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Algebraic Specification
Algebraic specification is a software engineering technique for formally specifying system behavior. It was a very active subject of computer science research around 1980. Overview Algebraic specification seeks to systematically develop more efficient programs by: # formally defining types of data, and mathematical operations on those data types # abstracting implementation details, such as the size of representations (in memory) and the efficiency of obtaining outcome of computations # formalizing the computations and operations on data types # allowing for automation by formally restricting operations to this limited set of behaviors and data types. An algebraic specification achieves these goals by defining one or more data types, and specifying a collection of functions that operate on those data types. These functions can be divided into two classes: # Constructor functions: Functions that create or initialize the data elements, or construct complex elements from simpler ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Engineering
Software engineering is a systematic engineering approach to software development. A software engineer is a person who applies the principles of software engineering to design, develop, maintain, test, and evaluate computer software. The term '' programmer'' is sometimes used as a synonym, but may also lack connotations of engineering education or skills. Engineering techniques are used to inform the software development process which involves the definition, implementation, assessment, measurement, management, change, and improvement of the software life cycle process itself. It heavily uses software configuration management which is about systematically controlling changes to the configuration, and maintaining the integrity and traceability of the configuration and code throughout the system life cycle. Modern processes use software versioning. History Beginning in the 1960s, software engineering was seen as its own type of engineering. Additionally, the development of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 dispense ... [...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] |
Common Algebraic Specification Language
The Common Algebraic Specification Language (CASL) is a general-purpose specification language based on first-order logic with induction. Partial functions and subsorting are also supported. Overview CASL has been designed by CoFI, the Common Framework Initiative (CoFI), with the aim to subsume many existing specification languages. CASL comprises four levels: * basic specifications, for the specification of single software modules, * structured specifications, for the modular specification of modules, * architectural specifications, for the prescription of the structure of implementations, * specification libraries, for storing specifications distributed over the Internet. The four levels are orthogonal to each other. In particular, it is possible to use CASL structured and architectural specifications and libraries with logics other than CASL. For this purpose, the logic has to be formalized as an institution. This feature is also used by the CASL extensions. Extensions Seve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book '' Disquisitiones Arithmeticae'', published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in , but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic ''modulo'' 12. In terms of the definition below, 15 is ''congruent'' to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock. Congruence Given an integer , called a modulus, two integers and are said to be congruent modulo , if is a divisor of their difference (that is, if there is an integer such that ). Congruence modu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Form (abstract Rewriting)
In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an object may rewrite to several normal forms or none at all. Many properties of rewriting systems relate to normal forms. Definitions Stated formally, if (''A'',→) is an abstract rewriting system, ''x''∈''A'' is in normal form if no ''y''∈''A'' exists such that ''x''→''y'', i.e. ''x'' is an irreducible term. An object ''a'' is weakly normalizing if there exists at least one particular sequence of rewrites starting from ''a'' that eventually yields a normal form. A rewriting system has the weak normalization property or is ''(weakly) normalizing'' (WN) if every object is weakly normalizing. An object ''a'' is strongly normalizing if every sequence of rewrites starting from ''a'' eventually terminates with a normal form. An abstract rewriting system is ''strongly normalizing'', ''terminating'', ''noetherian'', or has the (str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Confluence (abstract Rewriting)
In computer science, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result. This article describes the properties in the most abstract setting of an abstract rewriting system. Motivating examples The usual rules of elementary arithmetic form an abstract rewriting system. For example, the expression (11 + 9) × (2 + 4) can be evaluated starting either at the left or at the right parentheses; however, in both cases the same result is eventually obtained. If every arithmetic expression evaluates to the same result regardless of reduction strategy, the arithmetic rewriting system is said to be ground-confluent. Arithmetic rewriting systems may be confluent or only ground-confluent depending on details of the rewriting system. A second, more abstract example is obtained from the following proof of each group element equalling the inverse of its inverse: This proof starts fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 dispense ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negation
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P, \mathord P or \overline. It is interpreted intuitively as being true when P is false, and false when P is true. Negation is thus a unary logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes ''truth'' to ''falsity'' (and vice versa). In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition P is the proposition whose proofs are the refutations of P. Definition ''Classical negation'' is an operation on one logical value, typically the value of a proposition, that produces a value of ''true'' when its operand is false, and a value of ''false'' when its operand is true. Thus if statement is true, then \neg P ... [...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] |
Logical Conjunction
In logic, mathematics and linguistics, And (\wedge) is the truth-functional operator of logical conjunction; the ''and'' of a set of operands is true if and only if ''all'' of its operands are true. The logical connective that represents this operator is typically written as \wedge or . A \land B is true if and only if A is true and B is true, otherwise it is false. An operand of a conjunction is a conjunct. Beyond logic, the term "conjunction" also refers to similar concepts in other fields: * In natural language, the denotation of expressions such as English "and". * In programming languages, the short-circuit and control structure. * In set theory, intersection. * In lattice theory, logical conjunction (greatest lower bound). * In predicate logic, universal quantification. Notation And is usually denoted by an infix operator: in mathematics and logic, it is denoted by \wedge, or ; in electronics, ; and in programming languages, &, &&, or and. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
