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Moore Machine
In the theory of computation, a Moore machine is a finite-state machine whose current output values are determined only by its current state. This is in contrast to a Mealy machine, whose output values are determined both by its current state and by the values of its inputs. Like other finite state machines, in Moore machines, the input typicallinfluences the next state Thus the input may indirectly influence subsequent outputs, but not the current or immediate output. The Moore machine is named after Edward F. Moore, who presented the concept in a 1956 paper, “ Gedanken-experiments on Sequential Machines.” Formal definition A Moore machine can be defined as a 6-tuple (Q, q_0, \Sigma, O, \delta, G) consisting of the following: * A finite set of states Q * A start state (also called initial state) q_0 which is an element of Q * A finite set called the input alphabet \Sigma * A finite set called the output alphabet O * A transition function \delta : Q \times \Sigma \righ ...
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Theory Of Computation
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: ''"What are the fundamental capabilities and limitations of computers?".'' In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" mo ...
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Clocked Sequential System
In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contrast to ''combinational logic'', whose output is a function of only the present input. That is, sequential logic has ''state'' (''memory'') while combinational logic does not. Sequential logic is used to construct finite-state machines, a basic building block in all digital circuitry. Virtually all circuits in practical digital devices are a mixture of combinational and sequential logic. A familiar example of a device with sequential logic is a television set with "channel up" and "channel down" buttons. Pressing the "up" button gives the television an input telling it to switch to the next channel above the one it is currently receiving. If the television is on channel 5, pressing "up" switches it to receive channel 6. However, if the television is on channel 8, pressing "up" swi ...
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Algorithmic State Machine
The algorithmic state machine (ASM) method is a method for designing finite state machines (FSMs) originally developed by Thomas E. Osborne at the University of California, Berkeley (UCB) since 1960, introduced to and implemented at Hewlett-Packard in 1968, formalized and expanded since 1967 and written about by Christopher R. Clare since 1970. It is used to represent diagrams of digital integrated circuits. The ASM diagram is like a state diagram but more structured and, thus, easier to understand. An ASM chart is a method of describing the sequential operations of a digital system. ASM method The ASM method is composed of the following steps: :''1''. Create an algorithm, using ''pseudocode'', to describe the desired operation of the device. :''2''. Convert the pseudocode into an ''ASM chart''. :''3''. Design the ''datapath'' based on the ASM chart. :''4''. Create a ''detailed ASM chart'' based on the datapath. :''5''. Design the ''control logic'' based on the detailed ASM ch ...
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Synchronous Circuit
In digital electronics, a synchronous circuit is a digital circuit in which the changes in the state of memory elements are synchronized by a clock signal. In a sequential digital logic circuit, data are stored in memory devices called flip-flops or latches. The output of a flip-flop is constant until a pulse is applied to its "clock" input, upon which the input of the flip-flop is latched into its output. In a synchronous logic circuit, an electronic oscillator called the ''clock'' generates a string (sequence) of pulses, the "clock signal". This clock signal is applied to every storage element, so in an ideal synchronous circuit, every change in the logical levels of its storage components is simultaneous. Ideally, the input to each storage element has reached its final value before the next clock occurs, so the behaviour of the whole circuit can be predicted exactly. Practically, some delay is required for each logical operation, resulting in a maximum speed limitation ...
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Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ...
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Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious university in the country. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches (including five foreign ones in the Commonwealth of Independent States countries). Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 List of Nobel laureates, Nobel laureates, six Fields Medal winners, and one Turing Award winner had been affiliated with the university. The university was ranked 18th by ''The Three University Missions Ranking'' in 2022, and 76th by the ''QS World University Rankings'' in 2022, #293 in the world by the global ''Times Higher World University Rankings'', and #326 by ''U.S. News & World Report'' in 2022. It was the highest-ran ...
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Anatolii Alexeevitch Karatsuba
Anatoly Alexeyevich Karatsuba (his first name often spelled Anatolii) (russian: Анато́лий Алексе́евич Карацу́ба; Grozny, Soviet Union, 31 January 1937 – Moscow, Russia, 28 September 2008) was a Russian people, Russian mathematician working in the field of analytic number theory, p-adic number, ''p''-adic numbers and Dirichlet series. For most of his student and professional life he was associated with the MSU Faculty of Mechanics and Mathematics, Faculty of Mechanics and Mathematics of Moscow State University, defending a Doktor nauk, D.Sc. there entitled "The method of trigonometric sums and intermediate value theorems" in 1966. He later held a position at the Steklov Institute of Mathematics of the Russian Academy of Sciences, Academy of Sciences. His textbook ''Foundations of Analytic Number Theory'' went to two editions, 1975 and 1983. The Karatsuba algorithm is the earliest known divide and conquer algorithm for multiplication and lives on as ...
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Moore Machine
In the theory of computation, a Moore machine is a finite-state machine whose current output values are determined only by its current state. This is in contrast to a Mealy machine, whose output values are determined both by its current state and by the values of its inputs. Like other finite state machines, in Moore machines, the input typicallinfluences the next state Thus the input may indirectly influence subsequent outputs, but not the current or immediate output. The Moore machine is named after Edward F. Moore, who presented the concept in a 1956 paper, “ Gedanken-experiments on Sequential Machines.” Formal definition A Moore machine can be defined as a 6-tuple (Q, q_0, \Sigma, O, \delta, G) consisting of the following: * A finite set of states Q * A start state (also called initial state) q_0 which is an element of Q * A finite set called the input alphabet \Sigma * A finite set called the output alphabet O * A transition function \delta : Q \times \Sigma \righ ...
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Solenoid
upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whose length is substantially greater than its diameter, which generates a controlled magnetic field. The coil can produce a uniform magnetic field in a volume of space when an electric current is passed through it. The term ''solenoid'' was coined in 1823 by André-Marie Ampère. The helical coil of a solenoid does not necessarily need to revolve around a straight-line axis; for example, William Sturgeon's electromagnet of 1824 consisted of a solenoid bent into a horseshoe shape (not unlike an arc spring). Solenoids provide magnetic focusing of electrons in vacuums, notably in television camera tubes such as vidicons and image orthicons. Electrons take helical paths within the magnetic field. These solenoids, focus coils, surround nearly th ...
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Glitch
A glitch is a short-lived fault in a system, such as a transient fault that corrects itself, making it difficult to troubleshoot. The term is particularly common in the computing and electronics industries, in circuit bending, as well as among players of video games. More generally, all types of systems including human organizations and nature experience glitches. A glitch, which is slight and often temporary, differs from a more serious bug which is a genuine functionality-breaking problem. Alex Pieschel, writing for ''Arcade Review'', said: bug' is often cast as the weightier and more blameworthy pejorative, while 'glitch' suggests something more mysterious and unknowable inflicted by surprise inputs or stuff outside the realm of code." Etymology Some reference books, including ''Random House's American Slang'', claim that the term comes from the German word ''glitschen'' ("to slip") and the Yiddish word ''glitshn'' ("to slide", "to skid"). Either way, it is a relatively n ...
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Combinational Logic
In automata theory, combinational logic (also referred to as time-independent logic or combinatorial logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has ''memory'' while combinational logic does not. Combinational logic is used in computer circuits to perform Boolean algebra on input signals and on stored data. Practical computer circuits normally contain a mixture of combinational and sequential logic. For example, the part of an arithmetic logic unit, or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such as half adders, full adders, half subtractors, full subtractors, multiplexers, demultiplexers, encoders and decoders are also made by using combin ...
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