General-Purpose Serial Interface, also known as GPSI, 7-wire interface, or 7WS, is a 7 wire communications interface. It is used as an interface between Ethernet MAC and PHY blocks. Data is received and transmitted using separate data paths (TXD, RXD) and separate data clocks (TXCLK, RXCLK). Other signals consist of transmit enable (TXEN), receive carrier sense (CRS), and collision (COL).
Ray tracing (graphics)
In 3D computer graphics, ray tracing is a technique for modeling light transport for use in a wide variety of rendering algorithms for generating digital images. On a spectrum of computational cost and visual fidelity, ray tracing-based rendering techniques, such as ray casting, recursive ray tracing, distribution ray tracing, photon mapping and path tracing, are generally slower and higher fidelity than scanline rendering methods. Thus, ray tracing was first deployed in applications where taking a relatively long time to render could be tolerated, such as still CGI images, and film and television visual effects (VFX), but was less suited to real-time applications such as video games, where speed is critical in rendering each frame. Since 2018, however, hardware acceleration for real-time ray tracing has become standard on new commercial graphics cards, and graphics APIs have followed suit, allowing developers to use hybrid ray tracing and rasterization-based rendering in games and other real-time applications with a lesser hit to frame render times. Ray tracing is capable of simulating a variety of optical effects, such as reflection, refraction, soft shadows, scattering, depth of field, motion blur, caustics, ambient occlusion and dispersion phenomena (such as chromatic aberration). It can also be used to trace the path of sound waves in a similar fashion to light waves, making it a viable option for more immersive sound design in video games by rendering realistic reverberation and echoes. In fact, any physical wave or particle phenomenon with approximately linear motion can be simulated with ray tracing. Ray tracing–based rendering techniques that sample light over a domain typically generate multiple rays and often rely on denoising to reduce the resulting noise. == History == The idea of ray tracing comes from as early as the 16th century, when it was described by Albrecht Dürer, who is credited for its invention. Dürer described multiple techniques for projecting 3-D scenes onto an image plane. Some of these project chosen geometry onto the image plane, as is done with rasterization today. Others determine what geometry is visible along a given ray, as is done with ray tracing. Using a computer for ray tracing to generate shaded pictures was first accomplished by Arthur Appel in 1968. Appel used ray tracing for primary visibility (determining the closest surface to the camera at each image point) by tracing a ray through each point to be shaded into the scene to identify the visible surface. The closest surface intersected by the ray was the visible one. This non-recursive ray tracing-based rendering algorithm is today called "ray casting". His algorithm then traced secondary rays to the light source from each point being shaded to determine whether the point was in shadow or not. Later, in 1971, Goldstein and Nagel of MAGI (Mathematical Applications Group, Inc.) published "3-D Visual Simulation", wherein ray tracing was used to make shaded pictures of solids. At the ray-surface intersection point found, they computed the surface normal and, knowing the position of the light source, computed the brightness of the pixel on the screen. Their publication describes a short (30-second) film "made using the University of Maryland's display hardware outfitted with a 16mm camera. The film showed the helicopter and a simple ground-level gun emplacement. The helicopter was programmed to undergo a series of maneuvers including turns, take-offs, and landings, etc., until it eventually is shot down and crashed." A CDC 6600 computer was used. MAGI produced an animation video called MAGI/SynthaVision Sampler in 1974. Another early instance of ray casting came in 1976, when Scott Roth created a flip book animation in Bob Sproull's computer graphics course at Caltech. The scanned pages are shown as a video in the accompanying image. Roth's computer program noted an edge point at a pixel location if the ray intersected a bounded plane different from that of its neighbors. Of course, a ray could intersect multiple planes in space, but only the surface point closest to the camera was noted as visible. The platform was a DEC PDP-10, a Tektronix storage-tube display, and a printer which would create an image of the display on rolling thermal paper. Roth extended the framework, introduced the term ray casting in the context of computer graphics and solid modeling, and in 1982 published his work while at GM Research Labs. Turner Whitted was the first to show recursive ray tracing for mirror reflection and for refraction through translucent objects, with an angle determined by the solid's index of refraction, and to use ray tracing for anti-aliasing. Whitted also showed ray traced shadows. He produced a recursive ray traced film called The Compleat Angler in 1979 while an engineer at Bell Labs. Whitted's deeply recursive ray tracing algorithm reframed rendering from being primarily a matter of surface visibility determination to being a matter of light transport. His paper inspired a series of subsequent work by others that included distribution ray tracing and finally unbiased path tracing, which provides the rendering equation framework that has allowed computer-generated imagery to be faithful to reality. For decades, global illumination in major films using computer-generated imagery was approximated with additional lights. Ray tracing-based rendering eventually changed that by enabling physically based light transport. Early feature films rendered entirely using path tracing include Monster House (2006), Cloudy with a Chance of Meatballs (2009), and Monsters University (2013). == Algorithm overview == Optical ray tracing describes a method for producing visual images constructed in 3D computer graphics environments, with more photorealism than either ray casting or scanline rendering techniques. It works by tracing a path from an imaginary eye through each pixel in a virtual screen, and calculating the color of the object visible through it. Scenes in ray tracing are described mathematically by a programmer or by a visual artist (normally using intermediary tools). Scenes may also incorporate data from images and models captured by means such as digital photography. Typically, each ray must be tested for intersection with some subset of all the objects in the scene. Once the nearest object has been identified, the algorithm will estimate the incoming light at the point of intersection, examine the material properties of the object, and combine this information to calculate the final color of the pixel. Certain illumination algorithms and reflective or translucent materials may require more rays to be re-cast into the scene. It may at first seem counterintuitive or "backward" to send rays away from the camera, rather than into it (as actual light does in reality), but doing so is many orders of magnitude more efficient. Since the overwhelming majority of light rays from a given light source do not make it directly into the viewer's eye, a "forward" simulation could potentially waste a tremendous amount of computation on light paths that are never recorded. Therefore, the shortcut taken in ray tracing is to presuppose that a given ray intersects the view frame. After either a maximum number of reflections or a ray traveling a certain distance without intersection, the ray ceases to travel and the pixel's value is updated. === Calculate rays for rectangular viewport === On input we have (in calculation we use vector normalization and cross product): E ∈ R 3 {\displaystyle E\in \mathbb {R^{3}} } eye position T ∈ R 3 {\displaystyle T\in \mathbb {R^{3}} } target position θ ∈ [ 0 , π ] {\displaystyle \theta \in [0,\pi ]} field of view - for humans, we can assume ≈ π / 2 rad = 90 ∘ {\displaystyle \approx \pi /2{\text{ rad}}=90^{\circ }} m , k ∈ N {\displaystyle m,k\in \mathbb {N} } numbers of square pixels on viewport vertical and horizontal direction i , j ∈ N , 1 ≤ i ≤ k ∧ 1 ≤ j ≤ m {\displaystyle i,j\in \mathbb {N} ,1\leq i\leq k\land 1\leq j\leq m} numbers of actual pixel v → ∈ R 3 {\displaystyle {\vec {v}}\in \mathbb {R^{3}} } vertical vector which indicates where is up and down, usually v → = [ 0 , 1 , 0 ] {\displaystyle {\vec {v}}=[0,1,0]} - roll component which determine viewport rotation around point C (where the axis of rotation is the ET section) The idea is to find the position of each viewport pixel center P i j {\displaystyle P_{ij}} which allows us to find the line going from eye E {\displaystyle E} through that pixel and finally get the ray described by point E {\displaystyle E} and vector R → i j = P i j − E {\displaystyle {\vec {R}}_{ij}=P_{ij}-E} (or its normalization r → i j {\displaystyle {\vec {r}}_{ij}} ). First we need to find the coordinates of the bottom left viewport pixel P 1 m {\displaystyle P_{1m}} and find the next pixel by making a shift along directions parallel to viewport (vectors b → n {\displaystyle {\vec {b}}_{n
Chinese speech synthesis
Chinese speech synthesis is the application of speech synthesis to the Chinese language (usually Standard Chinese). It poses additional difficulties due to Chinese characters frequently having different pronunciations in different contexts and the complex prosody, which is essential to convey the meaning of words, and sometimes the difficulty in obtaining agreement among native speakers concerning what the correct pronunciation is of certain phonemes. == Concatenation (Ekho and KeyTip) == Recordings can be concatenated in any desired combination, but the joins sound forced (as is usual for simple concatenation-based speech synthesis) and this can severely affect prosody; these synthesizers are also inflexible in terms of speed and expression. However, because these synthesizers do not rely on a corpus, there is no noticeable degradation in performance when they are given more unusual or awkward phrases. Ekho is an open source TTS which simply concatenates sampled syllables. It currently supports Cantonese, Mandarin, and experimentally Korean. Some of the Mandarin syllables have been pitched-normalised in Praat. A modified version of these is used in Gradint's "synthesis from partials". cjkware.com used to ship a product called KeyTip Putonghua Reader which worked similarly; it contained 120 Megabytes of sound recordings (GSM-compressed to 40 Megabytes in the evaluation version), comprising 10,000 multi-syllable dictionary words plus single-syllable recordings in 6 different prosodies (4 tones, neutral tone, and an extra third-tone recording for use at the end of a phrase). == Lightweight synthesizers (eSpeak and Yuet) == The lightweight open-source speech project eSpeak, which has its own approach to synthesis, has experimented with Mandarin and Cantonese. eSpeak was used by Google Translate from May 2010 until December 2010. The commercial product "Yuet" is also lightweight (it is intended to be suitable for resource-constrained environments like embedded systems); it was written from scratch in ANSI C starting from 2013. Yuet claims a built-in NLP model that does not require a separate dictionary; the speech synthesised by the engine claims clear word boundaries and emphasis on appropriate words. Communication with its author is required to obtain a copy. Both eSpeak and Yuet can synthesis speech for Cantonese and Mandarin from the same input text, and can output the corresponding romanisation (for Cantonese, Yuet uses Yale and eSpeak uses Jyutping; both use Pinyin for Mandarin). eSpeak does not concern itself with word boundaries when these don't change the question of which syllable should be spoken. == Corpus-based == A "corpus-based" approach can sound very natural in most cases but can err in dealing with unusual phrases if they can't be matched with the corpus. The synthesiser engine is typically very large (hundreds or even thousands of megabytes) due to the size of the corpus. === iFlyTek === Anhui USTC iFlyTek Co., Ltd (iFlyTek) published a W3C paper in which they adapted Speech Synthesis Markup Language to produce a mark-up language called Chinese Speech Synthesis Markup Language (CSSML) which can include additional markup to clarify the pronunciation of characters and to add some prosody information. The amount of data involved is not disclosed by iFlyTek but can be seen from the commercial products that iFlyTek have licensed their technology to; for example, Bider's SpeechPlus is a 1.3 Gigabyte download, 1.2 Gigabytes of which is used for the highly compressed data for a single Chinese voice. iFlyTek's synthesiser can also synthesise mixed Chinese and English text with the same voice (e.g. Chinese sentences containing some English words); they claim their English synthesis to be "average". The iFlyTek corpus appears to be heavily dependent on Chinese characters, and it is not possible to synthesize from pinyin alone. It is sometimes possible by means of CSSML to add pinyin to the characters to disambiguate between multiple possible pronunciations, but this does not always work. === NeoSpeech === There is an online interactive demonstration for NeoSpeech speech synthesis, which accepts Chinese characters and also pinyin if it's enclosed in their proprietary "VTML" markup. === Mac OS === Mac OS had Chinese speech synthesizers available up to version 9. This was removed in 10.0 and reinstated in 10.7 (Lion). === Historical corpus-based synthesizers (no longer available) === A corpus-based approach was taken by Tsinghua University in SinoSonic, with the Harbin dialect voice data taking 800 Megabytes. This was planned to be offered as a download but the link was never activated. Nowadays, only references to it can be found on Internet Archive. Bell Labs' approach, which was demonstrated online in 1997 but subsequently removed, was described in a monograph "Multilingual Text-to-Speech Synthesis: The Bell Labs Approach" (Springer, October 31, 1997, ISBN 978-0-7923-8027-6), and the former employee who was responsible for the project, Chilin Shih (who subsequently worked at the University of Illinois) put some notes about her methods on her website.
Iteration
Iteration means repeating a process to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. == Mathematics == In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a common use and a well-known example. == Computing == In computing, iteration is a technique that marks out of a block of statements within a computer program for a defined number of repetitions. That block of statements is said to be iterated. A computer programmer might also refer to that block of statements as an iteration. === Implementations === Loops constitute the most common language constructs for performing iterations. The following pseudocode "iterates" three times the line of code between begin & end through a for loop, and uses the values of i as increments. It is permissible, and often necessary, to use values from other parts of the program outside the bracketed block of statements, to perform the desired function. Iterators constitute alternative language constructs to loops, which ensure consistent iterations over specific data structures. They can eventually save time and effort in later coding attempts. In particular, an iterator allows one to repeat the same kind of operation at each node of such a data structure, often in some pre-defined order. Iteratees are purely functional language constructs, which accept or reject data during the iterations. === Relation with recursion === Recursions and iterations have different algorithmic definitions, even though they can generate identical results. The primary difference is that recursion can be a solution without prior knowledge as to how many times the action must repeat, while a successful iteration requires that foreknowledge. Some types of programming languages, known as functional programming languages, are designed such that they do not set up a block of statements for explicit repetition, as with the for loop. Instead, those programming languages exclusively use recursion. Rather than call out a block of code to repeate a pre-defined number of times, the executing code block instead "divides" the work into a number of separate pieces, after which the code block executes itself on each individual piece. Each piece of work is divided repeatedly until the "amount" of work is as small as possible, at which point the algorithm does that work very quickly. The algorithm then "reverses" and reassembles the pieces into a complete whole. The classic example of recursion is in list-sorting algorithms, such as merge sort. The merge sort recursive algorithm first repeatedly divides the list into consecutive pairs. Each pair is then ordered, then each consecutive pair of pairs, and so forth until the elements of the list are in the desired order. The code below is an example of a recursive algorithm in the Scheme programming language that outputs the same result as the pseudocode under the previous heading. == Education == In some schools of pedagogy, iterations are used to describe the process of teaching or guiding students to repeat experiments, assessments, or projects, until more accurate results are found, or the student has mastered the technical skill. This idea is found in the old adage, "Practice makes perfect." In particular, "iterative" is defined as the "process of learning and development that involves cyclical inquiry, enabling multiple opportunities for people to revisit ideas and critically reflect on their implication." Unlike computing and math, educational iterations are not predetermined; instead, the task is repeated until success according to some external criteria (often a test) is achieved.
Artificial intelligence industry in Taiwan
The artificial intelligence (AI) industry in Taiwan refers to the development, application, and commercialization of artificial intelligence technologies within Taiwan. The industry has grown alongside Taiwan's established strengths in semiconductor manufacturing and information and communications technology (ICT), and is supported by government policy, research institutions, and private sector participation. AI development in Taiwan has focused on integrating hardware capabilities with software applications across sectors such as manufacturing, healthcare, and smart infrastructure. Artificial intelligence has been identified as a strategic area of development in Taiwan since the late 2010s. While Taiwan has historically played a limited role in early theoretical and expert-system phases of AI development, its position in global electronics manufacturing has provided a foundation for participation in the contemporary era of machine learning and data-driven AI systems. Taiwan's AI industry is characterized by a strong hardware base, particularly in semiconductor production and AI server manufacturing, combined with increasing investment in software, data infrastructure, and applied AI services. The sector has been shaped by global demand for computing power, advances in deep learning, and the expansion of AI applications in industrial and commercial contexts. == Government policy and development == The Taiwanese government has promoted AI development through a series of national strategies. In 2017, the Ministry of Science and Technology launched the "AI Grand Strategy for a Small Country" initiative, investing approximately US$517 million between 2017 and 2021 to support research, infrastructure, and talent development. This initiative aimed to build a domestic AI ecosystem by funding research centers, expanding data infrastructure, and supporting industrial adoption. The Executive Yuan also introduced the AI Taiwan Action Plan 1.0 (2018–2021), which focused on integrating AI technologies into existing industries and strengthening research and development capabilities. A subsequent plan, AI Taiwan Action Plan 2.0 (2023–2026), expanded the focus to include ethical governance, regulatory frameworks, and risk management in response to the growth of generative AI technologies. In 2023, the Taiwan AI Center of Excellence (Taiwan AICoE), a government-backed hub, was established by the National Science and Technology Council to accelerate AI development, foster international collaboration, and train talent in Taiwan. It acts as a specialized think tank focusing on creating a "smart technology island" by integrating AI resources and developing trusted, human-centric AI technologies. In 2024, the Taiwan Chip-based Industrial Innovation Program (CbI) was launched by the Executive Yuan as a 10-year, NT$300 billion (US$9.3 billion) initiative to leverage Taiwan's semiconductor dominance, driving innovation in AI, smart mobility, manufacturing, and healthcare. It aims to combine generative AI with IC technology, cultivate talent, and attract global startups to build a "Silicon Island". In parallel, the Taiwanese government has explored legislative frameworks such as a proposed Artificial Intelligence Fundamental Act in December 2025, addressing issues including data protection, safety standards, and intellectual property. == Industrial structure == === Semiconductor and hardware foundation === Taiwan's AI industry is closely linked to its semiconductor sector. In 2020, Taiwan accounted for approximately 77.3% of the global wafer foundry market and 57.7% of packaging and testing, with a 20.1% share in integrated circuit (IC) design. These capabilities provide critical infrastructure for AI systems, which rely on high-performance computing hardware. Taiwanese firms are also involved in the production of AI servers and related components, contributing significantly to global supply chains for data centers and cloud computing. The integration of chip design, manufacturing, and assembly has enabled Taiwan to play a central role in providing the computational resources required for AI development. On 20 November 2025, Google established the "Google Taiwan AI Infrastructure R&D Center", second only to its US headquarters and largest AI hardware infrastructure engineering center outside of the United States. === Software and services === Compared to its hardware capabilities, Taiwan's AI software sector is less developed. The absence of large-scale global AI platform companies has been noted as a structural limitation. As a result, much of Taiwan's AI industry focuses on applied solutions, including customization of existing AI models for specific industries. Therefore, efforts to strengthen software capabilities have included investment in research institutions, startup ecosystems, and collaborations between academia and industry. == Applications == === Smart manufacturing === AI has been widely applied in Taiwan's manufacturing sector, which is a major component of the economy. Applications include process automation, predictive maintenance, quality control, and fault detection. AI-enabled smart manufacturing systems aim to improve efficiency, reduce production costs, and enhance product quality. Taiwan's manufacturing industry has incorporated AI technologies into production lines, particularly in electronics and machinery sectors. === Healthcare === The use of AI in healthcare in Taiwan has expanded in areas such as medical imaging, diagnostics, and drug development. AI systems are used to analyze CT scans, MRI data, and other clinical information to support diagnosis and treatment planning. Taiwan's healthcare sector, which includes medical devices, pharmaceuticals, and medical services, has benefited from the integration of AI technologies, particularly in precision medicine and clinical decision support systems. A notable example of AI healthcare deployment in Taiwan is the collaboration between Siemens Healthineers, Ever Fortune AI, and Asia University Hospital. === Edge computing and IoT === AI applications in Taiwan increasingly involve edge computing, where data processing occurs near the source rather than in centralized cloud systems. This approach reduces latency and bandwidth requirements and is used in smart devices, sensors, and industrial equipment. Edge AI technologies are applied in areas such as smart appliances, industrial automation, and transportation systems. == Education and talent development == Human capital development has been a key focus of Taiwan's AI strategy. The Taiwan AI Academy, established in 2018 with support from Academia Sinica and industry partners, provides training programs for professionals and students aimed at accelerating the adoption of artificial intelligence technologies across industries. The academy offers a range of courses, including executive-level programs, technical training, and specialized tracks in areas such as smart manufacturing, smart healthcare, and edge AI. These programs are designed to provide intensive and practical instruction over relatively short periods. A notable component of the curriculum is project-based learning, in which participants are required to complete proof-of-concept (POC) projects addressing real-world industrial problems. These projects are often developed further for implementation within companies, facilitating technology transfer and commercialization. Between 2018 and 2021, more than 8,000 individuals completed AI training programs across campuses in Taipei, Hsinchu, Taichung, and Tainan. Graduates of the academy have contributed to the introduction of AI systems in sectors such as manufacturing, healthcare, and finance, supporting broader industrial transformation efforts. In addition to the Taiwan AI Academy, universities and research institutions in Taiwan play a significant role in AI education and research. Leading universities have expanded programs in computer science, data science, and machine learning, while research institutes conduct applied and fundamental studies in artificial intelligence. Collaboration between academia, government, and industry is a common feature of Taiwan's AI ecosystem, with joint research projects, internship programs, and technology incubation initiatives supporting talent development. Government-supported initiatives have also sought to attract and retain AI talent, including funding for graduate education, international collaboration programs, and incentives for industry–academic partnerships. These efforts aim to address talent shortages and strengthen Taiwan's capacity in both applied and foundational AI research. == Regulation and governance == Taiwan has developed guidelines and policy frameworks to address the risks associated with AI technologies. In 2023, the Executive Yuan issued guidelines for the use of generative AI in government agencies, focusing on data security and privacy. Ongoing policy discussions hav
Developmental robotics
Developmental robotics (DevRob), sometimes called epigenetic robotics, is a scientific field which aims at studying the developmental mechanisms, architectures and constraints that allow lifelong and open-ended learning of new skills and new knowledge in embodied machines. As in human children, learning is expected to be cumulative and of progressively increasing complexity, and to result from self-exploration of the world in combination with social interaction. The typical methodological approach consists in starting from theories of human and animal development elaborated in fields such as developmental psychology, neuroscience, developmental and evolutionary biology, and linguistics, then to formalize and implement them in robots, sometimes exploring extensions or variants of them. The experimentation of those models in robots allows researchers to confront them with reality, and as a consequence, developmental robotics also provides feedback and novel hypotheses on theories of human and animal development. Developmental robotics is related to but differs from evolutionary robotics (ER). ER uses populations of robots that evolve over time, whereas DevRob is interested in how the organization of a single robot's control system develops through experience, over time. DevRob is also related to work done in the domains of robotics and artificial life. == Background == Can a robot learn like a child? Can it learn a variety of new skills and new knowledge unspecified at design time and in a partially unknown and changing environment? How can it discover its body and its relationships with the physical and social environment? How can its cognitive capacities continuously develop without the intervention of an engineer once it is "out of the factory"? What can it learn through natural social interactions with humans? These are the questions at the center of developmental robotics. Alan Turing, as well as a number of other pioneers of cybernetics, already formulated those questions and the general approach in 1950, but it is only since the end of the 20th century that they began to be investigated systematically. Because the concept of adaptive intelligent machines is central to developmental robotics, it has relationships with fields such as artificial intelligence, machine learning, cognitive robotics or computational neuroscience. Yet, while it may reuse some of the techniques elaborated in these fields, it differs from them from many perspectives. It differs from classical artificial intelligence because it does not assume the capability of advanced symbolic reasoning and focuses on embodied and situated sensorimotor and social skills rather than on abstract symbolic problems. It differs from cognitive robotics because it focuses on the processes that allow the formation of cognitive capabilities rather than these capabilities themselves. It differs from computational neuroscience because it focuses on functional modeling of integrated architectures of development and learning. More generally, developmental robotics is uniquely characterized by the following three features: It targets task-independent architectures and learning mechanisms, i.e. the machine/robot has to be able to learn new tasks that are unknown by the engineer; It emphasizes open-ended development and lifelong learning, i.e. the capacity of an organism to acquire continuously novel skills. This should not be understood as a capacity for learning "anything" or even “everything”, but just that the set of skills that is acquired can be infinitely extended at least in some (not all) directions; The complexity of acquired knowledge and skills shall increase (and the increase be controlled) progressively. Developmental robotics emerged at the crossroads of several research communities including embodied artificial intelligence, enactive and dynamical systems cognitive science, connectionism. Starting from the essential idea that learning and development happen as the self-organized result of the dynamical interactions among brains, bodies and their physical and social environment, and trying to understand how this self-organization can be harnessed to provide task-independent lifelong learning of skills of increasing complexity, developmental robotics strongly interacts with fields such as developmental psychology, developmental and cognitive neuroscience, developmental biology (embryology), evolutionary biology, and cognitive linguistics. As many of the theories coming from these sciences are verbal and/or descriptive, this implies a crucial formalization and computational modeling activity in developmental robotics. These computational models are then not only used as ways to explore how to build more versatile and adaptive machines but also as a way to evaluate their coherence and possibly explore alternative explanations for understanding biological development. == Research directions == === Skill domains === Due to the general approach and methodology, developmental robotics projects typically focus on having robots develop the same types of skills as human infants. A first category that is important being investigated is the acquisition of sensorimotor skills. These include the discovery of one's own body, including its structure and dynamics such as hand-eye coordination, locomotion, and interaction with objects as well as tool use, with a particular focus on the discovery and learning of affordances. A second category of skills targeted by developmental robots are social and linguistic skills: the acquisition of simple social behavioural games such as turn-taking, coordinated interaction, lexicons, syntax and grammar, and the grounding of these linguistic skills into sensorimotor skills (sometimes referred as symbol grounding). In parallel, the acquisition of associated cognitive skills are being investigated such as the emergence of the self/non-self distinction, the development of attentional capabilities, of categorization systems and higher-level representations of affordances or social constructs, of the emergence of values, empathy, or theories of mind. === Mechanisms and constraints === The sensorimotor and social spaces in which humans and robot live are so large and complex that only a small part of potentially learnable skills can actually be explored and learnt within a life-time. Thus, mechanisms and constraints are necessary to guide developmental organisms in their development and control of the growth of complexity. There are several important families of these guiding mechanisms and constraints which are studied in developmental robotics, all inspired by human development: Motivational systems, generating internal reward signals that drive exploration and learning, which can be of two main types: extrinsic motivations push robots/organisms to maintain basic specific internal properties such as food and water level, physical integrity, or light (e.g. in phototropic systems); intrinsic motivations push robot to search for novelty, challenge, compression or learning progress per se, thus generating what is sometimes called curiosity-driven learning and exploration, or alternatively active learning and exploration; Social guidance: as humans learn a lot by interacting with their peers, developmental robotics investigates mechanisms that can allow robots to participate to human-like social interaction. By perceiving and interpreting social cues, this may allow robots both to learn from humans (through diverse means such as imitation, emulation, stimulus enhancement, demonstration, etc. ...) and to trigger natural human pedagogy. Thus, social acceptance of developmental robots is also investigated; Statistical inference biases and cumulative knowledge/skill reuse: biases characterizing both representations/encodings and inference mechanisms can typically allow considerable improvement of the efficiency of learning and are thus studied. Related to this, mechanisms allowing to infer new knowledge and acquire new skills by reusing previously learnt structures is also an essential field of study; The properties of embodiment, including geometry, materials, or innate motor primitives/synergies often encoded as dynamical systems, can considerably simplify the acquisition of sensorimotor or social skills, and is sometimes referred as morphological computation. The interaction of these constraints with other constraints is an important axis of investigation; Maturational constraints: In human infants, both the body and the neural system grow progressively, rather than being full-fledged already at birth. This implies, for example, that new degrees of freedom, as well as increases of the volume and resolution of available sensorimotor signals, may appear as learning and development unfold. Transposing these mechanisms in developmental robots, and understanding how it may hinder or on the contrary ease the acquisition of novel complex skills is a central questi
Certifying algorithm
In theoretical computer science, a certifying algorithm is an algorithm that outputs, together with a solution to the problem it solves, a proof that the solution is correct. A certifying algorithm is said to be efficient if the combined runtime of the algorithm and a proof checker is slower by at most a constant factor than the best known non-certifying algorithm for the same problem. The proof produced by a certifying algorithm should be in some sense simpler than the algorithm itself, for otherwise any algorithm could be considered certifying (with its output verified by running the same algorithm again). Sometimes this is formalized by requiring that a verification of the proof take less time than the original algorithm, while for other problems (in particular those for which the solution can be found in linear time) simplicity of the output proof is considered in a less formal sense. For instance, the validity of the output proof may be more apparent to human users than the correctness of the algorithm, or a checker for the proof may be more amenable to formal verification. Implementations of certifying algorithms that also include a checker for the proof generated by the algorithm may be considered to be more reliable than non-certifying algorithms. For, whenever the algorithm is run, one of three things happens: it produces a correct output (the desired case), it detects a bug in the algorithm or its implication (undesired, but generally preferable to continuing without detecting the bug), or both the algorithm and the checker are faulty in a way that masks the bug and prevents it from being detected (undesired, but unlikely as it depends on the existence of two independent bugs). == Examples == Many examples of problems with checkable algorithms come from graph theory. For instance, a classical algorithm for testing whether a graph is bipartite would simply output a Boolean value: true if the graph is bipartite, false otherwise. In contrast, a certifying algorithm might output a 2-coloring of the graph in the case that it is bipartite, or a cycle of odd length if it is not. Any graph is bipartite if and only if it can be 2-colored, and non-bipartite if and only if it contains an odd cycle. Both checking whether a 2-coloring is valid and checking whether a given odd-length sequence of vertices is a cycle may be performed more simply than testing bipartiteness. Analogously, it is possible to test whether a given directed graph is acyclic by a certifying algorithm that outputs either a topological order or a directed cycle. It is possible to test whether an undirected graph is a chordal graph by a certifying algorithm that outputs either an elimination ordering (an ordering of all vertices such that, for every vertex, the neighbors that are later in the ordering form a clique) or a chordless cycle. And it is possible to test whether a graph is planar by a certifying algorithm that outputs either a planar embedding or a Kuratowski subgraph. The extended Euclidean algorithm for the greatest common divisor of two integers x and y is certifying: it outputs three integers g (the divisor), a, and b, such that ax + by = g. This equation can only be true of multiples of the greatest common divisor, so testing that g is the greatest common divisor may be performed by checking that g divides both x and y and that this equation is correct.