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John V. Tucker
John Vivian Tucker (born 4 February 1952) is a British computer scientist and expert on computability theory, also known as recursion theory. Computability theory is about what can and cannot be computed by people and machines. His work has focused on generalising the classical theory to deal with all forms of discrete/digital and continuous/ analogue data; and on using the generalisations as formal methods for system design; based on abstract data types and on the interface between algorithms and physical equipment. Biography Born in Cardiff, Wales, he was educated at Bridgend Boys' Grammar School, where he was taught mathematics, logic and computing. He read mathematics at University of Warwick (BA in 1973), and studied mathematical logic and the foundations of computing at University of Bristol (MSc in 1974, PhD in 1977). He has held posts at Oslo University, the CWI Amsterdam, and at Bristol and Leeds Universities, before returning to Wales as Professor of Computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Welsh Affairs
The Institute of Welsh Affairs (IWA) () is an independent charity and membership-based think-tank based Cardiff, Wales, which specialises in public policy and debate around the economy, education, environment and health sectors in Wales. History The establishment of the IWA came amid, according to Schofield (2014), the launch and subsequent failure of the 1979 Welsh devolution referendum, and the resulting “tug-of-war between a desire for a measure of independence for Wales and concerns about the country's ability to function under such a system.” In 1986, controller of BBC Wales Geraint Talfan Davies and Cardiff lawyer Keith James (of Hugh James LLP) set out a paper which established their case for "a body that can provide a regular intellectual challenge to current practice in all those spheres of Welsh life and administration that impact on our industrial and economic performance." An initial £50,000 grant was provided by the Welsh Development Agency Chief Execu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hoare Logic
Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician Tony Hoare, and subsequently refined by Hoare and other researchers. The original ideas were seeded by the work of Robert W. Floyd, who had published a similar system for flowcharts. Hoare triple The central feature of Hoare logic is the Hoare triple. A triple describes how the execution of a piece of code changes the state of the computation. A Hoare triple is of the form : \ C \ where P and Q are '' assertions'' and C is a ''command''.Hoare originally wrote "P\Q" rather than "\C\". P is named the '' precondition'' and Q the '' postcondition'': when the precondition is met, executing the command establishes the postcondition. Assertions are formulae in predicate logic. Hoare logic provides axioms and inference rules for all th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Data Types
In computer science, an abstract data type (ADT) is a mathematical model for data types. An abstract data type is defined by its behavior ( semantics) from the point of view of a '' user'', of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete representations of data, and are the point of view of an implementer, not a user. Formally, an ADT may be defined as a "class of objects whose logical behavior is defined by a set of values and a set of operations"; this is analogous to an algebraic structure in mathematics. What is meant by "behaviour" varies by author, with the two main types of formal specifications for behavior being ''axiomatic (algebraic) specification'' and an ''abstract model;'' these correspond to axiomatic semantics and operational semantics of an abstract machine, respectively. Some authors also include t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperative Programming
In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program consists of commands for the computer to perform. Imperative programming focuses on describing ''how'' a program operates step by step, rather than on high-level descriptions of its expected results. The term is often used in contrast to declarative programming, which focuses on ''what'' the program should accomplish without specifying all the details of ''how'' the program should achieve the result. Imperative and procedural programming Procedural programming is a type of imperative programming in which the program is built from one or more procedures (also termed subroutines or functions). The terms are often used as synonyms, but the use of procedures has a dramatic effect on how imperative programs appear and how they are constructed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matiyasevich's Theorem
In mathematics, a Diophantine equation is an equation of the form ''P''(''x''1, ..., ''x''''j'', ''y''1, ..., ''y''''k'') = 0 (usually abbreviated ''P''(', ') = 0) where ''P''(', ') is a polynomial with integer coefficients, where ''x''1, ..., ''x''''j'' indicate parameters and ''y''1, ..., ''y''''k'' indicate unknowns. A Diophantine set is a subset ''S'' of \mathbb^j, the set of all ''j''-tuples of natural numbers, so that for some Diophantine equation ''P''(', ') = 0, :\bar \in S \iff (\exists \bar \in \mathbb^)(P(\bar,\bar)=0) . That is, a parameter value is in the Diophantine set ''S'' if and only if the associated Diophantine equation is satisfiable under that parameter value. The use of natural numbers both in ''S'' and the existential quantification merely reflects the usual applications in computability and model theory. It does not matter whether natural numbers refer to the set of nonnegative integers or positive integers since the two definitions for Diophantine set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Term Rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting. Example cases Logic In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Bergstra
Johannes Aldert "Jan" Bergstra (born 1951) is a Dutch computer scientist. His work has focussed on logic and the theoretical foundations of software engineering, especially on formal methods for system design. He is best known as an expert on algebraic methods for the specification of data and computational processes in general. Biography Jan Bergstra was born in 1951 in Rotterdam, the son of Tjeerd Bergstra and Johanna Bisschop.Jan A. Bergstra (2009)Curriculum Vitae Jan Aldert Bergstra at ''uva.nl''. October 20, 2009. Accessed August 30, 2013 He was educated at the Montessori Lyceum Rotterdam (gymnasium beta) and then studied mathematics at Utrecht University, starting in 1969. After an MSc he wrote a PhD thesis, defended in 1976, on recursion theory in higher types, under the supervision of Dirk van Dalen. Bergstra held posts at the Institute of Applied Mathematics and Computer Science of the University of Leiden (1976–82), and the Centrum Wiskunde & Informatica (CWI) in Ams ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular Group (mathematics), groups as the object of study, in universal algebra one takes the class of groups as an object of study. Basic idea In universal algebra, an algebra (or algebraic Structure (mathematical logic), structure) is a set (mathematics), set ''A'' together with a collection of operations on ''A''. An ''n''-arity, ary operation (mathematics), operation on ''A'' is a function (mathematics), function that takes ''n'' elements of ''A'' and returns a single element of ''A''. Thus, a 0-ary operation (or ''nullary operation'') can be represented simply as an element of ''A'', or a ''Constant (mathematics), constant'', often denoted by a letter like ''a''. A 1-ary operation (or ''unary operation'') is simply a function from ''A'' to ''A'', often denoted by a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal numbers'', and numbers used for ordering are called '' ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by succ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Type
In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers), characters and Booleans. A data type constrains the possible values that an expression, such as a variable or a function, might take. This data type defines the operations that can be done on the data, the meaning of the data, and the way values of that type can be stored. Concept A data type is a collection or grouping of data values. Such a grouping may be defined for many reasons: similarity, convenience, or to focus the attention. It is frequently a matter of good organization that aids the understanding of complex definitions. Almost all programming languages explicitly include the notion of da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Learned Society Of Wales
The Learned Society of Wales (Welsh: Cymdeithas Ddysgedig Cymru) is a learned society and charity that exists to "celebrate, recognise, preserve, protect and encourage excellence in all of the scholarly disciplines", and to serve the Welsh nation. The Learned Society of Wales is Wales's first and only all-embracing national scholarly academy. A registered charity, it was established and launched on 25 May 2010 at the National Museum of Wales and was granted a Royal Charter in 2015. The society is based in Cardiff. It is an independent, self-governing, pan-disciplinary, bilingual organisation operating throughout Wales. Purpose The Society describes its mission as to: * Celebrate, recognise, preserve, protect, and encourage excellence in all scholarly disciplines, and in the professions, industry and commerce, the arts and public service. * Promote the advancement of learning, scholarship, and the dissemination and application of the results of academic enquiry and research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
