 2 and 5) can produce relatively similar results when magnetically scanned; however, as a fallback if magnetic reading fails, E-13B also performs well under optical character recognition. The E-13B repertoire can be represented in Unicode (see below). The official Unicode names contain misnomers. For example, the ⑈ on-us symbol is official titled "OCR Dash". Prior to Unicode, it could be encoded according to ISO 2033:1983, which encodes digits in their usual ASCII locations, transit as 0x3A, on-us as 0x3C, amount as 0x3B, and dash as 0x3D. For EBCDIC, IBM code page 1001 encodes digits in their usual EBCDIC locations, transit as 0xDB, on-us as 0xEB, amount as 0xCB, and dash as 0xFB. IBM code page 1032 extends code page 1001 by adding alternative encodings for transit at 0x5C, 0x7A and 0xC1, on-us at 0x4C, 0x61 and 0xC3, amount at 0x5B, 0x5E and 0xC2 and dash at 0x60, 0x7E and 0xC4, in addition to a zero-width space at 0x5A. These alternative representations were added for interoperability with Siemens and Océ printers. === CMC-7 === CMC-7 includes 10 numeric digits, 26 capital letters, and 5 control characters: S I (internal), S II (terminator), S III (amount), S IV (an unused character), and S V (routing). CMC-7 has a barcode format, with every character having two distinct large gaps in different places, as well as distinct patterns in between, to minimize any chance for character confusion while reading magnetically; however, these bars are too close and narrow to be reliably recognised at a typical scan resolution if falling back to optical scanning. CMC-7 can also produce superficially successful, but incorrect, scans of upside-down MICR lines. Unicode does not include support for the CMC-7 control symbols. IBM code page 1033 encodes: Digits and capitals in their usual EBCDIC locations S I (internal) as 0x5E, 0x61 or 0xCB; S II (terminator) as 0x4C, 0x5B or 0xEB; S III (amount) as 0x60, 0x7E or 0xFB; S IV as 0x50, 0x7A or 0xDB; S V (routing) as 0x5C, 0x6E or 0xBB. == MICR reader == MICR characters are printed on documents in one of the two MICR fonts, using magnetizable (commonly known as magnetic) ink or toner, usually containing iron oxide. In scanning, the document is passed through a MICR reader, which performs two functions: magnetization of the ink, and detection of the characters. The characters are read by a MICR reader head, a device similar to the playback head of a tape recorder. As each character passes over the head, it produces a unique waveform that can be easily identified by the system. MICR readers are the primary tool for cheque sorting and are used across the cheque distribution network at multiple stages. For example, a merchant will use a MICR reader to sort cheques by bank and send the sorted cheques to a clearing house for redistribution to those banks. Upon receipt, the banks perform another MICR sort to determine which customer's account is charged and to which branch the cheque should be sent on its way back to the customer. However, many banks no longer offer this last step of returning the cheque to the customer. Instead, cheques are scanned and stored digitally. Sorting of cheques is done as per the geographical coverage of banks in a nation. == Unicode == OCR and MICR characters have been included in the Unicode Standard since at least version 1.1 (June 1993). Since the Unicode Character Database only tracks characters starting with version 1.1, they may also have been present in Unicode 1.0 or 1.0.1. The Unicode block that includes OCR and MICR characters is called Optical Character Recognition and covers U+2440–U+245F. Of the characters in this block, four are from the MICR E-13B font: U+2446 ⑆ OCR BRANCH BANK IDENTIFICATION U+2447 ⑇ OCR AMOUNT OF CHECK U+2448 ⑈ OCR DASH (corrected alias MICR ON US SYMBOL) U+2449 ⑉ OCR CUSTOMER ACCOUNT NUMBER (corrected alias MICR DASH SYMBOL) The names of the latter two characters were inadvertently switched when they were named in ISO/IEC 10646:1993, and they have been assigned accurate names as formal aliases. Per the Unicode Stability Policy, the existing names remain, allowing their use as stable identifiers. Additionally, all four characters have informative (non-formal) aliases in the Unicode charts: "transit", "amount", "on-us", and "dash" respectively. Prior to Unicode, these symbols had been encoded by the ISO-IR-98 encoding defined by ISO 2033:1983, in which they were simply named SYMBOL ONE through SYMBOL FOUR. They were encoded immediately following the digits, which were encoded at their ASCII locations. Although ISO 2033 also specifies encoding for OCR-A and OCR-B, its encoding for E-13B is known simply as ISO_2033-1983 by the IANA. == History == Before the mid-1940s, cheques were processed manually using the Sort-A-Matic or Top Tab Key method. The processing and cheque clearing was very time-consuming and was a significant cost in cheque clearance and bank operations. As the number of cheques increased, ways were sought for automating the process. Standards were developed to ensure uniformity in financial institutions. By the mid-1950s, the Stanford Research Institute and General Electric Computer Laboratory had developed the first automated system to process cheques using MICR. The same team also developed the E-13B MICR font. "E" refers to the font being the fifth considered, and "B" to the fact that it was the second version. The "13" refers to the 0.013-inch character grid. The trial of MICR E-13B font was shown to the American Bankers Association (ABA) in July 1956, which adopted it in 1958 as the MICR standard for negotiable documents in the United States. ABA adopted MICR as its standard because machines could read MICR accurately, and MICR could be printed using existing technology. In addition, MICR remained machine readable, even through overstamping, marking, mutilation and more. The first cheques using MICR were printed by the end of 1959. Although compliance with MICR standards was voluntary in the United States, it had been almost universally adopted in the United States by 1963. In 1963, ANSI adopted the ABA's E-13B font as the American standard for MICR printing, and E-13B was also standardized as ISO 1004:1995. Other countries set their own standards, though the MICR readers and m
Gato (DeepMind)
Gato is a deep neural network for a range of complex tasks that exhibits multimodality. It can perform tasks such as engaging in a dialogue, playing video games, controlling a robot arm to stack blocks, and more. == Overview == Gato was created by researchers at London-based AI firm DeepMind. It is a transformer, like GPT-3. According to MIT Technology Review, the system "learns multiple different tasks at the same time, which means it can switch between them without having to forget one skill before learning another" whereas "[t]he AI systems of today are called “narrow,” meaning they can only do a specific, restricted set of tasks such as generate text", and according to The Independent, it is a "'generalist agent' that can carry out a huge range of complex tasks, from stacking blocks to writing poetry". It uses supervised learning with 1.2B parameters. The technology has been described as "general purpose" artificial intelligence and a "step toward" artificial general intelligence.
Deadbot
A deadbot, deathbot, or griefbot is a digital avatar, created with artificial intelligence, which resembles a person who is dead. Griefbots employ natural language processing and machine-learning techniques to approximate the style and personality of a deceased person. They may appear as chatbots, voice assistants, or animated avatars, and are often trained on an individual's digital remains. == History == Among the earliest researchers, Muhammad Aurangzeb Ahmad of the University of Washington, developed the Grandpa Bot project, a conversational simulation of his late father designed for his children to interact with. Other efforts include journalist James Vlahos's Dadbot, which evolved into the commercial platform HereAfter AI. Hossein Rahnama's Augmented Eternity research at MIT Media Lab and Toronto Metropolitan University, and game designer Jason Rohrer's "Project December", have enabled users to converse with language-model representations of loved ones. Early commercial projects such as Eternime, founded by Marius Ursache, also popularized the notion of interactive digital immortality. == Cultural and societal impact == Scholars have proposed frameworks and critiques addressing the ethics of these technologies. Tomasz Hollanek and Katarzyna Nowaczyk-Basińska developed a design-ethics taxonomy distinguishing the data donor, data recipient, and interactant. Edina Harbinja and Lilian Edwards formalized the concept of post-mortem privacy, and Carl J. Öhman at the Oxford Internet Institute studied the management of large-scale digital remains. Cultural acceptance varies: while some view them as expressions of remembrance, others regard them as unsettling or ethically problematic. Concerns have been raised about deadbots' potential for creating psychological harm. Griefbots are considered part of the phenomenon of artificial intimacy.
Ω-automaton
In automata theory, a branch of theoretical computer science, an ω-automaton (or stream automaton) is a variation of a finite automaton that runs on infinite, rather than finite, strings as input. Since ω-automata do not stop, they have a variety of acceptance conditions rather than simply a set of accepting states. ω-automata are useful for specifying behavior of systems that are not expected to terminate, such as hardware, operating systems and control systems. For such systems, one may want to specify a property such as "for every request, an acknowledge eventually follows", or its negation "there is a request that is not followed by an acknowledge". The former is a property of infinite words: one cannot say of a finite sequence that it satisfies this property. Classes of ω-automata include the Büchi automata, Rabin automata, Streett automata, parity automata and Muller automata, each deterministic or non-deterministic. These classes of ω-automata differ only in terms of acceptance condition. They all recognize precisely the regular ω-languages except for the deterministic Büchi automata, which is strictly weaker than all the others. Although all these types of automata recognize the same set of ω-languages, they nonetheless differ in succinctness of representation for a given ω-language. == Deterministic ω-automata == Formally, a deterministic ω-automaton is a tuple A = ( Q , Σ , δ , q 0 , A a c c ) {\textstyle A=(Q,\Sigma ,\delta ,q_{0},A_{acc})} , that consists of the following components: Q {\textstyle Q} , is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } , is a finite set called the alphabet of A {\textstyle A} . δ : Q × Σ → Q {\textstyle \delta \colon Q\times \Sigma \rightarrow Q} is a function, called the transition function of A {\textstyle A} . Q 0 {\textstyle Q_{0}} is an element of Q {\textstyle Q} , called the initial state. A a c c {\textstyle A_{acc}} is a set of accepting states of A {\textstyle A} , formally a subset of Q ω {\textstyle Q^{\omega }} . An input for A {\textstyle A} is an infinite string over the alphabet Σ {\textstyle \Sigma } , i.e. it is an infinite sequence α = ( a 1 , a 2 , a 3 , … ) {\textstyle \alpha =(a_{1},a_{2},a_{3},\ldots )} . The run of A {\textstyle A} on such an input is an infinite sequence ρ = ( r 0 , r 1 , r 2 , … ) {\textstyle \rho =(r_{0},r_{1},r_{2},\ldots )} of states, defined as follows: r 0 = q 0 {\textstyle r_{0}=q_{0}} . r 1 = δ ( r 0 , a 1 ) {\textstyle r_{1}=\delta (r_{0},a_{1})} . r 2 = δ ( r 1 , a 2 ) {\textstyle r_{2}=\delta (r_{1},a_{2})} . ... that is, for every i {\textstyle i} : r i = δ ( r i − 1 , a i ) {\textstyle r_{i}=\delta (r_{i-1},a_{i})} . The main purpose of an ω-automaton is to define a subset of the set of all inputs: The set of accepted inputs. Whereas in the case of an ordinary finite automaton every run ends with a state r n {\textstyle r_{n}} and the input is accepted if and only if r n {\textstyle r_{n}} is an accepting state, the definition of the set of accepted inputs is more complicated for ω-automata. Here we must look at the entire run ρ {\textstyle \rho } . The input is accepted if the corresponding run is in Acc {\textstyle {\text{Acc}}} . The set of accepted input ω-words is called the recognized ω-language by the automaton, which is denoted as L ( A ) {\textstyle L(A)} . The definition of Acc {\textstyle {\text{Acc}}} as a subset of Q ω {\textstyle Q^{\omega }} is purely formal and not suitable for practice because normally such sets are infinite. The difference between various types of ω-automata (Büchi, Rabin etc.) consists in how they encode certain subsets Acc {\textstyle {\text{Acc}}} of Q ω {\textstyle Q^{\omega }} as finite sets, and therefore in which such subsets they can encode. == Nondeterministic ω-automata == Formally, a nondeterministic ω-automaton is a tuple A = ( Q , Σ , Δ , Q 0 , Acc ) {\textstyle A=(Q,\Sigma ,\Delta ,Q_{0},{\text{Acc}})} that consists of the following components: Q {\textstyle Q} is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } is a finite set called the alphabet of A {\textstyle A} . Δ {\textstyle \Delta } is a subset of Q × Σ × Q {\textstyle Q\times \Sigma \times Q} and is called the transition relation of A {\textstyle A} . Q 0 {\textstyle Q_{0}} is a subset of Q {\textstyle Q} , called the initial set of states. Acc {\textstyle {\text{Acc}}} is the acceptance condition, a subset of Q ω {\textstyle Q^{\omega }} . Unlike a deterministic ω-automaton, which has a transition function δ {\textstyle \delta } , the non-deterministic version has a transition relation Δ {\textstyle \Delta } . Note that Δ {\textstyle \Delta } can be regarded as a function Q × Σ → P ( Q ) {\textstyle Q\times \Sigma \rightarrow {\mathcal {P}}(Q)} from Q × Σ {\textstyle Q\times \Sigma } to the power set P ( Q ) {\textstyle {\mathcal {P}}(Q)} . Thus, given a state q n {\textstyle q_{n}} and a symbol a n {\textstyle a_{n}} , the next state q n + 1 {\textstyle q_{n+1}} is not necessarily determined uniquely, rather there is a set of possible next states. A run of A {\textstyle A} on the input α = ( a 1 , a 2 , a 3 , … ) {\textstyle \alpha =(a_{1},a_{2},a_{3},\ldots )} is any infinite sequence ρ = ( r 0 , r 1 , r 2 , … ) {\textstyle \rho =(r_{0},r_{1},r_{2},\ldots )} of states that satisfies the following conditions: r 0 {\textstyle r_{0}} is an element of Q 0 {\textstyle Q_{0}} . r 1 {\textstyle r_{1}} is an element of Δ ( r 0 , a 1 ) {\textstyle \Delta (r_{0},a_{1})} . r 2 {\textstyle r_{2}} is an element of Δ ( r 1 , a 2 ) {\textstyle \Delta (r_{1},a_{2})} . ... that is, for every i {\textstyle i} : r i {\textstyle r_{i}} is an element of Δ ( r i − 1 , a i ) {\textstyle \Delta (r_{i-1},a_{i})} . A nondeterministic ω-automaton may admit many different runs on any given input, or none at all. The input is accepted if at least one of the possible runs is accepting. Whether a run is accepting depends only on Acc {\textstyle {\text{Acc}}} , as for deterministic ω-automata. Every deterministic ω-automaton can be regarded as a nondeterministic ω-automaton by taking Δ {\textstyle \Delta } to be the graph of δ {\textstyle \delta } . The definitions of runs and acceptance for deterministic ω-automata are then special cases of the nondeterministic cases. == Acceptance conditions == Acceptance conditions may be infinite sets of ω-words. However, people mostly study acceptance conditions that are finitely representable. The following lists a variety of popular acceptance conditions. Before discussing the list, let's make the following observation. In the case of infinitely running systems, one is often interested in whether certain behavior is repeated infinitely often. For example, if a network card receives infinitely many ping requests, then it may fail to respond to some of the requests but should respond to an infinite subset of received ping requests. This motivates the following definition: For any run ρ {\textstyle \rho } , let Inf ( ρ ) {\textstyle {\text{Inf}}(\rho )} be the set of states that occur infinitely often in ρ {\textstyle \rho } . This notion of certain states being visited infinitely often will be helpful in defining the following acceptance conditions. A Büchi automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some subset F {\textstyle F} of Q {\textstyle Q} : Büchi condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } for which Inf ( ρ ) ∩ F ≠ ∅ {\textstyle {\text{Inf}}(\rho )\cap F\neq \emptyset } , i.e. there is an accepting state that occurs infinitely often in ρ {\textstyle \rho } . A Rabin automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some set Ω {\textstyle \Omega } of pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} of sets of states: Rabin condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } for which there exists a pair ( B i , G i ) {\textstyle (B_{i},G_{i})} in Ω {\textstyle \Omega } such that B i ∩ Inf ( ρ ) = ∅ {\textstyle B_{i}\cap {\text{Inf}}(\rho )=\emptyset } and G i ∩ Inf ( ρ ) ≠ ∅ {\textstyle G_{i}\cap {\text{Inf}}(\rho )\neq \emptyset } . A Streett automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some set Ω {\textstyle \Omega } of pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} of sets of states: Streett condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } such that for all pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} in Ω {\textstyle \Omega } , B i ∩ Inf ( ρ ) ≠ ∅ {\textstyle B_{i}\cap {\text{Inf}}(\rho )\neq \emptyset } or G i ∩ Inf ( ρ ) = ∅ {\textstyle G_{i}\cap {\text{Inf}}(\rho )=\emptyset } . A parity automaton is an automaton A {\textstyle A} whose set of states is Q = { 0 , 1 , 2 , … , k } {\textstyle Q=\{0,1,2,\ldots ,k\}} for some natural number k {\textst