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Widening (computer Science)
In computer science, especially model checking and abstract interpretation, widening refers to at least two different techniques in the analysis of abstract transition systems where infinite progressions of abstract states are replaced by a (computed or guessedAhmed Bouajjani and Tayssir Touili (2012), "Widening techniques for regular tree model checking", ''STTT'', Vol. 14, No. 2, pp. 145 -- 16/ref>) least fixed point. The use of the term in ''model checking'' is closely related to ''acceleration'' techniques, some authors reserving ''acceleration'' for exact computations.Sébastien Bardin, Alain Finkel, Jérôme Leroux and Philippe Schnoebelen, ''Flat acceleration in symbolic model checking'' (2005), Automated Technology for Verification and Analysis, pp. 474--488, Springer Intuition While many computer programs can be understood in terms of machine states and transitions (see formal semantics of programming languages), their state spaces may be too large to fully represent and ... [...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] |
Model Checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, data-flow) without performing all the calculations. Its main concrete application is formal static analysis, the automatic 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 optimizations or 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 and Radhia Cousot in the late 1970s. Intuition This section illustrates abstract interpretation by means of real-world, non-computing example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transition System
In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one transition. If the label set is a singleton, the system is essentially unlabeled, and a simpler definition that omits the labels is possible. Transition systems coincide mathematically with abstract rewriting systems (as explained further in this article) and directed graphs. They differ from finite-state automata in several ways: * The set of states is not necessarily finite, or even countable. * The set of transitions is not necessarily finite, or even countable. * No "start" state or "final" states are given. Transition systems can be represented as directed graphs. Formal definition Formally, a transition system is a pair (S, \rightarrow) where S is a set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Fixed Point
In order theory, a branch of mathematics, the least fixed point (lfp or LFP, sometimes also smallest fixed point) of a function from a partially ordered set to itself is the fixed point which is less than each other fixed point, according to the order of the poset. A function need not have a least fixed point, but if it does then the least fixed point is unique. For example, with the usual order on the real numbers, the least fixed point of the real function ''f''(''x'') = ''x''2 is ''x'' = 0 (since the only other fixed point is 1 and 0 < 1). In contrast, ''f''(''x'') = ''x'' + 1 has no fixed points at all, so has no least one, and ''f''(''x'') = ''x'' has infinitely many fixed points, but has no least one. Examples Let be a and be a vertex. ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Semantics Of Programming Languages
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation. History In 1967, Robert W. Floyd publishes the paper ''Assigning meanings to programs''; his chief aim is "a rigorous standard for proofs about computer programs, including proofs of correctness, equivalence, and termination". Floyd further writes: A semantic definition of a programming language, in our approach, is founded on a syntactic definition. It must specify which of the phrases in a syntactically correct program represent commands, and what conditions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction Model Checking
In computer science and in mathematics, abstraction model checking is for systems where an actual representation is too complex in developing the model alone. So, the design undergoes a kind of translation to scaled down "abstract" version. The set of variables are partitioned into visible and invisible depending on their change of values. The real state space A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the to ... is summarized into a smaller set of the visible ones. Galois connected The real and the abstract state spaces are Galois connected. This means that if we take an element from the abstract space, concretize it and abstract the concretized version, the result will be equal to the original. On the other hand, if you pick an element from the real space, abstract it and concretiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbolic Execution
In computer science, symbolic execution (also symbolic evaluation or symbex) is a means of analyzing a program to determine what inputs cause each part of a program to execute. An interpreter follows the program, assuming symbolic values for inputs rather than obtaining actual inputs as normal execution of the program would. It thus arrives at expressions in terms of those symbols for expressions and variables in the program, and constraints in terms of those symbols for the possible outcomes of each conditional branch. Finally, the possible inputs that trigger a branch can be determined by solving the constraints. The field of symbolic simulation applies the same concept to hardware. Symbolic computation applies the concept to the analysis of mathematical expressions. Example Consider the program below, which reads in a value and fails if the input is 6. int f() During a normal execution ("concrete" execution), the program would read a concrete input value (e.g., 5) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbolic Model Checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pushdown Systems
Pushdown may refer to: * Pushdown automaton, a concept in theoretical computer science ** More generally, anything relating to a stack Stack may refer to: Places * Stack Island, an island game reserve in Bass Strait, south-eastern Australia, in Tasmania’s Hunter Island Group * Blue Stack Mountains, in Co. Donegal, Ireland People * Stack (surname) (including a list of people ... * Push-down (exercise), a strength-training exercise {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Channel Systems
Channel, channels, channeling, etc., may refer to: Geography * Channel (geography), in physical geography, a landform consisting of the outline (banks) of the path of a narrow body of water. Australia * Channel Country, region of outback Australia in Queensland and partly in South Australia, Northern Territory and New South Wales. * Channel Highway, a regional highway in Tasmania, Australia. Europe * Channel Islands, an archipelago in the English Channel, off the French coast of Normandy * Channel Tunnel or Chunnel, a rail tunnel underneath the English Channel * English Channel, called simply "The Channel", the part of the Atlantic Ocean that separates Great Britain from northern France North America * Channel Islands of California, a chain of eight islands located in the Pacific Ocean off the coast of Southern California, United States * Channel Lake, Illinois, a census-designated place in Lake County, Illinois, United States * Channels State Forest, a state forest in Vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counter Systems
Counter may refer to: Mathematics and computing * Counter machine, a subclass of register machines * Counter (digital), an electronic device, mechanical device, or computer program for counting * Loop counter, the variable that controls the iterations of a loop * Jeton, a reckoning counter used on reckoning boards for calculations * Mechanical counter, a digital counter using mechanical components * Tally counter, a mechanical counting device * Web counter, a counter that counts the number of visits to a web page * Project COUNTER, a standard for reporting usage statistics of electronic resources Games and sport * Counter (board wargames), a playing piece used in board wargames * Counter run, an offensive play in American football * Counter turn, an element in figure skating * Counter (collectible card games), a small item used to represent certain objects or conditions in a collectible card game * Jones Counter, measures distance bicycles travel Linguistics and typography * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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