Vicarious (company)

Vicarious (company)

Vicarious was an artificial intelligence company based in the San Francisco Bay Area, California. They use the theorized computational principles of the brain to attempt to build software that can think and learn like a human. Vicarious describes its technology as "a turnkey robotics solution integrator using artificial intelligence to automate tasks too complex and versatile for traditional automations". Alphabet Inc acquired the company in 2022 for an undisclosed amount. == Founders == The company was founded in 2010 by D. Scott Phoenix and Dileep George. Before co-founding Vicarious, Phoenix was Entrepreneur in Residence at Founders Fund and CEO of Frogmetrics, a touchscreen analytics company he co-founded through the Y Combinator incubator program. Previously, George was Chief Technology Officer at Numenta, a company he co-founded with Jeff Hawkins and Donna Dubinsky while completing his PhD at Stanford University. == Funding == The company launched in February 2011 with funding from Founders Fund, Dustin Moskovitz, Adam D’Angelo (former Facebook CTO and co-founder of Quora), Felicis Ventures, and Palantir co-founder Joe Lonsdale. In August 2012, in its Series A round of funding, it raised an additional $15 million. The round was led by Good Ventures; Founders Fund, Open Field Capital and Zarco Investment Group also participated. The company received $40 million in its Series B round of funding. The round was led by individuals including Mark Zuckerberg, Elon Musk, and others. An additional undisclosed amount was later contributed by Amazon.com CEO Jeff Bezos, Yahoo! co-founder Jerry Yang, Skype co-founder Janus Friis and Salesforce.com CEO Marc Benioff. == Recursive Cortical Network == Vicarious is developing machine learning software based on the computational principles of the human brain. One such software is a vision system known as the Recursive Cortical Network (RCN), it is a generative graphical visual perception system that interprets the contents of photographs and videos in a manner similar to humans. The system is powered by a balanced approach that takes sensory data, mathematics, and biological plausibility into consideration. On October 22, 2013, beating CAPTCHA, Vicarious announced its model was reliably able to solve modern CAPTCHAs, with character recognition rates of 90% or better when trained on one style. However, Luis von Ahn, a pioneer of early CAPTCHA and founder of reCAPTCHA, expressed skepticism, stating: "It's hard for me to be impressed since I see these every few months." He pointed out that 50 similar claims to that of Vicarious had been made since 2003. Vicarious later published their findings in peer-reviewed journal Science. Vicarious has indicated that its AI was not specifically designed to complete CAPTCHAs and its success at the task is a product of its advanced vision system. Because Vicarious's algorithms are based on insights from the human brain, it is also able to recognize photographs, videos, and other visual data.

Luxafor

Luxafor () is a brand of office productivity tools designed to improve efficiency and communication in workplaces. The brands main product is LED status indicators for use in office settings. Luxafor is a product line under the company SIA Greynut, based in Riga, Latvia. == History == Luxafor was developed by the technology company SIA Greynut. The brand first gained attention through a Kickstarter campaign in 2015, which aimed to fund its initial product, the Luxafor Flag. Although the campaign was unsuccessful in reaching its funding goal, the product was still brought to market. In 2017, Luxafor launched another Kickstarter campaign for the Luxafor Bluetooth, a wireless version of its LED status indicator. This campaign also did not meet its funding goal, but like its predecessor, the product was still developed and released. Despite initial setbacks, Luxafor Bluetooth has become one of the brand's leading products. == Products == Luxafors main product range is LED status indicators, including: === Luxafor Flag === A USB-powered LED indicator that shows different colors to signal the user's availability. === Luxafor Bluetooth === A wireless LED indicator controlled via Bluetooth, integrating with productivity tools like Slack and Microsoft Teams. === Luxafor Switch === An advanced status indicator designed to manage room and workspace availability. === Other === Other Luxafor products include CO2 Dongle, Smart Button, Mute Button, Pomodoro Timer and others. == Features == Luxafor products are known for their customizable indicators, integration capabilities with IFTTT, Zapier, and remote control features. They are compatible with various operating systems, including Windows and macOS, and can be integrated with numerous communication and productivity platforms, like Microsoft Teams and Cisco Jabber.

Content format

A content format is an encoded format for converting a specific type of data to displayable information. Content formats are used in recording and transmission to prepare data for observation or interpretation. This includes both analog and digitized content. Content formats may be recorded and read by either natural or manufactured tools and mechanisms. In addition to converting data to information, a content format may include the encryption and/or scrambling of that information. Multiple content formats may be contained within a single section of a storage medium (e.g. track, disk sector, computer file, document, page, column) or transmitted via a single channel (e.g. wire, carrier wave) of a transmission medium. With multimedia, multiple tracks containing multiple content formats are presented simultaneously. Content formats may either be recorded in secondary signal processing methods such as a software container format (e.g. digital audio, digital video) or recorded in the primary format (e.g. spectrogram, pictogram). Observable data is often known as raw data, or raw content. A primary raw content format may be directly observable (e.g. image, sound, motion, smell, sensation) or physical data which only requires hardware to display it, such as a phonographic needle and diaphragm or a projector lamp and magnifying glass. The following are examples of some common content formats and content format categories (covering: sensory experience, model, and language used for encoding information):

Copyright

A copyright is a type of intellectual property that gives its owner the exclusive legal right to copy, distribute, adapt, display, and perform a creative work, usually for a limited time. The creative work may be in a literary, artistic, educational, or musical form. Copyright is intended to protect the original expression of an idea in the form of a creative work, but not the idea itself. A copyright is subject to limitations based on public interest considerations, such as the fair use doctrine in the United States and fair dealing doctrine in the United Kingdom. Some jurisdictions require "fixing" copyrighted works in a tangible form. It is often shared among multiple authors, each of whom holds a set of rights to use or license the work, and who are commonly referred to as rights holders. These rights normally include reproduction, control over derivative works, distribution, public performance, and moral rights such as attribution. Copyrights can be granted by public law and are in that case considered "territorial rights". This means that copyrights granted by the law of a certain state do not extend beyond the territory of that specific jurisdiction. Copyrights of this type vary by country; many countries, and sometimes a large group of countries, have made agreements with other countries on procedures applicable when works "cross" national borders or national rights are inconsistent. Typically, the public law duration of a copyright expires 50 to 100 years after the creator dies, depending on the jurisdiction. Some countries require certain copyright formalities to establishing copyright, others recognize copyright in any completed work, without a formal registration. When the copyright of a work expires, it enters the public domain. == History == === Background === The concept of copyright developed after the printing press came into use in Europe in the 15th and 16th centuries. It was associated with a common law and rooted in the civil law system. The printing press made it much cheaper to produce works, but as there was initially no copyright law, anyone could buy or rent a press and print any text. Popular new works were immediately re-set and re-published by competitors, so printers needed a constant stream of new material. Fees paid to authors for new works were high and significantly supplemented the incomes of many academics. Printing brought profound social changes. The rise in literacy across Europe led to a dramatic increase in the demand for reading matter. Prices of reprints were low, so publications could be bought by poorer people, creating a mass audience. In German-language markets before the advent of copyright, technical materials, like academic papers and handbooks, were inexpensive and widely available; it has been suggested this contributed to Germany's industrial and economic success. === Conception === The concept of copyright first developed in England. In reaction to the printing of "scandalous books and pamphlets", the English Parliament passed the Licensing of the Press Act 1662, which required all intended publications to be registered with the government-approved Stationers' Company, giving the Stationers the right to regulate what material could be printed. The Statute of Anne, enacted in 1710 in England and Scotland, provided the first legislation to protect copyrights (but not authors' rights). The Copyright Act 1814 extended more rights for authors but did not protect British publications from being reprinted in the US. The Berne International Copyright Convention of 1886 finally provided protection for authors among the countries who signed the agreement, although the US did not join the Berne Convention until 1989. In the US, the Constitution grants Congress the right to establish copyright and patent laws. Shortly after the Constitution was passed, Congress enacted the Copyright Act of 1790, modeling it after the Statute of Anne. While the national law protected authors' published works, authority was granted to the states to protect authors' unpublished works. The most recent major overhaul of copyright in the US, the Copyright Act of 1976, extended federal copyright to works as soon as they are created and "fixed", without requiring publication or registration. State law continues to apply to unpublished works that are not otherwise copyrighted by federal law. This act also changed the calculation of copyright term from a fixed term (then a maximum of fifty-six years) to "life of the author plus 50 years". These changes brought the US closer to conformity with the Berne Convention, and in 1989 the United States further revised its copyright law and joined the Berne Convention officially. Copyright laws allow products of creative human activities, such as literary and artistic production, to be preferentially exploited and thus incentivized. Different cultural attitudes, social organizations, economic models and legal frameworks are seen to account for why copyright emerged in Europe and not, for example, in Asia. In the Middle Ages in Europe, there was generally a lack of any concept of literary property due to the general relations of production, the specific organization of literary production and the role of culture in society. The latter refers to the tendency of oral societies, such as that of Europe in the medieval period, to view knowledge as the product and expression of the collective, rather than to see it as individual property. However, with copyright laws, intellectual production comes to be seen as a product of an individual, with attendant rights. The most significant point is that patent and copyright laws support the expansion of the range of creative human activities that can be commodified. This parallels the ways in which capitalism led to the commodification of many aspects of social life that earlier had no monetary or economic value perse. Copyright has developed into a concept that has a significant effect on nearly every modern industry, including not just literary work, but also forms of creative work such as sound recordings, films, photographs, software, and architecture. === National copyrights === Often seen as the first real copyright law, the 1709 British Statute of Anne gave authors and the publishers to whom they did chose to license their works, the right to publish the author's creations for a fixed period, after which the copyright expired. It was "An Act for the Encouragement of Learning, by Vesting the Copies of Printed Books in the Authors or the Purchasers of such Copies, during the Times therein mentioned." The act also alluded to individual rights of the artist. It began: "Whereas Printers, Booksellers, and other Persons, have of late frequently taken the Liberty of Printing ... Books, and other Writings, without the Consent of the Authors ... to their very great Detriment, and too often to the Ruin of them and their Families:". A right to benefit financially from the work is articulated, and court rulings and legislation have recognized a right to control the work, such as ensuring that the integrity of it is preserved. An irrevocable right to be recognized as the work's creator appears in some countries' copyright laws. The Copyright Clause of the United States, Constitution (1787) authorized copyright legislation: "To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." That is, by guaranteeing them a period of time in which they alone could profit from their works, they would be enabled and encouraged to invest the time required to create them, and this would be good for society as a whole. A right to profit from the work has been the philosophical underpinning for much legislation extending the duration of copyright, to the life of the creator and beyond, to their heirs. Yet scholars like Lawrence Lessig have argued that copyright terms have been extended beyond the scope imagined by the Framers. Lessig refers to the Copyright Clause as the "Progress Clause" to emphasize the social dimension of intellectual property rights. The original length of copyright in the United States was 14 years, and it had to be explicitly applied for. If the author wished, they could apply for a second 14‑year monopoly grant, but after that the work entered the public domain, so it could be used and built upon by others. === Continental law === In many jurisdictions of the European continent, comparable legal concepts to copyright did exist from the 16th century on but did change under Napoleonic rule into another legal concept: authors' rights or creator's right laws, from French: droits d'auteur and German Urheberrecht. In many modern-day publications the terms copyright and authors' rights are being mixed, or used as translations, but in a juridical sense the legal concepts do essentially differ. Authors' rights are, generally speaking,

Hike Messenger

Hike Messenger, aka Hike Sticker Chat, is a multifunctional Indian social media and social networking service offering instant messaging (IM) and Voice over IP (VoIP) services that was launched on December 11, 2012, by Kavin Bharti Mittal. Hike functioned through SMS. The app registration used a s‍tandard, one-time password (OTP) based authentication process. It was estimated to be worth $1.4 billion and had more than 100 million registered users. It went defunct on January 6, 2021, as they were unable to compete with global messaging platforms. The app re-appeared on google play store and apple app store on 19 September 2025. == History == Hike Messenger was launched on December 12, 2012, by its founder, Kavin Bharti Mittal. The majority of users were from India, with 80% under the age of 25. The company purchased startups like TinyMogul and Hoppr in 2015. After buying US-based free voice calling company Zip Phones, Hike provided VoIP calling services. On March 5, 2015, Hike launched the 'Great Indian Sticker Challenge' to create more stickers. In February 2017, Hike acquired the social networking app Pulse. From version 5.0, it became the first social messaging app to start a mobile payment service in India. The timeline feature came back after multiple user requests and the introduction of a personalized digital envelope called Blue Packets for sending monetary gifts through a built-in wallet. In 2017, the acquisition of Bengaluru-based startup Creo was announced to enable third-party developers to build services on top of the Hike platform. In 2018, Hike provided 1 billion users with internet access by targeting smaller cities. In January 2019, the company discarded the previous super-app approach, and began launching specialized apps for specific use-cases. In May 2019, Hike announced a collaboration with Indraprastha Institute of Information Technology, Delhi (IIIT-D) to develop a variety of machine learning models. In April 2019, the company launched its first standalone app, Hike Sticker Chat. A separate content app Hike News & Content was also launched. In 2021, Hike shut down its messaging service and shifted focus to gaming and community platforms. It launched Rush, a real-money gaming app featuring casual titles like ludo and carrom, which scaled to over 10 million users and generated more than US$500 million in gross revenue over four years. The company also introduced Vibe, an approval-only community app, as part of its pivot away from the super-app and messaging model. In September 2025, following the passage of the Promotion and Regulation of Online Gaming Act, which banned real-money gaming in India, Hike announced its complete closure. Founder Kavin Bharti Mittal stated that while the company had begun international expansion, scaling globally under the new regulatory regime would require a full reset that was not a viable use of capital or resources. On 19 September 2025, hike was relaunched on play store and app store by the name hike messenger. == Application == === Timeline of Features === On 15 April 2014, Hike introduced unlimited free SMS via a service called Hike Offline, through credits earned by users from regular chatting, as connectivity is still a major issue in many parts of India. In an attempt to appeal to its younger users, Hike introduced features that find resonance with the local market, such as Last Seen Privacy and localized sticker packs. It also introduced a two-way chat theme, allowing users to change the chat background for themselves and for their friends simultaneously. The app also started showing live Cricket scores in collaboration with Cricbuzz, as well as news, casual games, and social media feeds. Hike also added a file transfer service, allowing files less than 100MB of all formats, with a view on further increasing the size limit to 1 GB. With the launch of version 2.9.2.0 in January 2015, Hike implemented support for sending uncompressed images and a "quick upload" feature optimized for 2G speed. Later that month, Hike introduced a voice calling feature for its users. In September 2015, Hike launched free group call support with up to 100 people in a simultaneous conference call environment. In November 2016, Hike announced the launch of a feature called Stories that allows people to share real-life moments using fun live filters which automatically get deleted after 48 hours, and a new camera design with localized filters. Hike 4.0 launched on 26 August 2015 with the tagline 'Got a Gang? Get on Hike'. Hike 4.0 was an optimization-focused update, increasing the performance of the app on poor networks. It supported photo filters, doodles, and bite-sized news updates in under 100 characters. Hike launched News Feed with Hindi language support on 29 September 2015 to cater for the needs of the non-English population. Hike launched version 3.5 as the biggest update for Windows Phone 8.1 during December 2015 which changed the user interface for more simpler navigation, supported sending unlimited non-media files and documents of any format and better group admin settings. It also included ten brand new chat themes. Hike launched a microapp feature which was live for two days on 8 May 2016, as a Mother's Day special in which users could add images, quotes or messages as a token of love with customized e-cards and stickers on their timeline not only on Hike, but also on other platforms. On 26 October 2016, Hike Messenger rolled out the beta version of a video calling feature ahead of WhatsApp starting with the Android users which also lets recipients preview a video call before deciding to take it and is optimized to even work under 2G conditions. On 24 December 2016, Hike rolled out a short 20-second Video Stories feature that can be directly shared with friends or posted on a public timeline with different filters in collaboration with content creators with the same 48-hour time limit before being automatically deleted. The Stories feature continues to receive constant future updates to include and enable content, public story option, private user messaging and geo-tagging. In September 2017, Hike launched personalized sticker packs with 20,000+ graphical stickers for over 500 colleges that covered around 1,000 colleges by December 2018 across India which can be used across different geographies, and are highly customized for users with availability in 40+ local languages that support automatic sticker suggestions where the application suggests the best reply for any sticker message and also allows users to "nudge", a feature used to ping the receiver. Hike started supporting user comments on friend's posts, added a specific message reply function, a redesigned camera interface to support front flash and user mentions with the help of the @ symbol. In December, 2017, Hike launched group voting, bill splitting, checklists and event reminders for group chat that supports up to 1,000 users both on iOS and Android platform. Hike launched another feature called Hike Land, which is a virtual world with beta trial to start from March 2020, that will use Hike Moji where online users with their digital avatar can hang out with other users and will be built inside the Hike Sticker Chat application. It is mainly targeted but not restricted towards 16 to 21 years age group of people. Without unveiling much about Hike Land, a separate website has been created with option to reserve spots by giving details like name, gender and phone number that will link the user profile from the Hike Sticker Chat account though it is not a necessity. ==== Hike Direct ==== The Hike Direct feature is based on the technology known as WiFi Direct, which initially was also called WiFi P2P and got introduced to users by October 2015, which enables sharing of files such as music, apps, videos without a live internet connection within a 100-meter radius by creating a wireless network between two or more devices with a transfer speed of 100MB per minute. For privacy and security reasons, Hike didn't show the recipient's location or proximity and works only when two users are connected in the same room by adding one another into the contact list. ==== Hike Wallet ==== In June 2017, Hike announced the launch of version 5.0 with multiple new features like User Chat Themes, Night Mode and Magic Selfie. along with a built-in Wallet partnered with Yes Bank. This feature was first rolled out to Android users followed by iOS users at a later stage. Hike collaborated with Airtel Payment Bank to power its digital payment wallet by November 2017 where Hike users have access to Airtel Payments Bank's merchant & utility payment services and know your customer (KYC) infrastructure with 5 million transactions happening from services like recharge and P2P. Hike formed a partnership with Ola Cabs to bring a taxi and auto-rickshaw booking facility from 14 February 2018. With Hike Wallet facility users could now book bus tickets with 3

Digital sculpting

Digital sculpting, also known as sculpt modeling or 3D sculpting, is the use of software that offers tools to push, pull, smooth, grab, pinch or otherwise manipulate a digital object as if it were made of a real-life substance such as clay. == Sculpting technology == The geometry used in digital sculpting programs to represent the model can vary; each offers different benefits and limitations. The majority of digital sculpting tools on the market use mesh-based geometry, in which an object is represented by an interconnected surface mesh of polygons that can be pushed and pulled around. This is somewhat similar to the physical process of beating copper plates to sculpt a scene in relief. Other digital sculpting tools use voxel-based geometry, in which the volume of the object is the basic element. Material can be added and removed, much like sculpting in clay. Still other tools make use of more than one basic geometry representation. A benefit of mesh-based programs is that they support sculpting at multiple resolutions on a single model. Areas of the model that are finely detailed can have very small polygons while other areas can have larger polygons. In many mesh-based programs, the mesh can be edited at different levels of detail, and the changes at one level will propagate to higher and lower levels of model detail. A limitation of mesh-based sculpting is the fixed topology of the mesh; the specific arrangement of the polygons can limit the ways in which detail can be added or manipulated. A benefit of voxel-based sculpting is that voxels allow complete freedom over form. The topology of a model can be altered continually during the sculpting process as material is added and subtracted, which frees the sculptor from considering the layout of polygons on the model's surface. After sculpting, it may be necessary to retopologize the model to obtain a clean mesh for use in animation or real-time rendering. Voxels, however, are more limited in handling multiple levels of detail. Unlike mesh-based modeling, broad changes made to voxels at a low level of detail may completely destroy finer details. == Uses == Sculpting can often introduce details to meshes that would otherwise have been difficult or impossible to create using traditional 3D modeling techniques. This makes it preferable for achieving photorealistic and hyperrealistic results, though, many stylized results are achieved as well. Sculpting is primarily used in high poly organic modeling (the creation of 3D models which consist mainly of curves or irregular surfaces, as opposed to hard surface modeling). It is also used by auto manufacturers in their design of new cars. It can create the source meshes for low poly game models used in video games. In conjunction with other 3D modeling and texturing techniques and Displacement and Normal mapping, it can greatly enhance the appearance of game meshes often to the point of photorealism. Some sculpting programs like 3D-Coat, Zbrush, and Mudbox offer ways to integrate their workflows with traditional 3D modeling and rendering programs. Conversely, 3D modeling applications like 3ds Max, Maya and MODO are now incorporating sculpting capability as well, though these are usually less advanced than tools found in sculpting-specific applications. High poly sculpts are also extensively used in CG artwork for movies, industrial design, art, photorealistic illustrations, and for prototyping in 3D printing. == 3D print == Sculptors and digital artists use digital sculpting to create a model (or Digital Twin) to be materialized through CNC technologies including 3D printing. The final sculptures are often called Digital Sculpture or 3D printed art. While digital technologies have emerged in many art disciplines (painting, photography), this is less the case for digital sculpture due to the higher complexity and technology limitations to produce the final sculpture. == Sculpting Process == The best way to learn sculpture is by understanding primary, secondary and tertiary forms. First, break down the object you want to make down its basic shapes, such as a sphere or cube. Focus on making the large, overall shape of the object. After that, work on the bigger shapes on top of or inside the object. These can be protrusions or cut outs. Then, do a final detail pass, such as pores or lines to break up the shape. == Sculpting programs == There are a number of digital sculpting tools available. Some popular tools for creating are: Traditional 3D modeling suites are also beginning to include sculpting capability. 3D modeling programs which currently feature some form of sculpting include the following:

Hybrid argument (cryptography)

In cryptography, the hybrid argument is a proof technique used to show that two distributions are computationally indistinguishable. == History == Hybrid arguments had their origin in a papers by Andrew Yao in 1982 and Shafi Goldwasser and Silvio Micali in 1983. == Formal description == Formally, to show two distributions D1 and D2 are computationally indistinguishable, we can define a sequence of hybrid distributions D1 := H0, H1, ..., Ht =: D2 where t is polynomial in the security parameter n. Define the advantage of any probabilistic efficient (polynomial-bounded time) algorithm A as A d v H i , H i + 1 d i s t ( A ) := | Pr [ x ← $ H i : A ( x ) = 1 ] − Pr [ x ← $ H i + 1 : A ( x ) = 1 ] | , {\displaystyle {\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ):=\left|\Pr[x{\stackrel {\$}{\gets }}H_{i}:\mathbf {A} (x)=1]-\Pr[x{\stackrel {\$}{\gets }}H_{i+1}:\mathbf {A} (x)=1]\right|,} where the dollar symbol ($) denotes that we sample an element from the distribution at random. By triangle inequality, it is clear that for any probabilistic polynomial time algorithm A, A d v D 1 , D 2 d i s t ( A ) ≤ ∑ i = 0 t − 1 A d v H i , H i + 1 d i s t ( A ) . {\displaystyle {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )\leq \sum _{i=0}^{t-1}{\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ).} Thus there must exist some k s.t. 0 ≤ k < t(n) and A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) . {\displaystyle {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n).} Since t is polynomial-bounded, for any such algorithm A, if we can show that it has a fixed negligible advantage function ε(n) between distributions Hi and Hi+1 for every i, so in particular, ϵ ( n ) ≥ A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) , {\displaystyle \epsilon (n)\geq {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n),} then it immediately follows that its advantage to distinguish the distributions D1 = H0 and D2 = Ht must also be negligible. == Applications == The hybrid argument is extensively used in cryptography. Some simple proofs using hybrid arguments are: If one cannot efficiently predict the next bit of the output of some number generator, then this generator is a pseudorandom number generator (PRG). We can securely expand a PRG with 1-bit output into a PRG with n-bit output.