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...es compute set union, set intersection, and set complement, as well as the arithmetic operations addition and multiplication. == Circuits as functions == ...

...t=Håstad |first=Johan |chapter=Almost optimal lower bounds for small depth circuits |date=1986 |title=Proceedings of the eighteenth annual ACM symposium on The == Bounds on AC⁰ circuits == ...

...nce to propositional proof systems allows to interpret theories of bounded arithmetic as formal systems capturing various levels of feasible reasoning (see below ...{{cite news|first1=Samuel|last1=Buss|authorlink1=Samuel Buss|title=Bounded Arithmetic|journal=Bibliopolis, Naples, Italy, 1986.}}</ref> and a number of other log ...

....google.com/books?id=6XkgKydE0Z8C |title=Bounded Arithmetic, Propositional Logic and Complexity Theory |date=1995-11-24 |publisher=Cambridge University Pres ...-systems/218048250981F835B4B2A4080205A0BA |journal=The Journal of Symbolic Logic |language=en |volume=44 |issue=1 |pages=36–50 |doi=10.2307/2273702 |jstor=2 ...

...th is used.<ref>{{cite web |first=Louis Philippe |last=Lessard |title=Fast Arithmetic on FPGA Using Redundant Binary Apparatus |year=2008 |url=http://www.louisle ...nverter using Prefix Networks |conference=IEEE International Symposium on Circuits and Systems (ISCAS 2007) |date=May 2007 |location=New Orleans |doi=10.1109/ ...

...{{cite book |last1=Straubing |first1=Howard |title=Finite Automata, Formal Logic and Circuit Complexity |date=1994 |publisher=Birkhäser |isbn=978-1-4612-028 A predicate is regular if and only if it can be defined by a first order logic formula <math>\phi(x_0,\dots,x_{r-1})</math>, where the atomic predicates a ...

...Stochastic computing performs this operation using probability instead of arithmetic. ...y, (0011) AND (0101) is (0001), i.e., 1/2 x 1/2 = 1/4, which is exactly an arithmetic multiplication. As the information is presented in probability distribution ...

...8948}}</ref><ref>{{cite journal | last=Şahin | first=Engin | title=Quantum arithmetic operations based on quantum Fourier transform on signed integers | year=202 ...]] consisting of only <math>O(n^2)</math> [[Hadamard gate]]s and [[Quantum logic gate#Controlled gates|controlled]] [[phase shift gate]]s, where <math>n</ma ...

=== Symbolic logic === The paper used, as a [[Mathematical logic|logical language]] for describing neural networks, "Language II" from [[Log ...

...ot'') denoted as {{math|1=¬}}. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Bool ...duced by [[George Boole]] in his first book ''The Mathematical Analysis of Logic'' (1847),<ref name="Boole_2011"/> and set forth more fully in his ''[[An In ...

...o [0,1]</math>, there exists a polynomial time generated family of quantum circuits <math>Q={\{Q_n:n\in \N \}}</math>, where <math>Q_n</math> is a circuit whic == Simulation of quantum circuits == ...

...dfs/gordon_moore_1965_article.pdf Cramming More Components onto Integrated Circuits]," Electronics Magazine Vol. 38, No. 8 (April 19, 1965)</ref> by increasing ...gital logic components such as [[shift register]]s, and basic [[arithmetic logic unit|ALU]] digital circuit elements such as [[adder (electronics)|adder]]s ...

...ular biology tools act on the data to perform various operations (e.g., [[arithmetic]] or [[logical operations]]). ...circuits ([[binary counter]], [[bit-wise cumulative XOR]]), ribozymes for logic operations, molecular switches ([[DNA tweezers]]), and autonomous molecular ...

{{defn|A mathematical technique useful in analysis of three-phase circuits.}} {{defn|A network of individual logic elements in multiple layers that mimics the function of a biological nervou ...

{{wiktionary|Appendix:Glossary of logic}} This is a '''glossary of logic'''. [[Logic]] is the study of the principles of valid reasoning and argumentation. ...

...ro Borgi]] (1424–1484), mathematician, author of many of the best books on arithmetic written in the 15th Century ...d papers (1829, 1830) on the production of [[electric currents]] in closed circuits by the approach and withdrawal of a [[magnet]] ...

== Computer science and logic == ..., [[Boolean algebra]], as it is now known, became central to the design of circuits and computers in the following century.<ref>{{Cite book |last=Katz |first=V ...

...mputer programming}}, a {{gli|statement}} that a [[Predicate (mathematical logic)|predicate]] ([[Boolean-valued function]], i.e. a true–false {{gli|expressi {{defn|An area of {{gli|computer science}} and [[mathematical logic]] dedicated to understanding different aspects of [[reasoning]]. The study ...

..., such as a load, a store, a [[jump instruction|jump]], or an [[arithmetic logic unit]] (ALU) operation on one or more units of data in the CPU's [[processo ...itle=Automated Design of Both the Topology and Sizing of Analog Electrical Circuits Using Genetic Programming|conference=Artificial Intelligence in Design '96| ...

...}}</ref> The original [[Dartmouth BASIC]] had built-in commands for matrix arithmetic on arrays from its [[Dartmouth BASIC#Second Edition, CARDBASIC|second editi ...eeded for describing mechanical vibrations, and oscillations in electrical circuits.<ref>{{Harvard citations |last1=Riley |last2=Hobson |last3=Bence |year=1997 ...