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Speed Independent
In digital logic design, an asynchronous circuit is quasi delay-insensitive (QDI) when it operates correctly, independent of gate and wire delay with the weakest exception necessary to be turing-complete. Overview Pros * Robust to process variation, temperature fluctuation, circuit redesign, and FPGA remapping. * Natural event sequencing facilitates complex control circuitry. * Automatic clock gating and compute-dependent cycle time can save dynamic power and increase throughput by optimizing for average-case workload characteristics instead of worst-case. Cons * Delay insensitive encodings generally require twice as many wires for the same data. * Communication protocols and encodings generally require twice as many devices for the same functionality. Chips QDI circuits have been used to manufacture a large number of research chips, a small selection of which follows. * Caltech's asynchronous microprocessor * Tokyo University's TITAC and TITAC-2 processors Theory ...
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Digital Logic
A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more Binary number, binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see Ideal and real op-amps for comparison). Logic gates are primarily implemented using diodes or transistors acting as switch#Electronic switches, electronic switches, but can also be constructed using vacuum tubes, electromagnetic relays (relay logic), fluidic logic, pneumatics#Pneumatic logic, pneumatic logic, optics, molecular logic gate, molecules, or even analytical engine, mechanical elements. Now, most logic gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors). With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing t ...
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Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ri ...
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CMOS NAND
Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSFETs for logic functions. CMOS technology is used for constructing integrated circuit (IC) chips, including microprocessors, microcontrollers, memory chips (including CMOS BIOS), and other digital logic circuits. CMOS technology is also used for analog circuits such as image sensors (CMOS sensors), data converters, RF circuits (RF CMOS), and highly integrated transceivers for many types of communication. The CMOS process was originally conceived by Frank Wanlass at Fairchild Semiconductor and presented by Wanlass and Chih-Tang Sah at the International Solid-State Circuits Conference in 1963. Wanlass later filed US patent 3,356,858 for CMOS circuitry and it was granted in 1967. commercialized the technology with the trademark "COS-MOS" i ...
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C-element
In digital computing, the Muller C-element (C-gate, hysteresis flip-flop, coincident flip-flop, or two-hand safety circuit) is a small binary logic circuit widely used in design of asynchronous circuits and systems. It outputs 0 when all inputs are 0, it outputs 1 when all inputs are 1, and it retains its output state otherwise. It was specified formally in 1955 by David E. MullerD. E. MullerTheory of asynchronous circuits Report no. 66, Digital Computer Laboratory, University of Illinois at Urbana-Champaign, 1955. and first used in ILLIAC II computer. In terms of the theory of lattices, the C-element is a semimodular distributive circuit, whose operation in time is described by a Hasse diagram.D. E. Muller and W. S. Bartky"A theory of asynchronous circuits" Int. Symposium on the Switching Theory in Harvard University, pp. 204–243, 1959.I. Kimura,A comparison between two mathematical models of asynchronous circuits" Science Reports of the Tokyo Kyoiku Daigaku, Section A 10, ...
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Bipartite Graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets U and V may be thought of as a coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V red, each edge has endpoints of differing colors, as is required in the graph coloring problem.. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another red, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color. One often writes G=(U,V,E) to denote a bipartite graph whose partition has the parts U and V, with E denoting ...
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Boolean Expression
In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants true or false, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits. Boolean operators Most programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...s have the Boolean operators Logical disjunction, OR, Logical conjunction, AND and Negation, NOT; in C (programming language), C and some List of C-family programming languages, languages inspired by it, these are represented by ", , " ( ...
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Guarded Command Language
The Guarded Command Language (GCL) is a programming language defined by Edsger Dijkstra for predicate transformer semantics in EWD472. It combines programming concepts in a compact way. It makes it easier to develop a program and its proof hand-in-hand, with the proof ideas leading the way; moreover, parts of a program can actually be ''calculated''. An important property of GCL is nondeterminism. For example, in the if-statement, several alternatives may be true, and the choice of which to choose is done at runtime, when the if-statement is executed. This frees the programmer from having to make unnecessary choices and is an aid in the formal development of programs. GCL includes the multiple assignment statement. For example, execution of the statement is done by first evaluating the righthand side values and then storing them in the lefthand variables. Thus, this statement swaps the values of and . The following books discuss the development of programs using GCL: * * * * * ...
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Communicating Sequential Processes
In computer science, communicating sequential processes (CSP) is a formal language for describing patterns of interaction in concurrent systems. It is a member of the family of mathematical theories of concurrency known as process algebras, or process calculi, based on message passing via channels. CSP was highly influential in the design of the occam programming language and also influenced the design of programming languages such as Limbo, RaftLib, Erlang, Go, Crystal, and Clojure's core.async. CSP was first described in a 1978 article by Tony Hoare, but has since evolved substantially. CSP has been practically applied in industry as a tool for specifying and verifying the concurrent aspects of a variety of different systems, such as the T9000 Transputer, as well as a secure ecommerce system. The theory of CSP itself is also still the subject of active research, including work to increase its range of practical applicability (e.g., increasing the scale of the systems that can ...
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Tony Hoare
Sir Charles Antony Richard Hoare (Tony Hoare or C. A. R. Hoare) (born 11 January 1934) is a British computer scientist who has made foundational contributions to programming languages, algorithms, operating systems, formal verification, and concurrent computing. His work earned him the Turing Award, usually regarded as the highest distinction in computer science, in 1980. Hoare developed the sorting algorithm quicksort in 1959–1960. He developed Hoare logic, an axiomatic basis for verifying program correctness. In the semantics of concurrency, he introduced the formal language communicating sequential processes (CSP) to specify the interactions of concurrent processes, and along with Edsger Dijkstra, formulated the dining philosophers problem. He is also credited with development (and later criticism) of the null pointer, having introduced it in the ALGOL family of languages. Since 1977, he has held positions at the University of Oxford and Microsoft Research in Cambridge. ...
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