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X-Machine Testing
The (Stream) X-Machine Testing Methodology is a ''complete'' functional testing approach to software- and hardware testingM. Holcombe and F. Ipate (1998) ''Correct Systems - Building a Business Process Solution''. Springer, Applied Computing Series. that exploits the scalability of the Stream X-Machine model of computation.Gilbert Laycock (1993) ''The Theory and Practice of Specification Based Software Testing''. PhD Thesis, University of SheffieldAbstract Using this methodology, it is likely to identify a finite test-set that exhaustively determines whether the tested system's implementation matches its specification. This goal is achieved by a divide-and-conquer approach, in which the design is decomposed by refinementF. Ipate and M. Holcombe (1998) 'A method for refining and testing generalised machine specifications'. ''Int. J. Comp. Math.'' 68, pp. 197–219. into a collection of Stream X-Machines, which are implemented as separate modules, then tested bottom-up. At each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Testing
Functional testing is a quality assurance (QA) processPrasad, Dr. K.V.K.K. (2008) ''ISTQB Certification Study Guide'', Wiley, , p. vi and a type of black-box testing that bases its test cases on the specifications of the software component under test. Functions are tested by feeding them input and examining the output, and internal program structure is rarely considered (unlike white-box testing).Kaner, Falk, Nguyen. ''Testing Computer Software''. Wiley Computer Publishing, 1999, p. 42. . Functional testing is conducted to evaluate the compliance of a system or component with specified functional requirements. Functional testing usually describes ''what'' the system does. Since functional testing is a type of black-box testing, the software's functionality can be tested without knowing the internal workings of the software. This means that testers do not need to know programming languages or how the software has been implemented. This, in turn, could lead to reduced developer bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistent
In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term ''satisfiable'' is used instead. The syntactic definition states a theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences of T. Let A be a set of closed sentences (informally "axioms") and \langle A\rangle the set of closed sentences provable from A under some (specified, possibly implicitly) formal deductive system. The set of axioms A is consistent when \varphi, \lnot \varphi \in \langle A \rangle for no formula \varphi. If ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codomain
In mathematics, the codomain or set of destination of a function is the set into which all of the output of the function is constrained to fall. It is the set in the notation . The term range is sometimes ambiguously used to refer to either the codomain or image of a function. A codomain is part of a function if is defined as a triple where is called the '' domain'' of , its ''codomain'', and its '' graph''. The set of all elements of the form , where ranges over the elements of the domain , is called the '' image'' of . The image of a function is a subset In mathematics, set ''A'' is a subset of a set ''B'' if all elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset o ... of its codomain so it might not coincide with it. Namely, a function that is not surjective has elements in its codomain for which the equation does not have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Of A Function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by \operatorname(f) or \operatornamef, where is the function. More precisely, given a function f\colon X\to Y, the domain of is . Note that in modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that and are both subsets of \R, the function can be graphed in the Cartesian coordinate system. In this case, the domain is represented on the -axis of the graph, as the projection of the graph of the function onto the -axis. For a function f\colon X\to Y, the set is called the codomain, and the set of values attained by the function (which is a subset of ) is called its range or image. Any function can be restricted to a subset of its domain. The restriction of f \colon X \to Y to A, where A\subseteq X, is written as \left. f \_A \colon A \to Y. Natural domain If a real function is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite-state Machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-machine
The X-machine (''XM'') is a theoretical model of computation introduced by Samuel Eilenberg in 1974.S. Eilenberg (1974) ''Automata, Languages and Machines, Vol. A''. Academic Press, London. The ''X'' in "X-machine" represents the fundamental data type on which the machine operates; for example, a machine that operates on databases (objects of type ''database'') would be a ''database''-machine. The X-machine model is structurally the same as the finite-state machine, except that the symbols used to label the machine's transitions denote relations of type ''X''→''X''. Crossing a transition is equivalent to applying the relation that labels it (computing a set of changes to the data type ''X''), and traversing a path in the machine corresponds to applying all the associated relations, one after the other. Original theory Eilenberg's original X-machine was a completely general theoretical model of computation (subsuming the Turing machine, for example), which admitted determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samuel Eilenberg
Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra. Early life and education He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent much of his career as a professor at Columbia University. He earned his Ph.D. from University of Warsaw in 1936, with thesis ''On the Topological Applications of Maps onto a Circle''; his thesis advisors were Kazimierz Kuratowski and Karol Borsuk. He died in New York City in January 1998. Career Eilenberg's main body of work was in algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (and the Eilenberg–Steenrod axioms are named for the pair), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory. Eilenberg was a member of Bourbaki and, with Henri Cartan, wrote the 1956 book ''Homological Algebra''. La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete. The term "complete" is also used without qualification, with differing meanings depending on the context, mostly referring to the property of semantical validity. Intuitively, a system is called complete in this particular sense, if it can derive every formula that is true. Other properties related to completeness The property converse to completeness is called soundness: a system is sound with respect to a property (mostly semantical validity) if each of its theorems has that property. Forms of completeness Expressive completeness A formal language is expressively complete if it can express the subject matter for which it is intended. Functional completeness A set of logical connectives associated with a formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an Inference, inferential Argument-deduction-proof distinctions, argument for a Proposition, 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 evidence, 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 furthe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Testing
Software testing is the act of examining the artifacts and the behavior of the software under test by validation and verification. Software testing can also provide an objective, independent view of the software to allow the business to appreciate and understand the risks of software implementation. Test techniques include, but not necessarily limited to: * analyzing the product requirements for completeness and correctness in various contexts like industry perspective, business perspective, feasibility and viability of implementation, usability, performance, security, infrastructure considerations, etc. * reviewing the product architecture and the overall design of the product * working with product developers on improvement in coding techniques, design patterns, tests that can be written as part of code based on various techniques like boundary conditions, etc. * executing a program or application with the intent of examining behavior * reviewing the deployment infrastructure a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformance Testing
Conformance testing — an element of conformity assessment, and also known as compliance testing, or type testing — is testing or other activities that determine whether a process, product, or service complies with the requirements of a specification, technical standard, contract, or regulation. Testing is often either logical testing or physical testing. The test procedures may involve other criteria from mathematical testing or chemical testing. Beyond simple conformance, other requirements for efficiency, interoperability or compliance may apply. Conformance testing may be undertaken by the producer of the product or service being assessed, by a user, or by an accredited independent organization, which can sometimes be the author of the standard being used. When testing is accompanied by certification, the products or services may then be advertised as being certified in compliance with the referred technical standard. Manufacturers and suppliers of products and serv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Specification
In computer science, formal specifications are mathematically based techniques whose purpose are to help with the implementation of systems and software. They are used to describe a system, to analyze its behavior, and to aid in its design by verifying key properties of interest through rigorous and effective reasoning tools. These specifications are ''formal'' in the sense that they have a syntax, their semantics fall within one domain, and they are able to be used to infer useful information. Motivation In each passing decade, computer systems have become increasingly more powerful and, as a result, they have become more impactful to society. Because of this, better techniques are needed to assist in the design and implementation of reliable software. Established engineering disciplines use mathematical analysis as the foundation of creating and validating product design. Formal specifications are one such way to achieve this in software engineering reliability as once predicted. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
