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Linear Time Property
In model checking, a branch of computer science, linear time properties are used to describe requirements of a model of a computer system. Example properties include "the vending machine does not dispense a drink until money has been entered" (a safety property) or "the computer program eventually terminates" (a liveness property). Fairness properties can be used to rule out unrealistic paths of a model. For instance, in a model of two traffic lights, the liveness property "both traffic lights are green infinitely often" may only be true under the unconditional fairness constraint "each traffic light changes colour infinitely often" (to exclude the case where one traffic light is "infinitely faster" than the other). Formally, a linear time property is an ω-language over the power set of "atomic propositions". That is, the property contains sequences of sets of propositions, each sequence known as a "word". Every property can be rewritten as "''P'' and ''Q'' both occur" for some s ... [...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 d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Teller Machine
An automated teller machine (ATM) or cash machine (in British English) is an electronic telecommunications device that enables customers of financial institutions to perform financial transactions, such as cash withdrawals, deposits, funds transfers, balance inquiries or account information inquiries, at any time and without the need for direct interaction with bank staff. ATMs are known by a variety of names, including automatic teller machine (ATM) in the United States (sometimes redundantly as "ATM machine"). In Canada, the term ''automated banking machine'' (ABM) is also used, although ATM is also very commonly used in Canada, with many Canadian organizations using ATM over ABM. In British English, the terms ''cashpoint'', ''cash machine'' and ''hole in the wall'' are most widely used. Other terms include ''any time money'', ''cashline'', ''tyme machine'', ''cash dispenser'', ''cash corner'', ''bankomat'', or ''bancomat''. ATMs that are not operated by a financial i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computation Tree Logic
Computation tree logic (CTL) is a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined; there are different paths in the future, any one of which might be an actual path that is realized. It is used in formal verification of software or hardware artifacts, typically by software applications known as model checkers, which determine if a given artifact possesses safety or liveness properties. For example, CTL can specify that when some initial condition is satisfied (e.g., all program variables are positive or no cars on a highway straddle two lanes), then all possible executions of a program avoid some undesirable condition (e.g., dividing a number by zero or two cars colliding on a highway). In this example, the safety property could be verified by a model checker that explores all possible transitions out of program states satisfying the initial condition and ensures that all such executions satisfy the property. Comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precondition
In computer programming, a precondition is a condition or predicate that must always be true just prior to the execution of some section of code or before an operation in a formal specification. If a precondition is violated, the effect of the section of code becomes undefined and thus may or may not carry out its intended work. Security problems can arise due to incorrect preconditions. Often, preconditions are simply included in the documentation of the affected section of code. Preconditions are sometimes tested using guards or assertions within the code itself, and some languages have specific syntactic constructions for doing so. For example: the factorial is only defined for integers greater than or equal to zero. So a program that calculates the factorial of an input number would have preconditions that the number be an integer and that it be greater than or equal to zero. In object-oriented programming Preconditions in object-oriented software development are an ess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dense Set
In topology and related areas of mathematics, a subset ''A'' of a topological space ''X'' is said to be dense in ''X'' if every point of ''X'' either belongs to ''A'' or else is arbitrarily "close" to a member of ''A'' — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation). Formally, A is dense in X if the smallest closed subset of X containing A is X itself. The of a topological space X is the least cardinality of a dense subset of X. Definition A subset A of a topological space X is said to be a of X if any of the following equivalent conditions are satisfied: The smallest closed subset of X containing A is X itself. The closure of A in X is equal to X. That is, \operatorname_X A = X. The interior of the complement of A is empty. That is, \operatorname_X (X \setminus A) = \varnothing. Every point in X either be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation. This should not be confused with a closed manifold. Equivalent definitions By definition, a subset A of a topological space (X, \tau) is called if its complement X \setminus A is an open subset of (X, \tau); that is, if X \setminus A \in \tau. A set is closed in X if and only if it is equal to its closure in X. Equivalently, a set is closed if and only if it contains all of its limit points. Yet another equivalent definition is that a set is closed if and only if it contains all of its boundary points. Every subset A \subseteq X is always contained in its (topological) closure in X, which is denoted by \operatorname_X A; that is, if A \subseteq X then A \subseteq \o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric (mathematics)
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a '' topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Process (computing)
In computing, a process is the instance of a computer program that is being executed by one or many threads. There are many different process models, some of which are light weight, but almost all processes (even entire virtual machines) are rooted in an operating system (OS) process which comprises the program code, assigned system resources, physical and logical access permissions, and data structures to initiate, control and coordinate execution activity. Depending on the OS, a process may be made up of multiple threads of execution that execute instructions concurrently. While a computer program is a passive collection of instructions typically stored in a file on disk, a process is the execution of those instructions after being loaded from the disk into memory. Several processes may be associated with the same program; for example, opening up several instances of the same program often results in more than one process being executed. Multitasking is a method to allow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concurrent Computing
Concurrent computing is a form of computing in which several computations are executed '' concurrently''—during overlapping time periods—instead of ''sequentially—''with one completing before the next starts. This is a property of a system—whether a program, computer, or a network—where there is a separate execution point or "thread of control" for each process. A ''concurrent system'' is one where a computation can advance without waiting for all other computations to complete. Concurrent computing is a form of modular programming. In its paradigm an overall computation is factored into subcomputations that may be executed concurrently. Pioneers in the field of concurrent computing include Edsger Dijkstra, Per Brinch Hansen, and C.A.R. Hoare. Introduction The concept of concurrent computing is frequently confused with the related but distinct concept of parallel computing, Pike, Rob (2012-01-11). "Concurrency is not Parallelism". ''Waza conference'', 11 Janu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liveness
Properties of an execution of a computer program —particularly for concurrent and distributed systems— have long been formulated by giving ''safety properties'' ("bad things don't happen") and ''liveness properties'' ("good things do happen"). A simple example will illustrate safety and liveness. A program is totally correct with respect to a precondition P and postcondition Q if any execution started in a state satisfying P terminates in a state satisfying Q. Total correctness is a conjunction of a safety property and a liveness property: * The safety property prohibits these "bad things": executions that start in a state satisfying P and terminate in a final state that does not satisfy Q. For a program C, this safety property is usually written using the Hoare triple \ C \. * The liveness property, the "good thing", is that execution that starts in a state satisfying P terminates. Note that a ''bad thing'' is discrete, since it happens at a particular place during execution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Depth-first Search
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Extra memory, usually a stack, is needed to keep track of the nodes discovered so far along a specified branch which helps in backtracking of the graph. A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre Trémaux as a strategy for solving mazes. Properties The time and space analysis of DFS differs according to its application area. In theoretical computer science, DFS is typically used to traverse an entire graph, and takes time where , V, is the number of vertices and , E, the number of edges. This is linear in the size of the graph. In these applications it also uses space O(, V, ) in the worst case to store the stack of vertices on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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