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Formal Methods
In computer science, formal methods are mathematics, mathematically rigorous techniques for the formal specification, specification, development, Program analysis, analysis, and formal verification, verification of software and computer hardware, hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design. Formal methods employ a variety of theoretical computer science fundamentals, including logic in computer science, logic calculi, formal languages, automata theory, control theory, program semantics, type systems, and type theory. Uses Formal methods can be applied at various points through the software development process, development process. Specification Formal methods may be used to give a formal description of the system to be developed, at whatever level of detail desired. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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John Backus
John Warner Backus (December 3, 1924 – March 17, 2007) was an American computer scientist. He led the team that invented and implemented FORTRAN, the first widely used high-level programming language, and was the inventor of the Backus–Naur form (BNF), a widely used notation to define syntaxes of formal languages. He later did research into the function-level programming paradigm, presenting his findings in his influential 1977 Turing Award lecture "Can Programming Be Liberated from the von Neumann Style?" The IEEE awarded Backus the W. W. McDowell Award in 1967 for the development of FORTRAN. He received the National Medal of Science in 1975 and the 1977 Turing Award "for profound, influential, and lasting contributions to the design of practical high-level programming systems, notably through his work on FORTRAN, and for publication of formal procedures for the specification of programming languages". John Backus retired in 1991. He died at his home in Ashland, Oregon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Rule Of Inference
Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the Logical form, logical structure of Validity (logic), valid arguments. If an argument with true premises follows a rule of inference then the conclusion cannot be false. ''Modus ponens'', an influential rule of inference, connects two premises of the form "if P then Q" and "P" to the conclusion "Q", as in the argument "If it rains, then the ground is wet. It rains. Therefore, the ground is wet." There are many other rules of inference for different patterns of valid arguments, such as ''modus tollens'', disjunctive syllogism, constructive dilemma, and existential generalization. Rules of inference include rules of implication, which operate only in one direction from premises to conclusions, and rules of replacement, which state that two expressions are equivalent and can be freely swapped. Rules of inference contrast with formal fallaciesinvalid argu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an ''axiom'' may be a " logical axiom" or a " non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example ''a'' + 0 = ''a'' in integer arithmetic. N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Automated Theorem Proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science. Logical foundations While the roots of formalized Logicism, logic go back to Aristotelian logic, Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Gottlob Frege, Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional logic, propositional calculus and what is essentially modern predicate logic. His ''The Foundations of Arithmetic, Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Bertrand Russell, Russell and Alfred North Whitehead, Whitehead in their influential ''Principia Mathematica'', first published 1910� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Ambiguity
Ambiguity is the type of meaning (linguistics), meaning in which a phrase, statement, or resolution is not explicitly defined, making for several interpretations; others describe it as a concept or statement that has no real reference. A common aspect of ambiguity is uncertainty. It is thus an Attribute grammar, attribute of any idea or statement whose intention, intended meaning cannot be definitively resolved, according to a rule or process with a finite number of steps. (The prefix ''wikt:ambi-#Prefix, ambi-'' reflects the idea of "2 (number), two", as in "two meanings"). The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with vague information it is difficult to form any interpretation at the desired level of specificity. Linguistic forms Lexical ambiguity is contrasted with semantic ambiguity. The former represents a choice between a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Natural Language
A natural language or ordinary language is a language that occurs naturally in a human community by a process of use, repetition, and change. It can take different forms, typically either a spoken language or a sign language. Natural languages are distinguished from constructed and formal languages such as those used to program computers or to study logic. Defining natural language Natural languages include ones that are associated with linguistic prescriptivism or language regulation. ( Nonstandard dialects can be viewed as a wild type in comparison with standard languages.) An official language with a regulating academy such as Standard French, overseen by the , is classified as a natural language (e.g. in the field of natural language processing), as its prescriptive aspects do not make it constructed enough to be a constructed language or controlled enough to be a controlled natural language. Natural language are different from: * artificial and constructed la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Correctness (computer Science)
In theoretical computer science, an algorithm is correct with respect to a program specification, specification if it behaves as specified. Best explored is ''functional'' correctness, which refers to the input–output behavior of the algorithm: for each input it produces an output satisfying the specification. Within the latter notion, ''partial correctness'', requiring that ''if'' an answer is returned it will be correct, is distinguished from ''total correctness'', which additionally requires that an answer ''is'' eventually returned, i.e. the algorithm terminates. Correspondingly, to mathematical proof, prove a program's total correctness, it is sufficient to prove its partial correctness, and its termination. The latter kind of proof (termination proof) can never be fully automated, since the halting problem is undecidable problem, undecidable. For example, successively searching through integers 1, 2, 3, … to see if we can find an example of some phenomenon—say an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mathematical Proof
A mathematical proof is a deductive reasoning, deductive Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical evidence, empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Implementation
Implementation is the realization of an application, execution of a plan, idea, scientific modelling, model, design, specification, Standardization, standard, algorithm, policy, or the Management, administration or management of a process or Goal, objective. Industry-specific definitions Information technology In the information technology industry, implementation refers to the post-sales process of guiding a client from purchase to use of the software or hardware that was purchased. This includes requirements analysis, scope analysis, customizations, systems integrations, user policies, user training and delivery. These steps are often overseen by a project manager using project management methodologies. Software Implementations involve several professionals that are relatively new to the knowledge based economy such as Business analysis, business analysts, software implementation specialists, solutions architects, and project managers. To implement a system successfully, many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Communications Of The ACM
''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with backgrounds in all areas of computer science and information systems. The focus is on the practical implications of advances in information technology and associated management issues; ACM also publishes a variety of more theoretical journals. The magazine straddles the boundary of a science magazine, trade magazine, and a scientific journal. While the content is subject to peer review, the articles published are often summaries of research that may also be published elsewhere. Material published must be accessible and relevant to a broad readership. From 1960 onward, ''CACM'' also published algorithms, expressed in ALGOL. The collection of algorithms later became known as the Collected Algorithms of the ACM. CA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". Knuth is the author of the multi-volume work '' The Art of Computer Programming''. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |