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Vector Addition Systems
A vector addition system (VAS) is one of several mathematical modeling languages for the description of distributed systems. Vector addition systems were introduced by Richard M. Karp and Raymond E. Miller in 1969, and generalized to vector addition systems with states (VASS) by John E. Hopcroft and Jean-Jacques Pansiot in 1979. Both VAS and VASS are equivalent in many ways to Petri nets introduced earlier by Carl Adam Petri. Reachability in vector addition systems is Ackermann-complete (and hence nonelementary). Informal definition A ''vector addition system'' consists of a finite set of integer vectors. An initial vector is seen as the initial values of multiple counters, and the vectors of the VAS are seen as updates. These counters may never drop below zero. More precisely, given an initial vector with non negative values, the vectors of the VAS can be added componentwise, given that every intermediate vector has non negative values. A ''vector addition system with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributed Systems
A distributed system is a system whose components are located on different networked computers, which communicate and coordinate their actions by passing messages to one another from any system. Distributed computing is a field of computer science that studies distributed systems. The components of a distributed system interact with one another in order to achieve a common goal. Three significant challenges of distributed systems are: maintaining concurrency of components, overcoming the lack of a global clock, and managing the independent failure of components. When a component of one system fails, the entire system does not fail. Examples of distributed systems vary from SOA-based systems to massively multiplayer online games to peer-to-peer applications. A computer program that runs within a distributed system is called a distributed program, and ''distributed programming'' is the process of writing such programs. There are many different types of implementations for t ... [...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 dispense p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagrams
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term "illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, representat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concurrency (computer Science)
In computer science, concurrency is the ability of different parts or units of a program, algorithm, or problem to be executed out-of-order or in partial order, without affecting the outcome. This allows for parallel execution of the concurrent units, which can significantly improve overall speed of the execution in multi-processor and multi-core systems. In more technical terms, concurrency refers to the decomposability of a program, algorithm, or problem into order-independent or partially-ordered components or units of computation. According to Rob Pike, concurrency is the composition of independently executing computations, and concurrency is not parallelism: concurrency is about dealing with lots of things at once but parallelism is about doing lots of things at once. Concurrency is about structure, parallelism is about execution, concurrency provides a way to structure a solution to solve a problem that may (but not necessarily) be parallelizable. A number of mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Models Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Models Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite state machines * Post machines (Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model Functional models Functional models include: * Abstract rew ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Specification Languages
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to: Dress code and events * Formal wear, attire for formal events * Semi-formal attire, attire for semi-formal events * Informal attire, more controlled attire than casual but less than formal * Formal (university), official university dinner, ball or other event * School formal, official school dinner, ball or other event Logic and mathematics *Formal logic, or mathematical logic ** Informal logic, the complement, whose definition and scope is contentious *Formal fallacy, reasoning of invalid structure ** Informal fallacy, the complement *Informal mathematics, also called naïve mathematics *Formal cause, Aristotle's intrinsic, determining cause * Formal power series, a generalization of power series without requiring convergence, used in combinatorics *Formal calculation, a calculation which is systematic, but without a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trace Theory
In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi. The underpinning is provided by an abstract algebra, algebraic definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which provides a concrete algebraic foundation, analogous to the way that the free monoid provides the underpinning for formal languages. The power of trace theory stems from the fact that the algebra of dependency graphs (such as Petri nets) is isomorphic to that of trace monoids, and thus, one can apply both algebraic formal language tools, as well as tools from graph theory. While the trace monoid had been studied by Pierre_Cartier_(mathematician), Pierre Cartier and Dominique Foata for its combinatorics in the 1960s, trace theory was first formulated by Antoni Mazurkiewicz in the 1970s, in an attempt to evade some of the problems in the theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actor Model
The actor model in computer science is a mathematical model of concurrent computation that treats ''actor'' as the universal primitive of concurrent computation. In response to a message it receives, an actor can: make local decisions, create more actors, send more messages, and determine how to respond to the next message received. Actors may modify their own private state, but can only affect each other indirectly through messaging (removing the need for lock-based synchronization). The actor model originated in 1973. It has been used both as a framework for a theoretical understanding of computation and as the theoretical basis for several practical implementations of concurrent systems. The relationship of the model to other work is discussed in actor model and process calculi. History According to Carl Hewitt, unlike previous models of computation, the actor model was inspired by physics, including general relativity and quantum mechanics. It was also influenced by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Process Calculus
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. They also provide algebraic laws that allow process descriptions to be manipulated and analyzed, and permit formal reasoning about equivalences between processes (e.g., using bisimulation). Leading examples of process calculi include CSP, CCS, ACP, and LOTOS. More recent additions to the family include the π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus. Essential features While the variety of existing process calculi is very large (including variants that incorporate stochastic behaviour, timing information, and specializations for studying molecular interactions), there are several features that all process calculi have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kahn Process Networks
A Kahn process network (KPN, or process network) is a distributed ''model of computation'' in which a group of deterministic sequential processes communicate through unbounded first in, first out channels. The model requires that reading from a channel is blocking while writing is non-blocking. Due to these key restrictions, the resulting process network exhibits deterministic behavior that does not depend on the timing of computation nor on communication delays. Kahn process networks were originally developed for modeling parallel programs, but have proven convenient for modeling embedded systems, high-performance computing systems, signal processing systems, stream processing systems, dataflow programming languages, and other computational tasks. KPNs were introduced by Gilles Kahn in 1974. Execution model KPN is a common model for describing signal processing systems where infinite streams of data are incrementally transformed by processes executing in sequence or paralle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communicating Finite-state Machine
In computer science, a communicating finite-state machine is a finite state machine labeled with "receive" and "send" operations over some alphabet of channels. They were introduced by Brand and Zafiropulo,D. Brand and P. Zafiropulo. On communicating finite-state machines. Journal of the ACM, 30(2):323-342, 1983. and can be used as a model of concurrent processes like Petri nets A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that .... Communicating finite state machines are used frequently for modeling a communication protocol since they make it possible to detect major protocol design errors, including boundedness, deadlocks, and unspecified receptions.Rosier, Louis E; Gouda, Mohamed G. Deciding Progress for a Class of Communicating Finite State Machines. Austin: University of Texas at Aus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pair where * ''V'' is a set whose elements are called '' vertices'', ''nodes'', or ''points''; * ''A'' is a set of ordered pairs of vertices, called ''arcs'', ''directed edges'' (sometimes simply ''edges'' with the corresponding set named ''E'' instead of ''A''), ''arrows'', or ''directed lines''. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called ''edges'', ''links'' or ''lines''. The aforementioned definition does not allow a directed graph to have multiple arrows with the same source and target nodes, but some authors consider a broader definition that allows directed graphs to have such multiple arcs (namely, they allow the arc set to be a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
