In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA minimization is PSPACE-complete. No efficient (polynomial time) algorithms are known, and under the standard assumption that P ≠ PSPACE, none exist. The most efficient known algorithm is the Kameda–Weiner algorithm. == Non-uniqueness of minimal NFA == Unlike deterministic finite automata, minimal NFAs may not be unique. There may be multiple NFAs with the same number of states that accept the same regular language, but for which there is no equivalent NFA or DFA with fewer states.
Flutter (software)
Flutter is an open-source UI software development kit created by Google. It can be used to develop cross platform applications from a single codebase for the web, Fuchsia, Android, iOS, Linux, macOS, and Windows. First described in 2015, Flutter was released in May 2017. Flutter is used internally by Google in apps such as Google Pay and Google Earth as well as by other software developers including ByteDance and Alibaba. Flutter ships applications with its own rendering engine which directly outputs pixel data to the screen. This is in contrast to many other UI frameworks that rely on the target platform to provide a rendering engine, such as native Android apps which rely on the device-level Android SDK or iOS SDK which use the target platform's built-in UI stack. Flutter's control of its rendering pipeline simplifies multi-platform support as identical UI code can be used for all target platforms.One of Flutter’s key features is hot reload, which allows developers to see code changes instantly without restarting the application. == Architecture == The basic component in a Flutter program is a "widget", which can in turn consist of other widgets. A widget describes the logic, interaction, and design of a UI element with an implementation similar to React. Unlike other cross-platform toolkits such as React Native and Xamarin which draw widgets using native platform components, Flutter renders widgets itself on a per-pixel basis. Flutter has two types of widgets: stateless and stateful. Stateless widgets only update if their inputs change, meaning they otherwise won't need to be rebuilt when other elements of the screen change, while stateful widgets can call the setState() method to update an internal state and redraw. Although widgets are the primary method of constructing Flutter applications, they can also be bypassed in favor of directly drawing on a canvas. This feature has been occasionally used to implement game engines in Flutter. The Flutter framework contains two sets of widgets that conform to specific design languages: Material Design widgets implement Google's design language of the same name, and Cupertino widgets implement Apple's iOS Human interface guidelines. Flutter allows the developer to use either set of widgets on either platform. Developers can use Cupertino widgets on Android. Flutter apps are written in the Dart language. Release versions of Flutter apps on all platforms use ahead-of-time (AOT) compilation except for on the Web where code is transpiled to JavaScript or WebAssembly. Flutter inherits Dart's Pub package manager and software repository, which allows users to publish and use custom packages as well as Flutter-specific plugins. The Foundation library, written in Dart, provides basic classes and functions that are used to construct applications using Flutter, such as APIs to communicate with the engine. Flutter's engine, written primarily in C++, provides low-level rendering support using either Google's Skia graphics library or the custom "Impeller" graphics layer, which is enabled by default on iOS and Android API 29 and higher. The engine interfaces with platform-specific SDKs such as those provided by Android and iOS to implement features like accessibility, file and network I/O, native plugin support, etc. == History == The first version of Flutter was known as "Sky" and ran on the Android operating system. It was unveiled at the 2015 Dart developer summit with the stated intent of being able to render consistently at 120 frames per second. On December 4, 2018, Flutter 1.0 was released at the Flutter conference in London. On May 6, 2020, the Dart software development kit (SDK) version 2.8 and Flutter 1.17.0 were released, adding support for the Metal API. On March 3, 2021, Google released Flutter 2 during an online Flutter Engage event. It added a Canvas-based renderer for web in addition to the HTML-based renderer and early-access desktop application support for Windows, macOS, and Linux. It also shipped with Dart 2.0 which included support for null-safety. Null safety was initially optional as it was a breaking change and was made mandatory in Dart 3 released in 2023. On May 12, 2022, Flutter 3 and Dart 2.17 were released with support for all desktop platforms as stable. On October 27, 2024, a number of Flutter community developers announced Flock, a fork of Flutter intended to be easier to contribute to while still keeping in sync with all changes made in the upstream code base. In 2025, Google continued Flutter's evolution with enhanced modular architecture, foldable device support, and ARM IoT optimizations as outlined in the updated roadmap. === Major releases in Flutter === Prior to the Flutter 2.0 release in March of 2021, the Flutter framework was centered on mobile development. The developers of Flutter were primarily focused on the two main platforms, IOS and Android. Specifically, they wanted to deliver strong performance and improve access to native API and platform features and expand the widget system. With the release of Flutter 2.0, the framework moved beyond mobile and introduced support for the web platform. This marked a shift into a broader cross platform development environment. With this release, developers could produce applications for Web, Android and IOS from the same codebase. This release also brought the desktop platform closer to stable. There have been a number of improvements since then that have broadened platform support. They introduced enhancements to performance and workflow, redefined the developer’s toolkit, and added an improved rendering engine. "Flutter 2.10.0 release notes". docs.flutter.dev. Retrieved 2025-11-11.
Content adaptation
Content adaptation is the action of transforming content to adapt to device capabilities. Content adaptation is usually related to mobile devices, which require special handling because of their limited computational power, small screen size, and constrained keyboard functionality. Content adaptation could roughly be divided to two fields: Media content adaptation that adapts media files. Browsing content adaptation that adapts a website to mobile devices. == Browsing content adaptation == Advances in the capabilities of small, mobile devices such as mobile phones (cell phones) and Personal Digital Assistants have led to an explosion in the number of types of device that can now access the Web. Some commentators refer to the Web that can be accessed from mobile devices as the Mobile Web. The sheer number and variety of Web-enabled devices poses significant challenges for authors of websites who want to support access from mobile devices. The W3C Device Independence Working Group described many of the issues in its report Authoring Challenges for Device Independence. Content adaptation is one approach to a solution. Rather than requiring authors to create pages explicitly for each type of device that might request them, content adaptation transforms an author's materials automatically. For example, content might be converted from a device-independent markup language, such as XDIME, an implementation of the W3C's DIAL specification, into a form suitable for the device, such as XHTML Basic, C-HTML, or WML. Similarly, a suitable device-specific CSS style sheet or a set of in-line styles might be generated from abstract style definitions. Likewise, a device specific layout might be generated from abstract layout definitions. Once created, the device-specific materials form the response returned to the device from which the request was made. Another way is to use the latest trend responsive design based on CSS, covered in this article (RWD). Content adaptation requires a processor that performs the selection, modification, and generation of materials to form the device-specific result. IBM's Websphere Everyplace Mobile Portal (WEMP), BEA Systems' WebLogic Mobility Server, Morfeo's MyMobileWeb, and Apache Cocoon are examples of such processors. Wurfl and WALL are popular open source tools for content adaptation. WURFL is an XML-based Device Description Repository with APIs to access the data in Java and PHP (and other popular programming languages). WALL (Wireless Abstraction Library) lets a developer author mobile pages which look like plain HTML, but converts them to WML, C-HTML, or XHTML Mobile Profile, depending on the capabilities of the device from which the HTTP request originates. GreasySpoon lets the developer build plugins for content editing, in JavaScript, Ruby (programming language), and more, just like the Firefox application GreaseMonkey. Alembik (Media Transcoding Server) is a Java (J2EE) application providing transcoding services for variety of clients and for different media types (image, audio, video, etc.). It is fully compliant with OMA's Standard Transcoder Interface specification and is distributed under the LGPL open source license. In 2007, the first large scale carrier-grade deployments of content transformation, on existing mass-market handsets, with no software download required, were deployed by Vodafone in the UK and globally for Yahoo! oneSearch, using the Novarra Vision solution. Novarra's content adaptation solution had been used in enterprise intranet deployments as early as 2003 (at that time, the platform was named "Engines for Wireless Data"). InfoGin, the 9-year-old content-adaptation company with customers like Vodafone, Orange, Telefónica and PCCW. The patented "Web to Mobile adaptation", Mobile Matrix Transcoder, Multimedia and Documents transcoders, Video adaptation supporte. Launched in 2007, Bytemobile's Web Fidelity Service was another carrier-grade, commercial infrastructure solution, which provided wireless content adaptation to mobile subscribers on their existing mass-market handsets, with no client download required.
Media preservation
Preservation of documents, pictures, recordings, digital content, etc., is a major aspect of archival science. It is also an important consideration for people who are creating time capsules, family history, historical documents, scrapbooks and family trees. Common storage media are not permanent, and there are few reliable methods of preserving documents and pictures for the future. == Paper/prints (photos) == Color negatives and ordinary color prints may fade away to nothing in a relatively short period if not stored and handled properly. This happens even if the negatives and prints are kept in the dark, because ambient light is not the determining factor, but heat and humidity are. The color degradation is the result of the dyes used in the color processes. Because color processing results in a less stable image than traditional black-and-white processing, black-and-white pictures from the 1920s are more likely to survive long-term than color films and photographs from after the middle 20th century. Black-and-white photographic films using silver halide emulsions are the only film types that have proven to last for archival storage. The determining factors for longevity include the film base type, proper processing (develop, stop, fix and wash) and proper storage. Early films used a Cellulose nitrate base which was prone to decomposition and highly flammable. Nitrate film was replaced with acetate-base films. These Cellulose acetate films were later discovered to outgass acids (also referred to as vinegar syndrome). Acetate films were replaced in the early 1980s by polyester film base materials which have been determined to be more stable than film stocks with a nitrate or acetate base. Color prints made on most inkjet printers look very good at first but they have a very short lifespan, measured in months rather than in years. Even prints from commercial photo labs will start to fade in a matter of years if not processed properly and stored in cool, dry environments. == Documents/books == With documents for which the media are not so critical as what the documents contain, the information in documents can be copied by using photocopiers and image scanners. Books and manuscripts can also have their information saved without destruction by using a book scanner. Where the medium itself needs to be preserved, for example if a document is a crayon sketch by a famous artist on paper, a complex process of preservation may be used. Depending on the condition and importance of the item this can include gluing the media onto more stable media, or protective enclosing of the media. Polyester sleeves, acid-free folders, and pH buffered document boxes are common supportive protective enclosures whose selection must match the media's chemical and physical properties. Other considerations in preserving paper/books are: Damaging light, particularly UV light, which fades and destroys media over time by breaking down the molecules. Atmosphere contains small traces of sulfur dioxide and nitric acid which turn media yellow and break the fibers down. Humidity and moisture also aid in the breakdown of media. If there is too much, the document can be attacked by bacteria, and if too little, cellulose material breaks down. Temperature, particularly elevated ones, can destroy some media. Low temperatures can cause the water to form crystals which expands destroying the structure of paper-based documents. == Online photo albums == Although there are many websites that allow the upload of photographs and videos, digital preservation for the long-term is still considered an issue. There is a lack of confidence that such websites are capable of storing data for long periods of time (ex. 50 years) without data degradation or loss. == Optical media - CD, DVD, Blu-ray, M-Disc == Write-once optical media, such as CD-Rs and DVD-Rs, typically contain an organic dye that distinguishes data reading from data writing based on the dye's transparency along the disc. Conventional CDs and DVDs have finite shelf-life due to natural degradation of the dye; the newer M-DISC uses inorganic material technology to produce molded DVDs and Blu-Rays (up to 3-layer 100GB BDXL) with a claimed lifespan of 100-1000 years if stored correctly with most BD & BDXL rated read/writers enabling the higher power mode for the M-Disc format after 2011. The National Archives and Records Administration lists published life expectancies to be 10 or 25 years or more for normal CDs and DVDs and conservative life expectancies to be between 2 and 5 years. Storage environments, such as temperature and humidity, as well as handling conditions such as frequency of media use and compatibility between the recorder and media, affect media shelf-life. Improvements in media storage and migrations to new recording technologies can make certain formats obsolete within their respective lifespan. Technologists have pointed to internet streaming services, where services such as video-on-demand have contributed to the 33 percent decline in DVD sales the past 5 years, as a challenge for digital preservation. == Magnetic media - video cassettes, tapes, hard drives == Magnetic media such as audio and video tape and floppy disks also have limited life spans. Audio and video tapes require specific care and handling to ensure that the recorded information will be preserved. For information that must be preserved indefinitely, periodic transcription from old media to new ones is necessary, not only because the media are unstable but also because the recording technology may become obsolete. Magnetic media also deteriorates naturally with typical shelf lives between 10 and 20 years. Magnetic tape can degrade from binder hydrolysis or magnetic remanence decay. Binder hydrolysis, also known as sticky-shed syndrome, refers to the breakdown of binder, or glue, that holds the magnetic particles to the polyester base of the tape. Tapes which have been stored in hot, humid conditions are particularly vulnerable to this phenomenon and may suffer from accelerated degradation. Severe binder can cause the magnetic material to fall off or sheds from the base, leaving a pile of dust and clear backing. Archivists can bake the tape, which evaporates water molecules on the tape, to temporarily restore the binder before making a copy. Magnetic tape can also be destabilized by magnetic remanence decay, which refers to the weakening of the tape's magnetization over time. This weakens the affected tape's readability, leading to reduced sound clarity and volume or picture hue and contrast. Baking the tape will not restore magnetization. Media at risk include recorded media such as master audio recordings of symphonies and videotape recordings of the news gathered over the last 40 years. Threats to media that must be considered when archiving important record media include accidental erasure, physical loss due to disasters such as fires and floods, and media degradation. Along with the actual media being degraded over the years, the machines that are available to play back or reproduce the audio sources are becoming archaic themselves. Manufacturers and their support (parts, technical updates) for their machines have disappeared throughout the years. Even if the medium is vaulted and archived correctly, the mechanical properties of the machines have deteriorated to the point that they could do more harm than good to the tape being played. Many major film studios are now backing up their libraries by converting them to electronic media files, such as .AIFF or .WAV-based files via digital audio workstations. That way, even if the digital platform manufacturer goes out of business or no longer supports their product, the files can still be played on any common computer. There is a detailed process that must take place previous to the final archival product now that a digital solution is in place. Sample rates and their conversion and reference speed are both critical in this process. In floppy disks, the lubricants inside the plastic jackets of many older floppies promote the decay of the magnetic medium. Also, the alignment of the magnetic particles of the disk substrate may gradually degrade, leading to a loss of formatting and data. Early laser disk media were prone to degradation as the layers of the disk substrate were bonded with an adhesive that was vulnerable to decay and would crumble over time. This would lead the different layers of the disk to peel apart, damaging the pitted data surface and rendering the disk unreadable.
Static web page
A static web page, sometimes called a flat page or a stationary page, is a web page that is delivered to a web browser exactly as stored, in contrast to dynamic web pages which are generated by a web application. Consequently, a static web page displays the same information for all users, from all contexts, subject to modern capabilities of a web server to negotiate content-type or language of the document where such versions are available and the server is configured to do so. However, a webpage's JavaScript can introduce dynamic functionality which may make the static web page dynamic. == Overview == Static web pages are often HTML documents, stored as files in the file system and made available by the web server over HTTP (nevertheless URLs ending with ".html" are not always static). However, loose interpretations of the term could include web pages stored in a database, and could even include pages formatted using a template and served through an application server, as long as the page served is unchanging and presented essentially as stored. The content of static web pages remains stationary irrespective of the number of times it is viewed. Such web pages are suitable for the contents that rarely need to be updated, though modern web template systems are changing this. Maintaining large numbers of static pages as files can be impractical without automated tools, such as static site generators. Any personalization or interactivity has to run client-side, which is restricting. Cloud-based website builders, including Wix, Weebly, and Duda, offer no-code platforms for creating static and dynamic web pages through graphical interfaces, without requiring programming expertise. === Advantages === Provide improved security over dynamic websites (dynamic websites are at risk to web shell attacks if a vulnerability is present) Improved performance for end users compared to dynamic websites Fewer or no dependencies on systems such as databases or other application servers Cost savings from utilizing cloud storage, as opposed to a hosted environment Security configurations are easy to set up, which makes it more secure Static files can be cached by content delivery networks (CDNs) and other intermediate caches, which both reduces page load times at the user and also reduces load on the origin server. Static websites can have improved uptime, since they are still available through any available CDN exit node even when other CDN nodes or the origin webserver are temporarily offline. === Disadvantages === Dynamic functionality must be performed on the client side. After each update of a static website, some or all users may see old, stale, outdated previous versions instead of the latest version until the old version is flushed from CDNs and other caches. == Static site generators == Static site generators are applications that compile static websites - typically populating HTML templates in a predefined folder and file structure, with content supplied in a format such as Markdown or AsciiDoc. === Implementations === Jekyll (powers GitHub Pages) Middleman Hugo Next.js Astro.build Pelican Franklin
Affinity (software)
Affinity is a graphics editor developed by Serif, a subsidiary of Canva. It is simultaneously a vector graphics editor, a raster graphics editor and a desktop publishing application. It was first released in 2025 as a successor to Serif's Affinity Designer, Affinity Photo and Affinity Publisher, uniting the three editors into one application. While the previous versions competed individually against Adobe's Illustrator, Photoshop, and InDesign, Affinity 3.0 integrates their functionality into a single application. It uses a freemium model monetized by AI features exclusive to Canva Pro subscribers. == Functionality == Affinity is divided into a number of workspaces ("studios"), which are equivalent to the previous suite of Affinity applications: "vector" for vector graphics (Designer), "pixel" for raster editing (Photo), and "layout" for desktop publishing (Publisher). Additionally, it introduces the ability to create custom workspaces. The application supports real-time previews and non-destructive editing, which are based on GPU acceleration. Supported file formats include Adobe Photoshop, InDesign and Illustrator files, PDF, SVG, and TIFF, as well as a custom .af file format. === Vector editing === === Raster editing === Affinity includes photo editing tools including adjustments, masks, blend modes, batch processing, and retouching facilities. Additionally, the application can develop RAW files, similar to Adobe Lightroom. === Desktop publishing === Publishing features include master pages, text styles, and advanced typography. === AI features === The application supports Canva's existing AI features, such as background removal and generative fill. This requires a Canva subscription. == Development == === Background and acquisition (2014–2024) === Serif launched the original Affinity suite starting with Affinity Designer in 2014, followed by Photo (2015) and Publisher (2019). The software gained popularity for its one-time purchase model, contrasting with Adobe's subscription-based Creative Cloud. In November 2022, Serif released Version 2 of the suite, introducing a "Universal License" that covered all three apps across all platforms. In March 2024, Canva acquired Serif for approximately A$580 million (£300 million). Following user backlash regarding a potential shift to subscriptions, Canva and Serif issued a joint "Pledge" committing to four key principles: fair pricing, no mandatory subscriptions, perpetual licenses for existing products, and continued development of Affinity as a standalone suite. === Unified release (2025) === In September 2025, Serif pulled all existing versions of Affinity Designer, Affinity Photo and Affinity Publisher from sale ahead an upcoming announcement on 30 October; also ahead of the announcement, the iPadOS versions of the Affinity suite became free on App Store. During a "Creative Freedom" keynote on 30 October 2025, Canva released a new version now simply branded as "Affinity" (also known as "Affinity by Canva"), and referred to internally as version 3.0. Version 3 drops the separate applications and integrates their functionality into a singular application, and adds the ability to export directly to the Canva platform. It also adds a Canva AI studio, including background removal, "Expand & Edit", and generative fill. As of version 3, Affinity has switched to a freemium model; it is now available at no charge to users, although access to Canva AI features are locked behind the existing Canva Pro subscription service. Serif stated that the perpetually-licensed version 2 will remain available to existing owners, although it will no longer be actively maintained. The new version is currently available for macOS and Windows only, with an iPadOS version to be released soon. == Reception == The change in business model by Canva in 2025 was met with mixed reception, including concerns about its incorporation of AI features. Some users were concerned that their projects would be used for machine learning purposes, or that future versions would suffer from a lack of maintenance or become adware. Additionally, some felt it turned Affinity into fundamentally subscription-based software, given the prevalence of these features in professional contexts. Affinity publicly stated on social media that it would remain "free forever", users' projects would not be used to train AI models, and that "Canva has built a sustainable business model that allows this kind of generosity. And when more professionals use Affinity, Canva can sell more seats into businesses."
Modulation error ratio
The modulation error ratio (MER) is a measure used to quantify the performance of a digital radio (or digital TV) transmitter or receiver in a communications system using digital modulation (such as QAM). A signal sent by an ideal transmitter or received by a receiver would have all constellation points precisely at the ideal locations, however various imperfections in the implementation (such as noise, low image rejection ratio, phase noise, carrier suppression, distortion, etc.) or signal path cause the actual constellation points to deviate from the ideal locations. Transmitter MER can be measured by specialized equipment, which demodulates the received signal in a similar way to how a real radio demodulator does it. Demodulated and detected signal can be used as a reasonably reliable estimate for the ideal transmitted signal in MER calculation. == Definition == An error vector is a vector in the I-Q plane between the ideal constellation point and the point received by the receiver. The Euclidean distance between the two points is its magnitude. The modulation error ratio is equal to the ratio of the root mean square (RMS) power (in Watts) of the reference vector to the power (in Watts) of the error. It is defined in dB as: M E R ( d B ) = 10 log 10 ( P s i g n a l P e r r o r ) {\displaystyle \mathrm {MER(dB)} =10\log _{10}\left({P_{\mathrm {signal} } \over P_{\mathrm {error} }}\right)} where Perror is the RMS power of the error vector, and Psignal is the RMS power of ideal transmitted signal. MER is defined as a percentage in a compatible (but reciprocal) way: M E R ( % ) = P e r r o r P s i g n a l × 100 % {\displaystyle \mathrm {MER(\%)} ={\sqrt {P_{\mathrm {error} } \over P_{\mathrm {signal} }}}\times 100\%} with the same definitions. MER is closely related to error vector magnitude (EVM), but MER is calculated from the average power of the signal. MER is also closely related to signal-to-noise ratio. MER includes all imperfections including deterministic amplitude imbalance, quadrature error and distortion, while noise is random by nature.