The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision-makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating back to 1897. The subset sum problem is a special case of the decision and 0-1 problems where for each kind of item, the weight equals the value: w i = v i {\displaystyle w_{i}=v_{i}} . In the field of cryptography, the term knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. == Applications == Knapsack problems appear in real-world decision-making processes in a wide variety of fields, such as finding the least wasteful way to cut raw materials, selection of investments and portfolios, selection of assets for asset-backed securitization, and generating keys for the Merkle–Hellman and other knapsack cryptosystems. One early application of knapsack algorithms was in the construction and scoring of tests in which the test-takers have a choice as to which questions they answer. For small examples, it is a fairly simple process to provide the test-takers with such a choice. For example, if an exam contains 12 questions each worth 10 points, the test-taker need only answer 10 questions to achieve a maximum possible score of 100 points. However, on tests with a heterogeneous distribution of point values, it is more difficult to provide choices. Feuerman and Weiss proposed a system in which students are given a heterogeneous test with a total of 125 possible points. The students are asked to answer all of the questions to the best of their abilities. Of the possible subsets of problems whose total point values add up to 100, a knapsack algorithm would determine which subset gives each student the highest possible score. A 1999 study of the Stony Brook University Algorithm Repository showed that, out of 75 algorithmic problems related to the field of combinatorial algorithms and algorithm engineering, the knapsack problem was the 19th most popular and the third most needed after suffix trees and the bin packing problem. == Definition == The most common problem being solved is the 0-1 knapsack problem, which restricts the number x i {\displaystyle x_{i}} of copies of each kind of item to zero or one. Given a set of n {\displaystyle n} items numbered from 1 up to n {\displaystyle n} , each with a weight w i {\displaystyle w_{i}} and a value v i {\displaystyle v_{i}} , along with a maximum weight capacity W {\displaystyle W} , maximize ∑ i = 1 n v i x i {\displaystyle \sum _{i=1}^{n}v_{i}x_{i}} subject to ∑ i = 1 n w i x i ≤ W {\displaystyle \sum _{i=1}^{n}w_{i}x_{i}\leq W} and x i ∈ { 0 , 1 } {\displaystyle x_{i}\in \{0,1\}} . Here x i {\displaystyle x_{i}} represents the number of instances of item i {\displaystyle i} to include in the knapsack. Informally, the problem is to maximize the sum of the values of the items in the knapsack so that the sum of the weights is less than or equal to the knapsack's capacity. The bounded knapsack problem (BKP) removes the restriction that there is only one of each item, but restricts the number x i {\displaystyle x_{i}} of copies of each kind of item to a maximum non-negative integer value c {\displaystyle c} : maximize ∑ i = 1 n v i x i {\displaystyle \sum _{i=1}^{n}v_{i}x_{i}} subject to ∑ i = 1 n w i x i ≤ W {\displaystyle \sum _{i=1}^{n}w_{i}x_{i}\leq W} and x i ∈ { 0 , 1 , 2 , … , c } . {\displaystyle x_{i}\in \{0,1,2,\dots ,c\}.} The unbounded knapsack problem (UKP) places no upper bound on the number of copies of each kind of item and can be formulated as above except that the only restriction on x i {\displaystyle x_{i}} is that it is a non-negative integer. maximize ∑ i = 1 n v i x i {\displaystyle \sum _{i=1}^{n}v_{i}x_{i}} subject to ∑ i = 1 n w i x i ≤ W {\displaystyle \sum _{i=1}^{n}w_{i}x_{i}\leq W} and x i ∈ N . {\displaystyle x_{i}\in \mathbb {N} .} One example of the unbounded knapsack problem is given using the figure shown at the beginning of this article and the text "if any number of each book is available" in the caption of that figure. == Computational complexity == The knapsack problem is interesting from the perspective of computer science for many reasons: The decision problem form of the knapsack problem (Can a value of at least V be achieved without exceeding the weight W?) is NP-complete, thus there is no known algorithm that is both correct and fast (polynomial-time) in all cases. There is no known polynomial algorithm which can tell, given a solution, whether it is optimal (which would mean that there is no solution with a larger V). This problem is co-NP-complete. There is a pseudo-polynomial time algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine, described below. Many cases that arise in practice, and "random instances" from some distributions, can nonetheless be solved exactly. There is a link between the "decision" and "optimization" problems in that if there exists a polynomial algorithm that solves the "decision" problem, then one can find the maximum value for the optimization problem in polynomial time by applying this algorithm iteratively while increasing the value of k. On the other hand, if an algorithm finds the optimal value of the optimization problem in polynomial time, then the decision problem can be solved in polynomial time by comparing the value of the solution output by this algorithm with the value of k. Thus, both versions of the problem are of similar difficulty. One theme in research literature is to identify what the "hard" instances of the knapsack problem look like, or viewed another way, to identify what properties of instances in practice might make them more amenable than their worst-case NP-complete behaviour suggests. The goal in finding these "hard" instances is for their use in public-key cryptography systems, such as the Merkle–Hellman knapsack cryptosystem. More generally, better understanding of the structure of the space of instances of an optimization problem helps to advance the study of the particular problem and can improve algorithm selection. Furthermore, notable is the fact that the hardness of the knapsack problem depends on the form of the input. If the weights and profits are given as integers, it is weakly NP-complete, while it is strongly NP-complete if the weights and profits are given as rational numbers. However, in the case of rational weights and profits it still admits a fully polynomial-time approximation scheme. === Unit-cost models === The NP-hardness of the Knapsack problem relates to computational models in which the size of integers matters (such as the Turing machine). In contrast, decision trees count each decision as a single step. Dobkin and Lipton show an 1 2 n 2 {\displaystyle {1 \over 2}n^{2}} lower bound on linear decision trees for the knapsack problem, that is, trees where decision nodes test the sign of affine functions. This was generalized to algebraic decision trees by Steele and Yao. If the elements in the problem are real numbers or rationals, the decision-tree lower bound extends to the real random-access machine model with an instruction set that includes addition, subtraction and multiplication of real numbers, as well as comparison and either division or remaindering ("floor"). This model covers more algorithms than the algebraic decision-tree model, as it encompasses algorithms that use indexing into tables. However, in this model all program steps are counted, not just decisions. An upper bound for a decision-tree model was given by Meyer auf der Heide who showed that for every n there exists an O(n4)-deep linear decision tree that solves the subset-sum problem with n items. Note that this does not imply any upper bound for an algorithm that should solve the problem for any given n. == Solving == Several algorithms are available to solve knapsack problems, based on the dynamic programming approach, the branch and bound approach or hybridizations of both approaches. === Dynamic programming in-advance algorithm === The unbounded knapsack problem (UKP) places no restriction on the number of copies of each kind of item. Besides, here we assume that x i > 0 {\displaystyle x_{i}>0} m [ w ′ ] = max ( ∑ i = 1 n v i x i ) {\displaystyle m[w']=\max \left(\sum _{i=1}^{n}v_{i}x_{i}\right)} subject to ∑
Coda (document editor)
Coda is a cloud-based multi-user document editor. == Features == Coda is a document editor that provides features from spreadsheets, presentation documents, word processor files, and apps. Possible uses for Coda documents include using them as a wiki, database, or project management tool. Coda has built a formula system, much like spreadsheets commonly have, but in Coda documents, formulas can be used anywhere within the document, and can link to things that aren't just cells, including other documents, calendars or graphs. Coda also has the ability to integrate with custom third-party services, and has automations. It has offered $1 million in grants for developers that create such integrations. == Development == Coda Project, Inc. was founded by Shishir Mehrotra and Alex DeNeui in June 2014. Having met at MIT, they developed the project mostly privately before announcing a public beta in October 2017. The company was named Coda, which is an anadrome for “a doc”. Coda raised $60 million in venture capital funding over two rounds by 2017. The Coda software came out of beta in February 2019. Version 1.0 had an improved user interface, new features for folders and workspaces, and permission levels for accessing files. Coda raised another $80 million in 2020, and $100 million in 2021. The 2021 funding brought Coda's valuation to $1.4 billion, making it a unicorn. In December 2024, Coda was acquired by Grammarly in an all-stock deal for an undisclosed amount. In October 2025, Grammarly rebranded as Superhuman, incorporating Coda as a core product within the new Superhuman productivity suite alongside Grammarly's writing tools, Superhuman Mail, and a new AI assistant called Superhuman Go.
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Büchi automaton
In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machine should move to from its current state when it reads the next input character. Some states are accepting states and one state is the start state. The machine accepts an input if and only if it will pass through an accepting state infinitely many times as it reads the input. A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata. Büchi automata recognize the ω-regular languages, the infinite word version of regular languages. They are named after the Swiss mathematician Julius Richard Büchi, who invented them in 1962. Büchi automata are often used in model checking as an automata-theoretic version of a formula in linear temporal logic. == Formal definition == Formally, a deterministic Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\textstyle A=(Q,\Sigma ,\delta ,q_{0},\mathbf {F} )} that consists of the following components: Q {\textstyle Q} is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } is a finite set called the alphabet of A {\textstyle A} . δ : Q × Σ → Q {\textstyle \delta \colon Q\times \Sigma \to Q} is a function, called the transition function of A {\textstyle A} . q 0 {\textstyle q_{0}} is an element of Q {\textstyle Q} , called the initial state of A {\textstyle A} . F ⊆ Q {\textstyle \mathbf {F} \subseteq Q} is the acceptance condition. A run i _ = i 0 i 1 i 2 ⋯ ∈ Σ ω {\displaystyle {\underline {i}}=i_{0}i_{1}i_{2}\cdots \in \Sigma ^{\omega }} is an infinite string of inputs of A {\displaystyle A} . By calling δ {\displaystyle \delta } recursively, we can extend it to a function δ ω : Σ ω → Q ω {\displaystyle \delta ^{\omega }:\Sigma ^{\omega }\to Q^{\omega }} . A state q ∈ Q {\displaystyle q\in Q} is said to occur infinitely often for a run i _ {\displaystyle {\underline {i}}} when the set { n ∈ N ∣ δ ω ( i _ ) n = q } {\displaystyle \{n\in \mathbb {N} \mid \delta ^{\omega }({\underline {i}})_{n}=q\}} is infinite. Let I n f ( i _ ) {\displaystyle \mathrm {Inf} ({\underline {i}})} be the set of states occurring infinitely often for i _ {\displaystyle {\underline {i}}} . The language of A {\displaystyle A} is then the set of runs of A {\displaystyle A} in which at least one of the infinitely-often occurring states is in F {\textstyle \mathbf {F} } ; in symbols: L ( A ) = { i _ ∈ Σ ω ∣ I n f ( i _ ) ∩ F ≠ ∅ } . {\displaystyle L(A)=\{{\underline {i}}\in \Sigma ^{\omega }\mid \mathrm {Inf} ({\underline {i}})\cap \mathbf {F} \neq \varnothing \}.} In a (non-deterministic) Büchi automaton, the transition function δ {\textstyle \delta } is replaced with a transition relation Δ {\textstyle \Delta } that returns a set of states, and the single initial state q 0 {\textstyle q_{0}} is replaced by a set I {\textstyle I} of initial states. Generally, the term Büchi automaton without qualifier refers to non-deterministic Büchi automata. For more comprehensive formalism see also ω-automaton. == Closure properties == The set of Büchi automata is closed under the following operations. Let A = ( Q A , Σ , Δ A , I A , F A ) {\displaystyle A=(Q_{A},\Sigma ,\Delta _{A},I_{A},{F}_{A})} and B = ( Q B , Σ , Δ B , I B , F B ) {\displaystyle B=(Q_{B},\Sigma ,\Delta _{B},I_{B},{F}_{B})} be Büchi automata and C = ( Q C , Σ , Δ C , I C , F C ) {\displaystyle C=(Q_{C},\Sigma ,\Delta _{C},I_{C},{F}_{C})} be a finite automaton. Union: There is a Büchi automaton that recognizes the language L ( A ) ∪ L ( B ) . {\displaystyle L(A)\cup L(B).} Proof: If we assume, w.l.o.g., Q A ∩ Q B {\displaystyle Q_{A}\cap Q_{B}} is empty then L ( A ) ∪ L ( B ) {\displaystyle L(A)\cup L(B)} is recognized by the Büchi automaton ( Q A ∪ Q B , Σ ∪ Σ , Δ A ∪ Δ B , I A ∪ I B , F A ∪ F B ) . {\displaystyle (Q_{A}\cup Q_{B},\Sigma \cup \Sigma ,\Delta _{A}\cup \Delta _{B},I_{A}\cup I_{B},{F}_{A}\cup {F}_{B}).} Intersection: There is a Büchi automaton that recognizes the language L ( A ) ∩ L ( B ) . {\displaystyle L(A)\cap L(B).} Proof: The Büchi automaton A ′ = ( Q ′ , Σ , Δ ′ , I ′ , F ′ ) {\displaystyle A'=(Q',\Sigma ,\Delta ',I',F')} recognizes L ( A ) ∩ L ( B ) , {\displaystyle L(A)\cap L(B),} where Q ′ = Q A × Q B × { 1 , 2 } {\displaystyle Q'=Q_{A}\times Q_{B}\times \{1,2\}} Δ ′ = Δ 1 ∪ Δ 2 {\displaystyle \Delta '=\Delta _{1}\cup \Delta _{2}} Δ 1 = { ( ( q A , q B , 1 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q A ∈ F A then i = 2 else i = 1 } {\displaystyle \Delta _{1}=\{((q_{A},q_{B},1),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{A}\in F_{A}{\text{ then }}i=2{\text{ else }}i=1\}} Δ 2 = { ( ( q A , q B , 2 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q B ∈ F B then i = 1 else i = 2 } {\displaystyle \Delta _{2}=\{((q_{A},q_{B},2),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{B}\in F_{B}{\text{ then }}i=1{\text{ else }}i=2\}} I ′ = I A × I B × { 1 } {\displaystyle I'=I_{A}\times I_{B}\times \{1\}} F ′ = { ( q A , q B , 2 ) | q B ∈ F B } {\displaystyle F'=\{(q_{A},q_{B},2)|q_{B}\in F_{B}\}} By construction, r ′ = ( q A 0 , q B 0 , i 0 ) , ( q A 1 , q B 1 , i 1 ) , … {\displaystyle r'=(q_{A}^{0},q_{B}^{0},i^{0}),(q_{A}^{1},q_{B}^{1},i^{1}),\dots } is a run of automaton A' on input word w {\textstyle w} if r A = q A 0 , q A 1 , … {\displaystyle r_{A}=q_{A}^{0},q_{A}^{1},\dots } is run of A {\textstyle A} on w {\textstyle w} and r B = q B 0 , q B 1 , … {\displaystyle r_{B}=q_{B}^{0},q_{B}^{1},\dots } is run of B {\textstyle B} on w {\textstyle w} . r A {\textstyle r_{A}} is accepting and r B {\textstyle r_{B}} is accepting if r ′ {\textstyle r'} is concatenation of an infinite series of finite segments of 1-states (states with third component 1) and 2-states (states with third component 2) alternatively. There is such a series of segments of r ′ {\textstyle r'} if r ′ {\textstyle r'} is accepted by A ′ {\textstyle A'} . Concatenation: There is a Büchi automaton that recognizes the language L ( C ) ⋅ L ( A ) . {\displaystyle L(C)\cdot L(A).} Proof: If we assume, w.l.o.g., Q C ∩ Q A {\displaystyle Q_{C}\cap Q_{A}} is empty then the Büchi automaton A ′ = ( Q C ∪ Q A , Σ , Δ ′ , I ′ , F A ) {\displaystyle A'=(Q_{C}\cup Q_{A},\Sigma ,\Delta ',I',F_{A})} recognizes L ( C ) ⋅ L ( A ) {\displaystyle L(C)\cdot L(A)} , where Δ ′ = Δ A ∪ Δ C ∪ { ( q , a , q ′ ) | q ′ ∈ I A and ∃ f ∈ F C . ( q , a , f ) ∈ Δ C } {\displaystyle \Delta '=\Delta _{A}\cup \Delta _{C}\cup \{(q,a,q')|q'\in I_{A}{\text{ and }}\exists f\in F_{C}.(q,a,f)\in \Delta _{C}\}} if I C ∩ F C is empty then I ′ = I C otherwise I ′ = I C ∪ I A {\displaystyle {\text{ if }}I_{C}\cap F_{C}{\text{ is empty then }}I'=I_{C}{\text{ otherwise }}I'=I_{C}\cup I_{A}} ω-closure: If L ( C ) {\displaystyle L(C)} does not contain the empty word then there is a Büchi automaton that recognizes the language L ( C ) ω . {\displaystyle L(C)^{\omega }.} Proof: The Büchi automaton that recognizes L ( C ) ω {\displaystyle L(C)^{\omega }} is constructed in two stages. First, we construct a finite automaton A ′ {\textstyle A'} such that A ′ {\textstyle A'} also recognizes L ( C ) {\displaystyle L(C)} but there are no incoming transitions to initial states of A ′ {\textstyle A'} . So, A ′ = ( Q C ∪ { q new } , Σ , Δ ′ , { q new } , F C ) , {\displaystyle A'=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta ',\{q_{\text{new}}\},F_{C}),} where Δ ′ = Δ C ∪ { ( q new , a , q ′ ) | ∃ q ∈ I C . ( q , a , q ′ ) ∈ Δ C } . {\displaystyle \Delta '=\Delta _{C}\cup \{(q_{\text{new}},a,q')|\exists q\in I_{C}.(q,a,q')\in \Delta _{C}\}.} Note that L ( C ) = L ( A ′ ) {\displaystyle L(C)=L(A')} because L ( C ) {\displaystyle L(C)} does not contain the empty string. Second, we will construct the Büchi automaton A ″ {\textstyle A''} that recognize L ( C ) ω {\displaystyle L(C)^{\omega }} by adding a loop back to the initial state of A ′ {\textstyle A'} . So, A ″ = ( Q C ∪ { q new } , Σ , Δ ″ , { q new } , { q new } ) {\displaystyle A''=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta '',\{q_{\text{new}}\},\{q_{\text{new}}\})} , where Δ ″ = Δ ′ ∪ { ( q , a , q new ) | ∃ q ′ ∈ F C . ( q , a , q ′ ) ∈ Δ ′ } . {\displaystyle \Delta ''=\Delta '\cup \{(q,a,q_{\text{new}})|\exists q'\in F_{C}.(q,a,q')\in \Delta '\}.} Complementation:
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Synthesia (company)
Synthesia Limited is a British multinational artificial intelligence company based in London, United Kingdom. It is a synthetic media-generation software developer and creator of AI-generated video content, including audio-visual agents and cloned avatars. Britain's largest generative-AI firm, it is used by 70% of FTSE 100 and over 90% of Fortune 100 companies. == Overview == Synthesia is most often used by corporations for localized communication, orientation, employee training videos, advertising campaigns, reporting, product demonstrations, customer service, and to create chatbots. Its software algorithm mimics speech and facial movements based on video recordings of an individual’s speech and facial expressions. From this, a text-to-speech video is created to look and sound like the individual. Swiss bank UBS incorporated Synthesia AI-powered avatars of their human financial experts, for instance, in 2025. Users create content via the platform's pre-generated AI presenters or by creating digital representations of themselves, or personal avatars, using the platform's AI video editing tool. These avatars can be used to narrate videos generated from text. As of August 2021, Synthesia's voice database included multiple gender options in over 60 languages. Its free voice library doubled by 2025, to 140 languages and accents, and its Express-Voice technology can clone a user's own voice, or generate a synthetic one. === Deepfakes === The platform prohibits use of its software to create non-consensual clones, including of celebrities or political figures for satirical purposes. Explicit consent must be provided in addition to a strict pre-screening regimen for use of an individual's likeness to avoid “deepfaking”. While the company prohibits use of its technology for misinformation or "news-like content", an October 2023 Freedom House report stated that Synthesia tools had been used by governments in Venezuela, China, Burkina Faso, and Russia to create videos of fake TV news outlets with AI-generated avatars in order to spread propaganda. Actor Dan Dewhirst signed a contract with the company in 2021, becoming one of the first actors whose likeness would be made into an AI avatar, finding his likeness used in the Venezuelan generated-videos. The company stated, in February 2024, that it had improved its misuse detection systems, and, in April 2024, that new users of its technology are screened by the company, and content employing it is further vetted by Synthesia moderators. == History == Synthesia's software utilizes deep learning architecture developed by Lourdes Agapito and Matthias Niessner. The company was co-founded in 2017 by Agapito, Niessner, Victor Riparbelli, and Steffen Tjerrild. In 2018, the company first demonstrated the software's capabilities on the BBC programme Click when it presented a digitization of Matthew Amroliwala speaking Spanish, Mandarin, and Hindi. Through Synthesia's first two years of existence, it employed 10 people and struggled to make sales, leading to an expansion of the company's focus. It moved on from just targeting entertainment studios to a variety of businesses. In 2020, Synthesia users were reported to include Amazon, Tiffany & Co. and IHG Hotels & Resorts. In January 2024, the company introduced its AI video assistant, which turns text-to-video. That April, with a reported 55,000 customers, including half of the Fortune 100, Synthesia launched "expressive avatars". That September, an enhanced dubbing feature was launched, to translate video in 30 languages with naturalized lip-syncing. Peter Hill joined Synthesia as CTO in January 2025, following 25 years at Amazon, and two years as CEO and CPO of Wildfire Studios. That March, a million dollar base of shares was formed to furnish human actors, employed to generate digital avatars, with company stock, which all of its employees hold. By June of that year, 150,000 individuals from among Synthesia's 65,000 customers had created AI-generated avatars of themselves. In July 2025, the company's new global headquarters at Regent’s Place was opened by London mayor Sadiq Khan, who described Britain's largest generative-AI company, then valued at over $2 billion, as a "London success story". By that October, its technology was employed by 90% of the Fortune 100, and Synthesia 3.0 was launched, with hyper-realistic digital avatars equipped with AI-powered dubbing and translation, and a built-in video assistant. In January 2026, it reached a $4 billion valuation, with 70% of FTSE 100 companies noted among its customers. === Funding === The company raised $3.1 million in seed funding in 2019. In April 2021, the company raised $12.5 million in Series A funding. In December 2021, it raised $50 million in a Series B funding round led by Kleiner Perkins and GV (then Google Ventures). Synthesia gained a total valuation of $1 billion, and achieved unicorn status, when it raised $90 million from Accel and Nvidia partnership NVentures, in June 2023, during its Series C funding round. Counting 60,000 customers by January 2025, including over 60% of Fortune 100 companies; the company raised $180 million in a Series D round led by NEA, with new investors World Innovation Lab (WiL), Atlassian Ventures and PSP Growth, as well as existing investors GV, MMC Ventures and FirstMark, doubling Synthesia's valuation to $2.1 billion. Capital raised by 2025 had reached $330 million, with investments slated to further product innovation, talent growth, and company expansion in North America, Europe, Japan and Australia. In April 2025, Adobe Inc. invested £10 million in the company for a strategic partnership. Synthesia subsequently rejected a $3 billion acquisition offer from Adobe, choosing to remain independent. With a revenue stream then exceeding $100 million annually; GV led a Series E funding round in October 2025, resulting in Synthesia's $4 billion valuation, raising $200 million from GV, Nvidia and Accel to develop, in 2026, interactive audio-visual avatar "agents" that converse on topic, for automated sales training and corporate communications, such as recruiting. == Recognition == In 2021, Synthesia partnered with Lay's to create the Messi Messages campaign featuring Argentine footballer Lionel Messi. Users created personalized messages with Synthesia's software and sent custom artificial reality video messages from Messi based on their text input. The campaign received a Cannes Lion Award under the Bronze category. In February 2025, UK Science and Technology Minister Peter Kyle commended Synthesia's "pioneering generative AI innovations."
Karl Steinbuch
Karl W. Steinbuch (June 15, 1917 in Stuttgart-Bad Cannstatt – June 4, 2005 in Ettlingen) was a German computer scientist, cyberneticist, and electrical engineer. He was an early and influential researcher in German computer science, and was the developer of the Lernmatrix, an early implementation of artificial neural networks. From the late 1960s onwards the focus of his activity shifted from scientific research to right-wing political activism supporting the Neue Rechte. == Biography == Steinbuch joined the National Socialist German Students' League (NSDStB) and the Nazi Party. Steinbuch studied at the University of Stuttgart and in 1944 he received his PhD in physics. In 1948 he joined Standard Elektrik Lorenz (SEL, part of the ITT group) in Stuttgart, as a computer design engineer and later as a director of research and development, where he filed more than 70 patents. Steinbuch completed the first European fully transistorized computer, the ER 56 marketed by SEL. In 1958 he became professor and director of the Institute of Technology for information processing (ITIV) of the University of Karlsruhe, where he retired in 1980. In 1967 he began publishing books, in which he tried to influence German education policy. Together with books from colleagues like Jean Ziegler from Switzerland, Eric J. Hobsbawm from the UK, and John Naisbitt his books predicted what he regarded as the coming education disaster of the emerging civic lobby society. In 1957, together with Helmut Gröttrup, Steinbuch coined the term Informatik, the German word for computer science, which gave informatics, and the term kybernetische Anthropologie. == Awards and recognition == Wilhelm-Boelsche award - medal in Gold German non-fiction book award Gold medal award of the XXI. International Congresses on Aerospace Medicine Konrad Adenauer award of science Jakob Fugger award medal Medal of merit of the state of Baden-Wuerttemberg member, German Academy of Sciences Leopoldina member, International Academy of Science, Munich. grants from a state government grants program, named "Karl-Steinbuch-Stipendium" Steinbuch Centre for Computing at the Karlsruhe Institute of Technology named after him == Books == Steinbuch wrote several books and articles, including: 1957 Informatik: Automatische Informationsverarbeitung ("Informatics: automatic information processing"). 1963 Learning matrices and their applications (together with U. A. W. Piske) 1965 A critical comparison of two kinds of adaptive classification networks (together with Bernard Widrow) 1966 (1969): Die informierte Gesellschaft. Geschichte und Zukunft der Nachrichtentechnik (The informed society. History and Future of telecommunications) 1989: Die desinformierte Gesellschaft (The disinformed society) 1968: Falsch programmiert. Über das Versagen unserer Gesellschaft in der Gegenwart und vor der Zukunft und was eigentlich geschehen müßte. (as a bestseller listet in: Der Spiegel) (Programmed falsely. About our society's failure in the present and with respect to the future and what should be done.) 1969: Programm 2000. (as a bestseller listet in: Der Spiegel) 1971: Automat und Mensch. Auf dem Weg zu einer kybernetischen Anthropologie (Machine and Man. On the way to a cybernetic anthropology; 4th revised edition) 1971: Mensch Technik Zukunft. Probleme von Morgen (German non-fiction book award) (Man Technology Future. Problems of Tomorrow) 1973: Kurskorrektur (Correcting the Course) 1978: Maßlos informiert. Die Enteignung des Denkens (Excessively informed. The Deprivation of Thinking) 1984: Unsere manipulierte Demokratie. Müssen wir mit der linken Lüge leben? (Our Thought-controlled Democracy. Do we have to live with the leftist lie?)