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21-769: As of 2021, IBM Cloud contains more than 170 services including compute , storage , networking , database , analytics , machine learning , and developer tools . SoftLayer Technologies, Inc. (now IBM Cloud) was a dedicated server , managed hosting , and cloud computing provider, founded in 2005 and acquired by IBM in 2013. SoftLayer initially specialized in hosting workloads for gaming companies and startups, but shifted focus to enterprise workloads after its acquisition. SoftLayer had bare-metal compute offerings before other large cloud providers such as Amazon Web Services . SoftLayer has hosted workloads for companies such as The Hartford , WhatsApp , Whirlpool , Daimler , and Macy's . In June 2013, IBM acquired SoftLayer ,

42-448: A computational system is a complex object which consists of three parts. First, a mathematical dynamical system D S {\displaystyle DS} with discrete time and discrete state space; second, a computational setup H = ( F , B F ) {\displaystyle H=\left(F,B_{F}\right)} , which is made up of a theoretical part F {\displaystyle F} , and

63-604: A public cloud platform, to serve as the foundation for its IaaS offering. Bluemix was announced for public beta in February 2014 after having been developed since early 2013. Bluemix was based on the open source Cloud Foundry project and ran on SoftLayer infrastructure. IBM announced the general availability of the Bluemix Platform-as-a-Service (PaaS) offering in July 2014. By April 2015, Bluemix included

84-618: A purely physical process occurring inside a closed physical system called a computer . Turing's 1937 proof, On Computable Numbers, with an Application to the Entscheidungsproblem , demonstrated that there is a formal equivalence between computable statements and particular physical systems, commonly called computers . Examples of such physical systems are: Turing machines , human mathematicians following strict rules, digital computers , mechanical computers , analog computers and others. An alternative account of computation

105-422: A real part B F {\displaystyle B_{F}} ; third, an interpretation I D S , H {\displaystyle I_{DS,H}} , which links the dynamical system D S {\displaystyle DS} with the setup H {\displaystyle H} . United States Tennis Association Too Many Requests If you report this error to

126-437: A rule. "Medium-independence" requires that the property can be instantiated by multiple realizers and multiple mechanisms, and that the inputs and outputs of the mechanism also be multiply realizable . In short, medium-independence allows for the use of physical variables with properties other than voltage (as in typical digital computers); this is imperative in considering other types of computation, such as that which occurs in

147-563: A suite of over 100 cloud-based development tools "including social, mobile, security, analytics, database, and IoT ( internet of things ). Bluemix had grown to 83,000 users in India with growth of approximately 10,000 users each month. A year after announcement, Bluemix had made little headway in the cloud-computing platform space relative to its competition, and remained substantially behind market leaders Microsoft Azure and Amazon AWS . By August 2016, little had changed in market acceptance of

168-428: A well-defined statement or calculation as any statement that could be expressed in terms of the initialisation parameters of a Turing machine . Other (mathematically equivalent) definitions include Alonzo Church 's lambda-definability , Herbrand - Gödel - Kleene 's general recursiveness and Emil Post 's 1-definability . Today, any formal statement or calculation that exhibits this quality of well-definedness

189-423: Is an academic field that involves the study of computation. The notion that mathematical statements should be 'well-defined' had been argued by mathematicians since at least the 1600s , but agreement on a suitable definition proved elusive. A candidate definition was proposed independently by several mathematicians in the 1930s. The best-known variant was formalised by the mathematician Alan Turing , who defined

210-419: Is found throughout the works of Hilary Putnam and others. Peter Godfrey-Smith has dubbed this the "simple mapping account." Gualtiero Piccinini's summary of this account states that a physical system can be said to perform a specific computation when there is a mapping between the state of that system and the computation such that the "microphysical states [of the system] mirror the state transitions between

231-492: Is termed computable , while the statement or calculation itself is referred to as a computation . Turing's definition apportioned "well-definedness" to a very large class of mathematical statements, including all well-formed algebraic statements , and all statements written in modern computer programming languages. Despite the widespread uptake of this definition, there are some mathematical concepts that have no well-defined characterisation under this definition. This includes

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252-595: The United States Tennis Association (USTA) to provide new AI-powered tools for the US Open . In May 2020, IBM announced agreements with six European companies, including Osram and Crédit Mutuel , that use IBM Cloud to access advanced technologies such as AI, blockchain and analytics. IBM Cloud continued to be considered a leader in bare-metal in 2020, and distinguished itself by providing over 11 million possible custom configurations with

273-539: The brain or in a quantum computer . A rule, in this sense, provides a mapping among inputs, outputs, and internal states of the physical computing system. In the theory of computation , a diversity of mathematical models of computation has been developed. Typical mathematical models of computers are the following: Giunti calls the models studied by computation theory computational systems, and he argues that all of them are mathematical dynamical systems with discrete time and discrete state space. He maintains that

294-663: The Bluemix and Softlayer brands. In March 2018, IBM launched an industry first managed Kubernetes service on bare metal. In August 2019, 3 weeks after the close of Red Hat acquisition, IBM launched a managed Red Hat OpenShift on IBM Cloud. In November 2019, IBM has announced that it had designed the world's first financial services-ready public cloud and that Bank of America was its first committed collaborator and anchor customer, joined shortly thereafter in 2020 by BNP Paribas as its first European anchor client. IBM announced in April 2021

315-550: The Bluemix offering. In February 2016, IBM Bluemix includes IBM's Function as a Service (FaaS) system, or Serverless computing offering, that is built using open source from the Apache OpenWhisk incubator project largely credited to IBM for seeding. This system, equivalent to Amazon Lambda , Microsoft Azure Functions, Oracle Cloud Fn or Google Cloud Functions , allows calling of a specific function in response to an event without requiring any resource management from

336-403: The computational states." Philosophers such as Jerry Fodor have suggested various accounts of computation with the restriction that semantic content be a necessary condition for computation (that is, what differentiates an arbitrary physical system from a computing system is that the operands of the computation represent something). This notion attempts to prevent the logical abstraction of

357-735: The developer. In May 2017 IBM released Kubernetes support as the IBM Bluemix Container Service, later renamed to the IBM Cloud Kubernetes Service (IKS). IKS was built using the open source Kubernetes project. This system, equivalent to Amazon Web Services EKS, Microsoft Azure AKS, or Google Cloud GKE, aims to provide a platform for automating deployment, scaling, and operations of application containers across clusters of hosts. In October 2017, IBM announced that they would rebrand their cloud as IBM Cloud brand, merging all components, thus retiring

378-534: The general availability of IBM Cloud for Financial Services, including support for Red Hat OpenShift and other cloud-native technologies. In July 2021, it was announced that SAP is onboarding two of its finance and data management solutions to IBM Cloud for Financial Services. In September 2021, it was CaixaBank 's turn to boost digital capabilities with IBM Cloud for Financial Services and onboarding to new IBM Cloud Multizone Region in Spain. In 2019, IBM partnered with

399-402: The halting problem and the busy beaver game . It remains an open question as to whether there exists a more powerful definition of 'well-defined' that is able to capture both computable and 'non-computable' statements. Some examples of mathematical statements that are computable include: Some examples of mathematical statements that are not computable include: Computation can be seen as

420-527: The latest Power , Intel , and AMD CPUs and Nvidia GPUs . In 2021, IBM announced it would achieve net zero greenhouse gas emissions by 2030. Computation A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms . Mechanical or electronic devices (or, historically , people) that perform computations are known as computers . Computer science

441-411: The mapping account of pancomputationalism , the idea that everything can be said to be computing everything. Gualtiero Piccinini proposes an account of computation based on mechanical philosophy . It states that physical computing systems are types of mechanisms that, by design, perform physical computation, or the manipulation (by a functional mechanism) of a "medium-independent" vehicle according to

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