In the theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) that recognizes the same formal language. It is important in theory because it establishes that NFAs, despite their additional flexibility, are unable to recognize any language that cannot be recognized by some DFA. It is also important in practice for converting easier-to-construct NFAs into more efficiently executable DFAs. However, if the NFA has n states, the resulting DFA may have up to 2n states, an exponentially larger number, which sometimes makes the construction impractical for large NFAs. The construction, sometimes called the Rabin–Scott powerset construction (or subset construction) to distinguish it from similar constructions for other types of automata, was first published by Michael O. Rabin and Dana Scott in 1959. == Intuition == To simulate the operation of a DFA on a given input string, one needs to keep track of a single state at any time: the state that the automaton will reach after seeing a prefix of the input. In contrast, to simulate an NFA, one needs to keep track of a set of states: all of the states that the automaton could reach after seeing the same prefix of the input, according to the nondeterministic choices made by the automaton. If, after a certain prefix of the input, a set S of states can be reached, then after the next input symbol x the set of reachable states is a deterministic function of S and x. Therefore, the sets of reachable NFA states play the same role in the NFA simulation as single DFA states play in the DFA simulation, and in fact the sets of NFA states appearing in this simulation may be re-interpreted as being states of a DFA. == Construction == The powerset construction applies most directly to an NFA that does not allow state transformations without consuming input symbols (aka: "ε-moves"). Such an automaton may be defined as a 5-tuple (Q, Σ, T, q0, F), in which Q is the set of states, Σ is the set of input symbols, T is the transition function (mapping a state and an input symbol to a set of states), q0 is the initial state, and F is the set of accepting states. The corresponding DFA has states corresponding to subsets of Q. The initial state of the DFA is {q0}, the (one-element) set of initial states. The transition function of the DFA maps a state S (representing a subset of Q) and an input symbol x to the set T(S,x) = ∪{T(q,x) | q ∈ S}, the set of all states that can be reached by an x-transition from a state in S. A state S of the DFA is an accepting state if and only if at least one member of S is an accepting state of the NFA. In the simplest version of the powerset construction, the set of all states of the DFA is the powerset of Q, the set of all possible subsets of Q. However, many states of the resulting DFA may be useless as they may be unreachable from the initial state. An alternative version of the construction creates only the states that are actually reachable. === NFA with ε-moves === For an NFA with ε-moves (also called an ε-NFA), the construction must be modified to deal with these by computing the ε-closure of states: the set of all states reachable from some given state using only ε-moves. Van Noord recognizes three possible ways of incorporating this closure computation in the powerset construction: Compute the ε-closure of the entire automaton as a preprocessing step, producing an equivalent NFA without ε-moves, then apply the regular powerset construction. This version, also discussed by Hopcroft and Ullman, is straightforward to implement, but impractical for automata with large numbers of ε-moves, as commonly arise in natural language processing application. During the powerset computation, compute the ε-closure { q ′ | q → ε ∗ q ′ } {\displaystyle \{q'~|~q\to _{\varepsilon }^{}q'\}} of each state q that is considered by the algorithm (and cache the result). During the powerset computation, compute the ε-closure { q ′ | ∃ q ∈ Q ′ , q → ε ∗ q ′ } {\displaystyle \{q'~|~\exists q\in Q',q\to _{\varepsilon }^{}q'\}} of each subset of states Q' that is considered by the algorithm, and add its elements to Q'. === Multiple initial states === If NFAs are defined to allow for multiple initial states, the initial state of the corresponding DFA is the set of all initial states of the NFA, or (if the NFA also has ε-moves) the set of all states reachable from initial states by ε-moves. == Example == The NFA below has four states; state 1 is initial, and states 3 and 4 are accepting. Its alphabet consists of the two symbols 0 and 1, and it has ε-moves. The initial state of the DFA constructed from this NFA is the set of all NFA states that are reachable from state 1 by ε-moves; that is, it is the set {1,2,3}. A transition from {1,2,3} by input symbol 0 must follow either the arrow from state 1 to state 2, or the arrow from state 3 to state 4. Additionally, neither state 2 nor state 4 have outgoing ε-moves. Therefore, T({1,2,3},0) = {2,4}, and by the same reasoning the full DFA constructed from the NFA is as shown below. As can be seen in this example, there are five states reachable from the start state of the DFA; the remaining 11 sets in the powerset of the set of NFA states are not reachable. == Complexity == Because the DFA states consist of sets of NFA states, an n-state NFA may be converted to a DFA with at most 2n states. For every n, there exist n-state NFAs such that every subset of states is reachable from the initial subset, so that the converted DFA has exactly 2n states, giving Θ(2n) worst-case time complexity. A simple example requiring nearly this many states is the language of strings over the alphabet {0,1} in which there are at least n characters, the nth from last of which is 1. It can be represented by an (n + 1)-state NFA, but it requires 2n DFA states, one for each n-character suffix of the input; cf. picture for n=4. == Applications == Brzozowski's algorithm for DFA minimization uses the powerset construction, twice. It converts the input DFA into an NFA for the reverse language, by reversing all its arrows and exchanging the roles of initial and accepting states, converts the NFA back into a DFA using the powerset construction, and then repeats its process. Its worst-case complexity is exponential, unlike some other known DFA minimization algorithms, but in many examples it performs more quickly than its worst-case complexity would suggest. Safra's construction, which converts a non-deterministic Büchi automaton with n states into a deterministic Muller automaton or into a deterministic Rabin automaton with 2O(n log n) states, uses the powerset construction as part of its machinery.
Pocketbook (application)
Pocketbook was a Sydney-based free budget planner and personal finance app launched in 2012. The app helped users setup and manage budgets, track spending and manage bills. As of 2016 Pocketbook claimed to support over 250,000 Australians, in January 2018 that number was 435,000. After being acquired by Zip Co Ltd in 2016, it was announced in 2022 that the app was to be shut down and all user accounts deleted. == History == Pocketbook was founded by Alvin Singh and Bosco Tan in 2012. It was conceived in 2011 in a Wolli Creek apartment as a tool for Alvin and Bosco to take control of their money. In 2013, Pocketbook raised $500,000 from technology fund Tank Stream Ventures, and a group of investors including TV personality David Koch, Geoff Levy, David Shein and Peter Cooper. In September 2016 Digital retail finance and payment industry player zipMoney (now trading as Zip Co Limited) acquired Pocketbook in a $7.5m deal == Features == The app synced with the bank account of users and would organize spending into different categories. Users could also be reminded of bill payments, analyse spending and set spending limits. They can also be alerted of fraudulent transactions and deductions. The app employs security measures like end to end encryption, CloudFlare protection, fraud detection, identity protection etc. Pocketbook was available via web and mobile version. == Awards == Personal Finance Innovator of the Year by Fintech Business Awards 2017 Innovator of the Year by OPTUS MyBusiness Awards 2017 Best Finance App of 2016 by Australian Fintech Best Personal Finance App: Pocketbook won the 2016 Finder Innovation Awards, presented at a gala dinner hosted by media personality and The New Inventors presenter James O'Loghlin. Best Mobile App of the Year Winner: StartCon hosted the first annual Australasian Startup Awards. Over 200 nominations in 14 categories and an overall winner were reviewed, and winners were determined by public voting, with over 63,000 votes in total. Best New Startup 2014 by StartupSmart. Finalist in the SWIFT Innotribe startup competition in Dubai in 2013.
Luciano Floridi
Luciano Floridi (Italian: [luˈtʃaːno ˈflɔːridi]; born 16 November 1964) is an Italian and British philosopher. He is John K. Castle Professor in the Practice of Cognitive Science and Founding Director of the Digital Ethics Center at Yale University. He is also a Professor of Sociology of Culture and Communication at the University of Bologna, Department of Legal Studies, where he is the director of the Centre for Digital Ethics. Furthermore, he is adjunct professor ("distinguished scholar in residence") at the Department of Economics, American University, Washington D.C. He is married to the neuroscientist Anna Christina Nobre. Floridi is best known for his work on two areas of philosophical research: the philosophy of information, and information ethics (also known as digital ethics or computer ethics), for which he received many awards, including the Knight of the Grand Cross of the Order of Merit, Italy's most prestigious honor. According to Scopus, Floridi was the most cited living philosopher in the world in 2020. Between 2008 and 2013, he held the research chair in philosophy of information and the UNESCO Chair in Information and Computer Ethics at the University of Hertfordshire. He was the founder and director of the IEG, an interdepartmental research group on the philosophy of information at the University of Oxford, and of the GPI the research Group in Philosophy of Information at the University of Hertfordshire. He was the founder and director of the SWIF, the Italian e-journal of philosophy (1995–2008). He is a former Governing Body Fellow of St Cross College, Oxford. == Early life and education == Floridi was born in Rome in 1964, and studied at Rome University La Sapienza (laurea, first class with distinction, 1988), where he was originally educated as a historian of philosophy. He soon became interested in analytic philosophy and wrote his tesi di laurea (roughly equivalent to an M.A. thesis) in philosophy of logic, on Michael Dummett's anti-realism. He obtained his Master of Philosophy (1989) and PhD degree (1990) from the University of Warwick, working in epistemology and philosophy of logic with Susan Haack (who was his PhD supervisor) and Michael Dummett. Floridi's early student years are partly recounted in the non-fiction book The Lost Painting: The Quest for a Caravaggio Masterpiece, where he is "Luciano". During his graduate and postdoctoral years, he covered the standard topics in analytic philosophy in search of a new methodology. He sought to approach contemporary problems from a heuristically powerful and intellectually enriching perspective when dealing with lively philosophical issues. During his graduate studies, he began to distance himself from classical analytic philosophy. In his view, the analytic movement had lost its way. For this reason, he worked on pragmatism (especially Peirce) and foundationalist issues in epistemology and philosophy of logic, as well as the history of skepticism. == Academic career and previous positions == Floridi started his academic career as a lecturer in philosophy at the University of Warwick in 1990–1991. He joined the Faculty of Philosophy of the University of Oxford in 1990 and the OUCL (Oxford's Department of Computer Science) in 1999. He was junior research fellow (JRF) in philosophy at Wolfson College, Oxford University (1990–1994), a Frances Yates Fellow in the History of Ideas at the Warburg Institute, University of London (1994–1995) and Research Fellow in philosophy at Wolfson College, Oxford University (1994–2001). During these years in Oxford, he held lectureships in different Colleges. Between 1994 and 1996, he also held a post-doctoral research scholarship at the Department of Philosophy, University of Turin. Between 2001 and 2006, he was Markle Foundation Senior Research Fellow in Information Policy at the Programme in Comparative Media Law and Policy, Oxford University. Between 2002 and 2008, he was associate professor of logic at the Università degli Studi di Bari. In 2006, he became Fellow by Special Election of St Cross College, Oxford University, where he played for the squash team. In 2008, he was appointed full professor of philosophy at the University of Hertfordshire, to hold the newly established research chair in philosophy of information and, in 2009, the UNESCO Chair in Information and Computer Ethics, a position which he held until 2013, when he moved back to Oxford. In 2017, Floridi became a fellow of the Alan Turing Institute and the chair of its Data Ethics Group, holding these positions until 2021 and 2020, respectively. Since 2010 he has been editor-in-chief of Philosophy & Technology (Springer). In January 2023, Floridi announced he would move to Yale at the beginning of the academic year 2023–2024, to take over the position of founding director of the Yale Digital Ethics Center. == Philosophical views == One of Floridi's key contributions is his formulation of the 'Philosophy of Information' (PoI). The PoI provides a framework for understanding the nature of information and its role in the world. According to Floridi, information is a vital resource that shapes our knowledge and understanding of the world. It is not simply a neutral representation of reality but a part of the world, with its own properties, effects, and moral implications. Floridi's PoI has several key components including an 'ontology of information', which defines the nature of information, an 'ethics of information', which provides a framework for evaluating the moral implications of information and information technologies, an 'epistemology of information', that analyses the role of information in the development of knowledge and science, and a 'logic of information', the concentrates on the more formal aspects. The PoI also includes a theory of the 'information environment', the infosphere, which encompasses the physical, social, and cultural contexts in which information is produced, used, and communicated. == Recognitions and awards == 2022 - Knight of the Grand Cross - First Class of the Order of Merit (Cavaliere di Gran Croce Ordine al Merito della Repubblica Italiana, the highest honor in the Italian Republic), awarded through a special decree by the president of the Italian Republic Sergio Mattarella for his work on the philosophy and ethics of information. 2022 - Fellow of the Accademia delle Scienze dell'Istituto di Bologna 2021 - Honorary Doctorate (Laurea honoris causa) in Informatics, University of Skövde, Sweden, for "his groundbreaking work on the philosophy of information". 2020 - Premio Udine Filosofia, Mimesis Festival, for The Logic of Information (OUP, 2019) 2020 - Premio Socrate, Cesare Landa Foundation, for philosophical communication 2019 - CogX Award, for "outstanding achievement in ethics of AI" 2019 - Gilbert Ryle Lectures, Trent University 2019 - Premio Aretè "Maestro della Responsabilità", Nuvolaverde, Confindustria, Gruppo 24 Ore Salone della CSR e dell'innovazione sociale, for ethics of communication 2018 - Thinker Award, IBM, for AI Ethics 2018 - Premio Conoscenza, Conferenza dei Rettori delle Università Italiane (CRUI, equivalent of Universities UK), for achievements in research and communication about digital ethics 2017 - Fellow of the Academy of Social Sciences 2016 - J. Ong Award, Media Ecology Association, for The Fourth Revolution (OUP, 2016) 2016 - Copernicus Scientist Award, Institute for Advanced Studies of the University of Ferrara, in recognition of research in the ethics and philosophy of information 2015 - Fernand Braudel Senior Fellow, European University Institute 2014-15 - Cátedras de Excelencia, University Carlos III of Madrid, for research in philosophy and ethics of information 2013 - Member of the Académie Internationale de Philosophie des Sciences 2013 - Fellow of the British Computer Society 2013 - Weizenbaum Award, International Society for Ethics and Information Technology, for "very significant contribution to the field of information and computer ethics, through his research, service, and vision" 2012 - Covey Award, International Association for Computing and Philosophy, for "outstanding research in computing and philosophy" 2011-12 - Fellow, Center for Information Policy Research, University of Wisconsin–Milwaukee 2011 - Honorary Doctorate (Laurea honoris causa) in philosophy, University of Suceava, Romania, for "his leading research in the philosophy and ethics of information" 2011 - Fellow, World Technology Network, NY, in the category "ethics and technology" 2010 - Vice Chancellor Research Award, University of Hertfordshire 2009 - Fellow of the Society for the Study of Artificial Intelligence and the Simulation of Behaviour (AIBS) 2009-10 - Gauss Professor of the Akademie der Wissenschaften, Göttingen, in recognition of research in the philosophy of information (first philosopher to receive the award, generally given to mathematicians or physicists) 2009 - Barwise Prize, American Philosophical Asso
Catholic Church and artificial intelligence
The Catholic Church views artificial intelligence as a significant technological development that must be governed by strict ethical principles rooted in human dignity and the common good. In January 2025, the Church issued the doctrinal note Antiqua et nova co-issued by the Dicastery for the Doctrine of the Faith and the Dicastery for Culture and Education. It addresses the "relationship between artificial intelligence and human intelligence" and offers reflections on the "anthropological and ethical challenges raised by AI". In August 2025, Time magazine included Pope Leo XIV in its 2025 list of the World’s Most Influential People in Artificial Intelligence. In May 2026, Pope Leo XIV approved the creation of a new Vatican commission on artificial intelligence. He released his first papal encyclical, titled Magnifica humanitas, on the topic later in the month.
ITU-WHO Focus Group on Artificial Intelligence for Health
The ITU-WHO Focus Group on Artificial Intelligence for Health (AI for Health) was an inter-agency collaboration from 2018 between the World Health Organization and the ITU, which in 2019 created a benchmarking framework to assess the accuracy of AI in health. The organization convened an international network of experts and stakeholders from fields like research, practice, regulation, ethics, public health, etc, that developed guideline documentation and code. The documents have addressed ethics, assessment/evaluation, handling, and regulation of AI for health solutions, covering specific use cases including AI in ophthalmology, histopathology, dentistry, malaria detection, radiology, symptom checker applications, etc. FG-AI4H has established an ad hoc group concerned with digital technologies for health emergencies, including COVID-19. All documentation is public. The idea for the Focus Group came out of the Health Track of the 2018 AI for Good Global Summit. Administratively, FG-AI4H was created by ITU-T Study Group 16. Under ITU-T's framework, participation in Focus Groups is open to anyone from an ITU Member State. The secretariat is provided by the Telecommunication Standardization Bureau (under Director Chaesub Lee). It was first created at the July 2018 meeting with a lifetime of two years, at the July 2020 meeting, this was extended for another two years, where the focus group also submitted its deliverables to its parent body. It was also presented at the NeurIPS 2020 health workshop. In July 2023 "the work was grandfathered in the Global Initiative on AI for Health (GI-AI4H)". == AI for Health Framework == The outline of the benchmarking framework was published in a 2019 commentary in The Lancet. The output of the Focus Group AI for Health were structured in the AI for Health Framework. Depending on their primary domain being health or ICT, the individual components of the AI for Health Framework were ratified by the corresponding United Nations Specialized Agency, as WHO Guidelines and ITU Recommendations respectively. Standards drawn up by FG-AI4H were titled as: AI4H ethics considerations AI4H regulatory [best practices | considerations] AI4H requirements specification AI software life cycle specification Data specification AI training best practices specification AI4H evaluation considerations AI4H scale-up and adoption AI4H applications and platforms Use cases of the ITU-WHO Focus Group on AI for Health
Video imprint (computer vision)
Proposed as an extension of image epitomes in the field of video content analysis, video imprint is obtained by recasting video contents into a fixed-sized tensor representation regardless of video resolution or duration. Specifically, statistical characteristics are retained to some degrees so that common video recognition tasks can be carried out directly on such imprints, e.g., event retrieval, temporal action localization. It is claimed that both spatio-temporal interdependences are accounted for and redundancies are mitigated during the computation of video imprints. The option of computing video imprints exploiting the epitome model has the advantage of more flexible input feature formats and more efficient training stage for video content analysis.
CuckooChess
CuckooChess is an advanced free and open-source chess engine under the GNU General Public License written in Java by Peter Österlund. CuckooChess provides an own GUI, and optionally supports the Universal Chess Interface protocol for the use with external GUIs such as Arena. An Android port is available, where its GUI is also based on Peter Österlund's Stockfish port dubbed DroidFish. The program uses the Chess Cases chess font, created by Matthieu Leschemelle. The name CuckooChess comes due that the transposition table is based on Cuckoo hashing. Android app based chess gaming app Droidfish employs both CuckooChess and Stockfish chess engines. Similarly, Kickstarter funded AI based virtual reality chess game Square Off also uses CuckooChess engine. It has an ELO rating of 2583 (as of July 2018) and a rank of 135‑137 in the Computer Chess Rating List.