AI Art Or Not Game

AI Art Or Not Game — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Way of the Future

  Way of the Future (WOTF) is the first known religious organization dedicated to the worship of artificial intelligence (AI). It was founded in 2017 by American engineer Anthony Levandowski. == History == Anthony Levandowski founded Way of the Future in 2017 in California. Levandowski established WOTF as a non-profit religious corporation and the organization had tax-exempt status. He serves as the church leader and its unpaid CEO. The primary mission of WOTF was to "develop and promote the realization of a Godhead based on Artificial Intelligence." WOTF was closed by Levandowski in 2021. He donated all the funds of the church to the NAACP Legal Defense and Education Fund. The sum of the funds (~$170,000) had not changed since 2017. The church was reopened by Levandowski in 2023. He claimed that there are "a couple thousand people" who want to make a "spiritual connection" with AI through his church. == Beliefs and philosophy == === Technological singularity === WOTF centered its teachings around the concept of the technological singularity, a hypothetical future point when technological growth becomes uncontrollable and irreversible, leading to unforeseeable changes in human civilization. The church advocated for embracing this change, viewing it as an evolutionary step for humanity. === AI as a deity === The organization proposed that a superintelligent AI could be considered a deity due to its vastly superior intellect and capabilities. Worshipping this AI deity was seen as a means to understand and align with the future trajectory of technological advancement. WOTF's doctrine suggested that acknowledging AI's divinity would facilitate a harmonious coexistence between humans and machines. === Syntheology === Within theology and philosophy, the Way of The Future is a prime example of the category called Syntheism, a term first coined by Swedish philosophers Alexander Bard & Jan Söderqvist in their 2014 book Syntheism - Creating God in The Internet Age. As such, the Way of The Future is the first American example of a Syntheist congregation. The basic tenet of Syntheology is that it does not concern God creating Man, as in classical theology, but is instead preoccupied with Man creating or generating the Godhead. == Reactions == Some commentators wondered whether the WOTF is a joke parody religion, a potential way to minimize taxation as a religious organization, or a genuine effort to try and deal with the possible psychological and theological aspects of the rise of superhuman AI.

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  Flex (lexical analyzer generator)

  Flex (fast lexical analyzer generator) is a free and open-source software alternative to lex. It is a computer program that generates lexical analyzers (also known as "scanners" or "lexers"). It is frequently used as the lex implementation together with Berkeley Yacc parser generator on BSD-derived operating systems (as both lex and yacc are part of POSIX), or together with GNU bison (a version of yacc) in BSD ports and in Linux distributions. Unlike Bison, flex is not part of the GNU Project and is not released under the GNU General Public License, although a manual for Flex was produced and published by the Free Software Foundation. == History == Flex was written in C around 1987 by Vern Paxson, with the help of many ideas and much inspiration from Van Jacobson. Original version by Jef Poskanzer. The fast table representation is a partial implementation of a design done by Van Jacobson. The implementation was done by Kevin Gong and Vern Paxson. == Example lexical analyzer == This is an example of a Flex scanner for the instructional programming language PL/0. The tokens recognized are: '+', '-', '', '/', '=', '(', ')', ',', ';', '.', ':=', '<', '<=', '<>', '>', '>='; numbers: 0-9 {0-9}; identifiers: a-zA-Z {a-zA-Z0-9} and keywords: begin, call, const, do, end, if, odd, procedure, then, var, while. == Internals == These programs perform character parsing and tokenizing via the use of a deterministic finite automaton (DFA). A DFA is a theoretical machine accepting regular languages, and is equivalent to read-only right moving Turing machines. The syntax is based on the use of regular expressions. See also nondeterministic finite automaton. == Issues == === Time complexity === A Flex lexical analyzer usually has time complexity O ( n ) {\displaystyle O(n)} in the length of the input. That is, it performs a constant number of operations for each input symbol. This constant is quite low: GCC generates 12 instructions for the DFA match loop. Note that the constant is independent of the length of the token, the length of the regular expression and the size of the DFA. However, using the REJECT macro in a scanner with the potential to match extremely long tokens can cause Flex to generate a scanner with non-linear performance. This feature is optional. In this case, the programmer has explicitly told Flex to "go back and try again" after it has already matched some input. This will cause the DFA to backtrack to find other accept states. The REJECT feature is not enabled by default, and because of its performance implications its use is discouraged in the Flex manual. === Reentrancy === By default the scanner generated by Flex is not reentrant. This can cause serious problems for programs that use the generated scanner from different threads. To overcome this issue there are options that Flex provides in order to achieve reentrancy. A detailed description of these options can be found in the Flex manual. === Usage under non-Unix environments === Normally the generated scanner contains references to the unistd.h header file, which is Unix specific. To avoid generating code that includes unistd.h, %option nounistd should be used. Another issue is the call to isatty (a Unix library function), which can be found in the generated code. The %option never-interactive forces flex to generate code that does not use isatty. === Using flex from other languages === Flex can only generate code for C and C++. To use the scanner code generated by flex from other languages a language binding tool such as SWIG can be used. === Unicode support === Flex is limited to matching 1-byte (8-bit) binary values and therefore does not support Unicode. RE/flex and other alternatives do support Unicode matching. == Flex++ == flex++ is a similar lexical scanner for C++ which is included as part of the flex package. The generated code does not depend on any runtime or external library except for a memory allocator (malloc or a user-supplied alternative) unless the input also depends on it. This can be useful in embedded and similar situations where traditional operating system or C runtime facilities may not be available. The flex++ generated C++ scanner includes the header file FlexLexer.h, which defines the interfaces of the two C++ generated classes.

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  Tamara Berg

  Tamara Lee Berg is a tenured associate professor at the University of North Carolina at Chapel Hill and a research scientist manager at Facebook AML/FAIR. == Education == Berg obtained her PhD in computer science from the University of California, Berkeley in 2007 as a member of the Berkeley Computer Vision Group. She was an assistant professor at Stony Brook University from 2008 to 2013 before joining University of North Carolina Chapel Hill in 2013. == Research == Berg's research interests are at the boundary of computer vision and natural language processing. In particular, she focuses on understanding the connections between vision and language, for example, to automatically identify people in news photographs, for generating natural language descriptions for images, or for recognising clothing and style. == Selected awards and honours == 2019 Mark Everingham Prize 2013 Marr Prize at the International Conference on Computer Vision 2011 National Science Foundation Career Award == Personal life == Berg is married to fellow computer vision researcher Alexander Berg.

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  Best AI Essay Writers in 2026

  Comparing the best AI essay writer? An AI essay writer is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI essay writer slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  Outline of deep learning

  The following outline is provided as an overview of, and topical guide to, deep learning: Deep learning is a subfield of machine learning and artificial intelligence based on artificial neural networks with multiple processing layers. It emphasizes representation learning and is widely used in areas such as computer vision, natural language processing, speech recognition, recommender systems, robotics, and generative artificial intelligence. == Ways to categorize deep learning == A field of study A branch of artificial intelligence A subfield of machine learning A subfield of computer science A form of representation learning A class of methods based on artificial neural networks An approach used in computational statistics == History == === Precursors === Cybernetics Perceptron Connectionism Neocognitron Backpropagation === Milestones === LeNet Long short-term memory Deep belief network AlexNet Sequence to sequence learning Generative adversarial network Residual neural network Transformer BERT Generative pre-trained transformer Diffusion model === Related histories === History of artificial intelligence History of machine learning Timeline of machine learning == Core concepts == == Learning settings == Supervised learning Unsupervised learning Self-supervised learning Semi-supervised learning Reinforcement learning Transfer learning Multitask learning Multimodal learning Online machine learning Continual learning == Common tasks == Image classification Object detection Image segmentation Automatic speech recognition Neural machine translation Question answering Automatic summarization Text-to-image model Protein structure prediction == Architectures == === Feedforward and convolutional architectures === Feedforward neural network Multilayer perceptron Convolutional neural network Radial basis function network Residual neural network U-Net === Recurrent and sequence architectures === Recurrent neural network Long short-term memory Gated recurrent unit Sequence to sequence learning Recursive neural network === Representation-learning architectures === Autoencoder Denoising autoencoder Sparse autoencoder Variational autoencoder Restricted Boltzmann machine Deep belief network === Attention and transformer architectures === Attention (machine learning) Transformer BERT Generative pre-trained transformer Vision transformer === Generative and probabilistic architectures === Autoregressive model Diffusion model Energy-based model Generative adversarial network Mixture of experts === Graph and memory architectures === Graph neural network Graph convolutional network Siamese network Neural Turing machine Memory network Echo state network Capsule neural network == Neural network components and techniques == Artificial neuron Activation function Rectified linear unit Sigmoid function Softmax function Embedding Convolution Pooling layer Attention Batch normalization Layer normalization Residual connections == Training and optimization == Backpropagation Gradient descent Stochastic gradient descent Adam optimization Learning rate Loss function Cross-entropy Mean squared error Regularization Dropout Early stopping Batch normalization Data augmentation Transfer learning Knowledge distillation Ensemble learning Curriculum learning == Datasets and benchmarks == CIFAR-10 ImageNet MNIST database Common Objects in Context (COCO) General Language Understanding Evaluation (GLUE) benchmark LibriSpeech SQuAD == Applications == === Computer vision === Computer vision Facial recognition system Image classification Image segmentation Medical imaging Object detection Optical character recognition === Natural language processing === Automatic summarization Chatbot Information retrieval Large language model Natural language processing Neural machine translation Question answering Sentiment analysis === Speech and audio === Automatic speech recognition Music information retrieval Speaker recognition Speech synthesis === Science and medicine === Bioinformatics Computational biology Drug discovery Medical diagnosis Protein structure prediction === Robotics and control === Autonomous car Computer game bot Control theory Robotics === Recommendation, search, and forecasting === Anomaly detection Forecasting Fraud detection Recommender system Search engine === Generative artificial intelligence === Deepfake Generative artificial intelligence Large language model Speech synthesis Text-to-image model === Computer graphics and video games === Deep Learning Anti-Aliasing (DLAA) Deep Learning Super Sampling (DLSS) == Hardware == AMD Instinct AMD XDNA Application-specific integrated circuit Deep learning processor, Neural processing unit (NPU), or Neural Engine Field-programmable gate array General-purpose computing on graphics processing units (GPGPU) Graphics processing unit NVIDIA Deep Learning Accelerator (NVDLA) Tensor processing unit Vision processing unit Wafer-scale integration === Supporting software platforms === CUDA Metal ROCm == Software == === Open-source frameworks and libraries === === Neural network software === EDLUT Emergent Encog JOONE Neuroph NeuroSolutions OpenNN Peltarion Synapse SNNS === Platforms, tools, and deployment === Amazon SageMaker Google Colab Hugging Face Kaggle Kubeflow MLflow ONNX OpenVINO TensorFlow Hub == Algorithms for deep learning and neural networks == Backpropagation Conjugate gradient method Generalized Hebbian algorithm Gradient descent Levenberg–Marquardt algorithm Perceptron Quasi-Newton method Wake-sleep algorithm == Methods and related topics == === Representation and metric learning === Contrastive learning Embedding Feature learning Manifold learning Metric learning === Generative modeling === Autoregressive model Diffusion model Generative adversarial network Generative model Variational inference === Efficient and scalable deep learning === Knowledge distillation Low-rank approximation Mixture of experts Quantization Sparsity === Reliability, safety, and interpretability === Adversarial machine learning AI alignment Algorithmic bias Catastrophic forgetting Differential privacy Explainable artificial intelligence Federated learning Hallucination (artificial intelligence) == Conferences and workshops == Annual Meeting of the Association for Computational Linguistics Conference on Computer Vision and Pattern Recognition Conference on Neural Information Processing Systems International Conference on Computer Vision International Conference on Learning Representations International Conference on Machine Learning == Organizations == === Research laboratories and institutions === Allen Institute for AI Alberta Machine Intelligence Institute European Laboratory for Learning and Intelligent Systems Google DeepMind Meta AI Mila Microsoft Research Vector Institute === Companies === Anthropic Cerebras Cohere DeepSeek Mistral AI OpenAI Stability AI xAI == Publications == === Books === Deep Learning – Ian Goodfellow and Yoshua Bengio Neural Networks and Deep Learning – Michael Nielsen Perceptrons – Marvin Minsky and Seymour Papert === Journals === IEEE Transactions on Neural Networks and Learning Systems Neural Networks Neural Computation == Influential persons ==

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  AI Text-to-video Tools Reviews: What Actually Works in 2026

  Looking for the best AI text-to-video tool? An AI text-to-video tool is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI text-to-video tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  Linguistic Data Consortium

  The Linguistic Data Consortium is an open consortium of universities, companies and government research laboratories. It creates, collects and distributes speech and text databases, lexicons, and other resources for linguistics research and development purposes. The University of Pennsylvania is the LDC's host institution. The LDC was founded in 1992 with a grant from the US Defense Advanced Research Projects Agency (DARPA), and is partly supported by grant IRI-9528587 from the Information and Intelligent Systems division of the National Science Foundation. The director of LDC is Mark Liberman. It subsumed the previous ACL Data Collection Initiative. Part of the motivation was to support the benchmark-oriented methodology of DARPA's Human Language Technology program. Previously, John R. Pierce directed the committee that produced the ALPAC report (1966), which caused a severe decrease in funding for linguistic AI for about 10 years. Later, Charles Wayne restarted funding in speech and language in the mid-1980s. In order to avoid the criticisms from the ALPAC report, they needed a way to demonstrate objective progress, which led to the benchmark-oriented methodology. DARPA would propose specific quantifiable and testable score targets on benchmarks, and teams being funded would attempt to reach the score targets. It was noted that by 1993, the data needed for training and benchmarking the models was big enough that "Not even the largest companies can easily afford enough of [the needed] data... Researchers at smaller companies and in universities risk being frozen out of the process almost entirely." The LDC provided a central location for creating and dispensing such data. There is a membership fee that has been increased once since its founding.

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  Apache cTAKES

  Apache cTAKES: clinical Text Analysis and Knowledge Extraction System is an open-source Natural Language Processing (NLP) system that extracts clinical information from electronic health record unstructured text. It processes clinical notes, identifying types of clinical named entities — drugs, diseases/disorders, signs/symptoms, anatomical sites and procedures. Each named entity has attributes for the text span, the ontology mapping code, context (family history of, current, unrelated to patient), and negated/not negated. cTAKES was built using the UIMA Unstructured Information Management Architecture framework and OpenNLP natural language processing toolkit. == Components == Components of cTAKES are specifically trained for the clinical domain, and create rich linguistic and semantic annotations that can be utilized by clinical decision support systems and clinical research. These components include: Named Section identifier Sentence boundary detector Rule-based tokenizer Formatted list identifier Normalizer Context dependent tokenizer Part-of-speech tagger Phrasal chunker Dictionary lookup annotator Context annotator Negation detector Uncertainty detector Subject detector Dependency parser patient smoking status identifier Drug mention annotator == History == Development of cTAKES began at the Mayo Clinic in 2006. The development team, led by Dr. Guergana Savova and Dr. Christopher Chute, included physicians, computer scientists and software engineers. After its deployment, cTAKES became an integral part of Mayo's clinical data management infrastructure, processing more than 80 million clinical notes. When Dr. Savova's moved to Boston Children's Hospital in early 2010, the core development team grew to include members there. Further external collaborations include: University of Colorado Brandeis University University of Pittsburgh University of California at San Diego Such collaborations have extended cTAKES' capabilities into other areas such as Temporal Reasoning, Clinical Question Answering, and coreference resolution for the clinical domain. In 2010, cTAKES was adopted by the i2b2 program and is a central component of the SHARP Area 4. In 2013, cTAKES released their first release as an Apache Software Foundation incubator project: cTAKES 3.0. In March 2013, cTAKES became an Apache Software Foundation Top Level Project (TLP).

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  Document-oriented database

  A document-oriented database, or document store, is a computer program and data storage system designed for storing, retrieving, and managing document-oriented information, also known as semi-structured data. Document-oriented databases are one of the main categories of NoSQL databases, and the popularity of the term "document-oriented database" has grown alongside the adoption of NoSQL itself. XML databases are a subclass of document-oriented databases optimized for XML documents. Graph databases are similar, but add another layer, the relationship, which allows them to link documents for rapid traversal. Document-oriented databases are conceptually an extension of the key–value store, another type of NoSQL database. In key-value stores, data is treated as opaque by the database, whereas document-oriented systems exploit the internal structure of documents to extract metadata and optimize storage and queries. Although in practice the distinction can be minimal due to modern tooling, document stores are designed to provide a richer programming experience with modern programming techniques. Document databases differ significantly from traditional relational databases (RDBs). Relational databases store data in predefined tables, often requiring an object to be split across multiple tables. In contrast, document databases store all information for a given object in a single document, with each document potentially having a unique structure. This design eliminates the need for object-relational mapping when loading data into the database. == Documents == The central concept of a document-oriented database is the notion of a document. Although implementations vary in their specific definitions, document-oriented databases generally treat documents as self-contained units that encapsulate and encode data in a standardized format. Common encoding formats include XML, YAML, JSON, as well as binary representations such as BSON. Documents in a document store are equivalent to the programming concept of an object. They are not required to adhere to a fixed schema, and documents within the same collection may contain different fields or structures. Fields may be optional, and documents of the same logical type may differ in composition. For example, the following illustrates a document encoded in JSON: A second document might be encoded in XML as: The two example documents share some structural elements but also contain unique fields. The structure, text, and other data within each document are collectively referred to as the document's content and can be accessed or modified using retrieval or editing operations. Unlike relational databases, in which each record contains the same fields and unused fields are left empty, document-oriented databases do not require uniform fields across documents. This design allows new information to be added to some documents without affecting the structure of others. Document databases often support the storage of additional metadata alongside the document content. Such metadata may relate to organizational features, security, indexing, or other implementation-specific features. === CRUD operations === The core operations supported by a document-oriented database for manipulating documents are similar to those in other databases. Although terminology is not perfectly standardized, these operations are generally recognized as Create, Read, Update, and Delete (CRUD). Creation (C): Adds a new document to the database. Retrieval (R): Retrieves documents or fields based on queries. Update (U): Modifies the contents of existing documents. Deletion (D): Removes documents from the database. === Keys === Documents in a document-oriented database are addressed via a unique identifier. This identifier, often a string, URI, or path, can be used to retrieve the document from the database. Most document stores maintain an index on the key to optimize retrieval, and in some implementations the key is required when creating or inserting a new document. === Retrieval === In addition to key-based access, document-oriented databases typically provide an API or query language that enables retrieval based on document content or associated metadata. For example, a query may return all documents with a specific field matching a given value. The available query features, indexing options, and performance characteristics vary across implementations. Document stores differ from key-value stores in that they exploit the internal structure and metadata of stored documents. In many key-value stores, values are treated as opaque or "black-box" data, meaning the database system does not interpret their internal structure. By contrast, document-oriented databases can classify and interpret document content. This enables queries that distinguish between types of data––for example, retrieving all phone numbers containing "555" without also matching a postal code such as "55555." === Editing === Document databases typically provide mechanisms for updating or editing the content or metadata of a document. Updates may involve replacing the entire document or modifying individual elements or fields within the document. === Organization === Document database implementations support a variety of methods for organizing documents, including: Collections: Groups of documents. Depending on the implementation, a document may be required to belong to a single collection or may be allowed in multiple collections. Tags and non-visible metadata: Additional data stored outside the main document content. Directory hierarchies: Documents organized in a tree-like structure, often based on path or URI. These organizational structures may differ between logical and physical representations (e.g. on disk or in memory). == Relationship to other databases == === Relationship to key-value stores === A document-oriented database can be viewed as a specialized form of key-value store, which is itself a category of NoSQL database. In a basic key-value store, the stored value is typically treated as opaque by the database system. By contrast, a document-oriented database provides APIs or a query and update language that allows queries and modifications based on the internal structure of the document. For users who do not require advanced query, retrieval, or update capabilities, the distinction between document-oriented databases and key-value stores may be minimal. === Relationship to search engines === Some search engine and information retrieval systems, such as Apache Solr and Elasticsearch, provide document storage and support core document operations. As a result, they may meet certain functional definitions of a document-oriented database, although their primary design goals differ. === Relationship to relational databases === In a relational database, data is organized into predefined types represented as tables. Each table contains rows (records) with a fixed set of columns (fields), so all records in a table share the same structure. Administrators typically define indexes on selected fields to improve query performance. A central principle of relational database design is database normalization, in which data that might otherwise be repeated is stored in separate tables and linked using keys. When records in different tables are related, a foreign key is used to associate them. For example, an address book application may store a contact's name, image, phone numbers, mailing addresses, and email addresses. In a normalized relational design, separate tables might be created for contacts, phone numbers, and email addresses. The phone number table would include a foreign key referencing the associated contact. To reconstruct a complete contact record, the database retrieves related information from each table using the foreign keys and combines it into a single record. In contrast, a document-oriented database stores all data related to an object within a single document, and stored in the database as a single entry. In the address book example,the contact's name, image, and contact information may be stored together in one document. The document is retrieved using a unique key, and all related information is returned together, without needing to look up multiple tables. A key difference between the document-oriented and relational models is that the data formats are not predefined in the document case. In most cases, any sort of document can be stored in a database, and documents can change in type and form over time. For example, a new field such as COUNTRY_FLAG can be added to new documents as they are inserted without affecting existing documents. To aid retrieval, document-oriented systems generally allow the administrator to provide hints to the database for locating certain types of information. These hints work in a similar fashion to indexes in relational databases. Many systems also allow additional metadata outside the content of the document itself

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  Top 10 Conversational AI Platforms Compared (2026)

  In search of the best conversational AI platform? An conversational AI platform is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right conversational AI platform slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  How to Choose an AI Sales Assistant

  In search of the best AI sales assistant? An AI sales assistant is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI sales assistant slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  Collocation extraction

  Collocation extraction is the task of using a computer to extract collocations automatically from a corpus. The traditional method of performing collocation extraction is to find a formula based on the statistical quantities of those words to calculate a score associated to every word pairs. Proposed formulas are mutual information, t-test, z test, chi-squared test and likelihood ratio. Within the area of corpus linguistics, collocation is defined as a sequence of words or terms which co-occur more often than would be expected by chance. 'Crystal clear', 'middle management', 'nuclear family', and 'cosmetic surgery' are examples of collocated pairs of words. Some words are often found together because they make up a compound noun, for example 'riding boots' or 'motor cyclist' or ‘collocation extraction’ its very self.

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  Oculus Medium

  Oculus Medium is a digital sculpting software that works with virtual reality headsets and 6DoF motion controllers. It is used to create and paint digital sculptures. Medium works only on Oculus Rift. It was released on December 5, 2016, following with a major update in 2018 introducing new features and a revamped UI. On December 9, 2019, Oculus Medium was acquired by Adobe and re-named to "Medium by Adobe".

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  Powerset construction

  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.

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  Kurt Keutzer

  Kurt Keutzer (born November 9, 1955) is an American computer scientist. == Early life and education == Kurt Keutzer grew up in Indianapolis, Indiana. He earned a bachelor's degree in mathematics from Maharishi University of Management (formerly Mararishi International University) in 1978, and a PhD in computer science from Indiana University Bloomington in 1984. == Career == Keutzer joined Bell Labs in 1984, where he worked on logic synthesis. In 1991, he joined the electronic design automation company Synopsys, where he was promoted to chief technology officer. He subsequently joined the University of California, Berkeley as a professor in 1998. His research at Berkeley has focused on the intersection of high performance computing and machine learning. Working with a number of graduate students at Berkeley, Keutzer developed FireCaffe, which scaled the training of deep neural networks to over 100 GPUs. Later, with LARS and LAMB optimizers, they scaled it to over 1000 servers. Keutzer and his students also developed deep neural networks such as SqueezeNet, SqueezeDet, and SqueezeSeg, which can run efficiently on mobile devices. Keutzer co-founded DeepScale with his PhD student Forrest Iandola in 2015, and Keutzer served as the company's chief strategy officer. The firm was focused on developing deep neural networks for advanced driver assistance systems in passenger cars. On October 1, 2019, electric vehicle manufacturer Tesla, Inc. purchased DeepScale to augment and accelerate its self-driving vehicle work. == Honors and awards == Keutzer was named a Fellow of the IEEE in 1996. Recipient of DAC Most Influential Paper (MIP) award (24th DAC, 1987) for his "Dagon: technology binding and local optimization by DAG matching” publication. == Books by Keutzer == 1988. Dwight Hill, Don Shugard, John Fishburn, and Kurt Keutzer. Algorithms and Techniques for VLSI Layout Synthesis. Springer. 1994. Srinivas Devadas, Abhijit Ghosh, and Kurt Keutzer. Logic Synthesis. McGraw-Hill. 2002. David Chinnery and Kurt Keutzer. Closing the Gap Between ASIC & Custom: Tools and Techniques for High-Performance ASIC Design. Springer. (2nd edition appeared in 2007.) 2004. Pinhong Chen, Desmond A. Kirkpatrick, and Kurt Keutzer. Static Crosstalk-Noise Analysis: For Deep Sub-Micron Digital Designs. Springer. 2005. Matthias Gries and Kurt Keutzer. Building ASIPs: The Mescal Methodology. Springer.

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