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Rippling Spring Waltz Frontispiece
In computer science, more particularly in automated theorem proving, rippling refers to a group of meta-level heuristics, developed primarily in the Mathematical Reasoning Group in the School of Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as a restricted form of rewrite system, where special object level annotations are used to ensure fertilization upon the completion of rewriting, with a measure decreasing requirement ensuring termination for any set of rewrite rules and expression. History Raymond Aubin was the first person to use the term "rippling out" whilst working on his 1976 PhD thesis at the University of Edinburgh. He recognised a common pattern of movement during the rewriting stage of inductive proofs. Alan Bundy later turned this concept on its head by defining rippling to be this pattern of movement, rather than a side effect. Since then, "rippling sideways", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. 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 for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Hypothesis
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for ''n'' = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case ''n'' = ''k'', ''then'' it must also hold for the next case ''n'' = ''k'' + 1. These two steps establish that the statement holds for every natural number ''n''. The base case does not necessarily begin with ''n'' = 0, but often with ''n'' = 1, and possibly with any fixed natural number ''n'' = ''N'', establishing the truth of the statement for all natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Automated Reasoning
The ''Journal of Automated Reasoning'' was established in 1983 by Larry Wos, who was its editor in chief until 1992. It covers research and advances in automated reasoning, mechanical verification of theorems, and other deductions in classical and non-classical logic. The journal is published by Springer Science+Business Media. As of 2021, the editor-in-chief is Jasmin Blanchette, an associate professor of computer science at the Vrije Universiteit Amsterdam. The journal's 2019 impact factor is 1.431, and it is indexed by several science indexing services, including the Science Citation Index Expanded and Scopus. References External links * {{Official, 1=https://www.springer.com/computer/theoretical+computer+science/journal/10817 Computer science journals Logic journals English-language journals Publications established in 1983 Logic in computer science Formal methods publications Springer Science+Business Media academic journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rippling Ripple
In computer science, more particularly in automated theorem proving, rippling refers to a group of meta-level heuristics, developed primarily in the Mathematical Reasoning Group in the School of Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as a restricted form of rewrite system, where special object level annotations are used to ensure fertilization upon the completion of rewriting, with a measure decreasing requirement ensuring termination for any set of rewrite rules and expression. History Raymond Aubin was the first person to use the term "rippling out" whilst working on his 1976 PhD thesis at the University of Edinburgh. He recognised a common pattern of movement during the rewriting stage of inductive proofs. Alan Bundy later turned this concept on its head by defining rippling to be this pattern of movement, rather than a side effect. Since then, "rippling sideway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rippling Annotated Step Case
In computer science, more particularly in automated theorem proving, rippling refers to a group of meta-level heuristics, developed primarily in the Mathematical Reasoning Group in the School of Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as a restricted form of rewrite system, where special object level annotations are used to ensure fertilization upon the completion of rewriting, with a measure decreasing requirement ensuring termination for any set of rewrite rules and expression. History Raymond Aubin was the first person to use the term "rippling out" whilst working on his 1976 PhD thesis at the University of Edinburgh. He recognised a common pattern of movement during the rewriting stage of inductive proofs. Alan Bundy later turned this concept on its head by defining rippling to be this pattern of movement, rather than a side effect. Since then, "rippling sideway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rippling Wave Rules
In computer science, more particularly in automated theorem proving, rippling refers to a group of meta-level heuristics, developed primarily in the Mathematical Reasoning Group in the School of Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as a restricted form of rewrite system, where special object level annotations are used to ensure fertilization upon the completion of rewriting, with a measure decreasing requirement ensuring termination for any set of rewrite rules and expression. History Raymond Aubin was the first person to use the term "rippling out" whilst working on his 1976 PhD thesis at the University of Edinburgh. He recognised a common pattern of movement during the rewriting stage of inductive proofs. Alan Bundy later turned this concept on its head by defining rippling to be this pattern of movement, rather than a side effect. Since then, "rippling sideway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rippling Rewrite Rules
In computer science, more particularly in automated theorem proving, rippling refers to a group of meta-level heuristics, developed primarily in the Mathematical Reasoning Group in the School of Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as a restricted form of rewrite system, where special object level annotations are used to ensure fertilization upon the completion of rewriting, with a measure decreasing requirement ensuring termination for any set of rewrite rules and expression. History Raymond Aubin was the first person to use the term "rippling out" whilst working on his 1976 PhD thesis at the University of Edinburgh. He recognised a common pattern of movement during the rewriting stage of inductive proofs. Alan Bundy later turned this concept on its head by defining rippling to be this pattern of movement, rather than a side effect. Since then, "rippling sideway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rippling Step Case
In computer science, more particularly in automated theorem proving, rippling refers to a group of meta-level heuristics, developed primarily in the Mathematical Reasoning Group in the School of Informatics at the University of Edinburgh, and most commonly used to guide inductive proofs in automated theorem proving systems. Rippling may be viewed as a restricted form of rewrite system, where special object level annotations are used to ensure fertilization upon the completion of rewriting, with a measure decreasing requirement ensuring termination for any set of rewrite rules and expression. History Raymond Aubin was the first person to use the term "rippling out" whilst working on his 1976 PhD thesis at the University of Edinburgh. He recognised a common pattern of movement during the rewriting stage of inductive proofs. Alan Bundy later turned this concept on its head by defining rippling to be this pattern of movement, rather than a side effect. Since then, "rippling sideway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutativity
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as ''noncommutative operations''. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Numbers
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 success ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Termination Proof
Termination may refer to: Science *Termination (geomorphology), the period of time of relatively rapid change from cold, glacial conditions to warm interglacial condition *Termination factor, in genetics, part of the process of transcribing RNA *Termination type, in lithic reduction, a characteristic indicating the manner in which the distal end of a lithic flake detaches from a core *Chain termination, in chemistry, a chemical reaction which halts polymerization *Termination shock, in solar studies, a feature of the heliosphere * Terminating computation, in computer science **Termination analysis, a form of program analysis in computer science ** Termination proof, a mathematical proof concerning the termination of a program ** Termination (term rewriting), in particular for term rewriting systems Technology *Electrical termination, ending a wire or cable properly to prevent interference *Termination of wires to a **Crimp connection ** Electrical connector ** Solder joint *Abor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a 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 which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which 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 further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
