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Abstract Interpretation
In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which gains information about its semantics (e.g., control-flow analysis, control-flow, data-flow analysis, data-flow) without performing all the calculations. Its main concrete application is formal static code analysis, static analysis, the automatic information extraction, extraction of information about the possible executions of computer programs; such analyses have two main usages: * inside compilers, to analyse programs to decide whether certain Optimization (computer science), optimizations or Program transformation, transformations are applicable; * for debugging or even the certification of programs against classes of bugs. Abstract interpretation was formalized by the French computer scientist working couple Patrick Cousot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Patrick Cousot
Patrick Cousot (born 3 December 1948) is a French computer scientist, currently Silver Professor of Computer Science at the Courant Institute of Mathematical Sciences, New York University, USA. Before he was Professor at the École Normale Supérieure (ENS), Paris, France, the École Polytechnique, Palaiseau, France and the University of Metz, France and a Research Scientist at the French National Center for Scientific Research (CNRS) at the Joseph Fourier University, Grenoble, France. Together with his wife Radhia Cousot (1947–2014), Patrick Cousot is the originator of abstract interpretation, an influential technique in formal methods. In the 2000s, he has worked on practical methods of static analysis for critical embedded software ( Astrée), such as found in avionics. In 1999 he received the CNRS Silver Medal and in 2006 the great prize of the EADS Foundation. In 2001, he was bestowed an honorary doctorate by Saarland University, Germany. With Radhia Cousot, he receive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Function
In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to . The subset , that is, the '' domain'' of viewed as a function, is called the domain of definition or natural domain of . If equals , that is, if is defined on every element in , then is said to be a total function. In other words, a partial function is a binary relation over two sets that associates to every element of the first set ''at most'' one element of the second set; it is thus a univalent relation. This generalizes the concept of a (total) function by not requiring ''every'' element of the first set to be associated to an element of the second set. A partial function is often used when its exact domain of definition is not known, or is difficult to specify. However, even when the exact domain of definition is known, partial functions are often used for simplicity or brevity. This is the case in calculus, where, for example, the quotient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Interpretation Of Integers By Signs Svg
Abstract may refer to: *"Abstract", a 2017 episode of the animated television series ''Adventure Time'' * ''Abstract'' (album), 1962 album by Joe Harriott * Abstract algebra, sets with specific operations acting on their elements * Abstract of title, a summary of the documents affecting the title to a parcel of land * Abstract (law), a summary of a legal document * Abstract (summary), in academic publishing * Abstract art, artistic works that do not attempt to represent reality or concrete subjects * '' Abstract: The Art of Design'', 2017 Netflix documentary series * Abstract music, music that is non-representational * Abstract object in philosophy * Abstract structure in mathematics * Abstract type in computer science * The property of an abstraction * Q-Tip (musician), also known as "The Abstract" * Abstract and concrete In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ariane 5 Flight 501
Ariane flight V88 was the failed maiden flight of the Arianespace Ariane 5 rocket, vehicle no. 501, on 4 June 1996. It carried the Cluster spacecraft, a constellation of four European Space Agency research satellites. The launch ended in failure due to multiple errors in the software design: dead code, intended only for Ariane 4, with inadequate protection against integer overflow led to an exception handled inappropriately, halting the whole otherwise unaffected inertial navigation system. This caused the rocket to veer off its flight path 37 seconds after launch, beginning to disintegrate under high aerodynamic forces, and finally self-destructing via its automated flight termination system. The failure has become known as one of the most infamous and expensive software bugs in history. The failure resulted in a loss of more than US$370 million. Launch failure The Ariane 5 reused the code from the inertial reference platform from the Ariane 4, but the early part ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Both areas are highly related, as the complexity of an algorithm is always an upper bound on the complexity of the problem solved by this algorithm. Moreover, for designing efficient algorithms, it is often fundamental to compare the complexity of a specific algorithm to the complexity of the problem to be solved. Also, in most cases, the only thing that is known about the complexity of a problem is that it is lower than the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability Theory (computation)
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] |
Multiplication
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathematics), product''. Multiplication is often denoted by the cross symbol, , by the mid-line dot operator, , by juxtaposition, or, in programming languages, by an asterisk, . The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''; both numbers can be referred to as ''factors''. This is to be distinguished from term (arithmetic), ''terms'', which are added. :a\times b = \underbrace_ . Whether the first factor is the multiplier or the multiplicand may be ambiguous or depend upon context. For example, the expression 3 \times 4 , can be phrased as "3 ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperative Programming
In computer science, imperative programming is a programming paradigm of software that uses Statement (computer science), statements that change a program's state (computer science), state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program consists of command (computing), commands for the computer to perform. Imperative programming focuses on describing ''how'' a program operates step by step (with general order of the steps being determined in source code by the placement of statements one below the other), 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. Procedural programming Procedural programming is a type of imperative programming in which the program is built from one or more procedures (also termed s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction
Abstraction is a process where general rules and concepts are derived from the use and classifying of specific examples, literal (reality, real or Abstract and concrete, concrete) signifiers, first principles, or other methods. "An abstraction" is the outcome of this process — a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''.Suzanne K. Langer (1953), ''Feeling and Form: A Theory of Art Developed from Philosophy in a New Key'', p. 90: "Sculpture, Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through sensory system, touch and sight." Conceptual abstractions may be made by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halting Problem
In computability theory (computer science), computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is ''Undecidable problem, undecidable'', meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs. The problem comes up often in discussions of computability since it demonstrates that some functions are mathematically Definable set, definable but not Computable function, computable. A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually via a Turing machine. The proof then shows, for any program that might determine whether programs halt, that a "pathological" program exists for which makes an incorrect determination. Specifically, is the program that, when called with some input, passes its own s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rice's Theorem
In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable problem, undecidable. A ''semantic'' property is one about the program's behavior (for instance, "does the program halting problem, terminate for all inputs?"), unlike a syntactic property (for instance, "does the program contain an if-then-else statement?"). A ''non-trivial'' property is one which is neither true for every program, nor false for every program. The theorem generalizes the undecidability of the halting problem. It has far-reaching implications on the feasibility of static program analysis, static analysis of programs. It implies that it is impossible, for example, to implement a tool that checks whether any given program is correctness (computer science), correct, or even executes without error (it is possible to implement a tool that always overestimates or always underestimates, so in practice one has to decide what is less of a problem). The theorem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
