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UNITY (programming Language)
UNITY is a programming language constructed by K. Mani Chandy and Jayadev Misra for their book ''Parallel Program Design: A Foundation''. It is a theoretical language which focuses on ''what'', instead of ''where'', ''when'' or ''how''. The language contains no method of flow control, and program statements run in a nondeterministic way until statements cease to cause changes during execution. This allows for programs to run indefinitely, such as auto-pilot or power plant safety systems, as well as programs that would normally terminate (which here converge to a fixed point). Description All statements are assignments, and are separated by #. A statement can consist of multiple assignments, of the form a,b,c := x,y,z, or a := x , , b := y , , c := z. You can also have a ''quantified statement list'', <# x,y : ''expression'' :: ''statement''>, where x and y are chosen randomly among the values that satisfy ''expression''. A ''quantified assignment'' is similar. In < ...
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Jayadev Misra
Jayadev Misra is an Indian-born computer scientist who has spent most of his professional career in the United States. He is the Schlumberger Centennial Chair Emeritus in computer science and a University Distinguished Teaching Professor Emeritus at the University of Texas at Austin. Professionally he is known for his contributions to the formal aspects of concurrent programming and for jointly spearheading, with Sir Tony Hoare, the project on Verified Software Initiative (VSI). Education and early career Misra received a B.Tech. in electrical engineering from IIT Kanpur, India in 1969 and a Ph.D. in electrical engineering and computer science from the Johns Hopkins University, Baltimore, Maryland in 1972. After a brief period working for IBM, he joined the University of Texas at Austin in 1974 where he has remained throughout his career, except for a sabbatical year spent at Stanford University during 1983–1984. He retired from active teaching in 2015. Major professional c ...
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Flow Control (data)
In data communications, flow control is the process of managing the rate of data transmission between two nodes to prevent a fast sender from overwhelming a slow receiver. Flow control should be distinguished from congestion control, which is used for controlling the flow of data when congestion has actually occurred. Flow control mechanisms can be classified by whether or not the receiving node sends feedback to the sending node. Flow control is important because it is possible for a sending computer to transmit information at a faster rate than the destination computer can receive and process it. This can happen if the receiving computers have a heavy traffic load in comparison to the sending computer, or if the receiving computer has less processing power than the sending computer. Stop-and-wait Stop-and-wait flow control is the simplest form of flow control. In this method the message is broken into multiple frames, and the receiver indicates its readiness to receive a fra ...
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Statement (programming)
In computer programming, a statement is a Syntax (programming languages), syntactic unit of an Imperative programming, imperative programming language that expresses some action to be carried out. A Computer program, program written in such a language is formed by a sequence of one or more statements. A statement may have internal components (e.g., Expression (computer science), expressions). Many programming languages (e.g. Ada (programming language), Ada, Algol 60, C (programming language), C, Java (programming language), Java, Pascal (programming language), Pascal) make a distinction between statements and Declaration (computer programming), definitions/declarations. A definition or declaration specifies the data on which a program is to operate, while a statement specifies the actions to be taken with that data. Statements which cannot contain other statements are ''simple''; those which can contain other statements are ''compound''.Revised ALGOL 60 report section. 4.1. The ap ...
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Nondeterministic Programming
A nondeterministic programming language is a language which can specify, at certain points in the program (called "choice points"), various alternatives for program flow. Unlike an if-then statement, the method of choice between these alternatives is not directly specified by the programmer; the program must decide at run time between the alternatives, via some general method applied to all choice points. A programmer specifies a limited number of alternatives, but the program must later choose between them. ("Choose" is, in fact, a typical name for the nondeterministic operator.) A hierarchy of choice points may be formed, with higher-level choices leading to branches that contain lower-level choices within them. One method of choice is embodied in backtracking systems (such as Amb, or unification in Prolog), in which some alternatives may "fail," causing the program to backtrack and try other alternatives. If all alternatives fail at a particular choice point, then an entire b ...
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Fixed Point Combinator
In mathematics and computer science in general, a '' fixed point'' of a function is a value that is mapped to itself by the function. In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) is a higher-order function \textsf that returns some fixed point of its argument function, if one exists. Formally, if the function ''f'' has one or more fixed points, then : \textsf\ f = f\ (\textsf\ f)\ , and hence, by repeated application, : \textsf\ f = f\ (f\ ( \ldots f\ (\textsf\ f) \ldots))\ . Y combinator In the classical untyped lambda calculus, every function has a fixed point. A particular implementation of fix is Curry's paradoxical combinator Y, represented by : \textsf = \lambda f. \ (\lambda x.f\ (x\ x))\ (\lambda x.f\ (x\ x))\ .Throughout this article, the syntax rules given in Lambda calculus#Notation are used, to save parentheses.For an arbitrary lambda term ''f'', the fixed-point property can be validated by beta reducing the left- an ...
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Assignment (computer Science)
In computer programming, an assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable. In most imperative programming languages, the assignment statement (or expression) is a fundamental construct. Today, the most commonly used notation for this operation is ''x'' = ''expr'' (originally Superplan 1949–51, popularized by Fortran 1957 and C). The second most commonly used notation is ''x'' := ''expr'' (originally ALGOL 1958, popularised by Pascal). Many other notations are also in use. In some languages, the symbol used is regarded as an operator (meaning that the assignment statement as a whole returns a value). Other languages define assignment as a statement (meaning that it cannot be used in an expression). Assignments typically allow a variable to hold different values at different times during its life-span and scope. However, some languages (primarily strictly f ...
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Bubble Sort
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps had to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list. This simple algorithm performs poorly in real world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java. Analysis Performance Bubble sort has a worst-case and average complexity of O(n^2), where n is the number of items being sorted. Most practical sorting algorithms have substantially better worst-case or average complexity, ...
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Floyd–Warshall Algorithm
In computer science, the Floyd–Warshall algorithm (also known as Floyd's algorithm, the Roy–Warshall algorithm, the Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding shortest paths in a directed weighted graph with positive or negative edge weights (but with no negative cycles). A single execution of the algorithm will find the lengths (summed weights) of shortest paths between all pairs of vertices. Although it does not return details of the paths themselves, it is possible to reconstruct the paths with simple modifications to the algorithm. Versions of the algorithm can also be used for finding the transitive closure of a relation R, or (in connection with the Schulze voting system) widest paths between all pairs of vertices in a weighted graph. History and naming The Floyd–Warshall algorithm is an example of dynamic programming, and was published in its currently recognized form by Robert Floyd in 1962. However, it is essentially the same as ...
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Shortest Path Problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment. Definition The shortest path problem can be defined for graphs whether undirected, directed, or mixed. It is defined here for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge. Two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices P = ( v_1, v_2, \ldots, v_n ) \in V \times V \times \cdots \times V such that v_i is adjacent to v_ for 1 \leq i ...
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