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Model of computation
computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be
Boolean_circuit
Programming language construct
Short-circuit evaluation, minimal evaluation, or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming
Short-circuit_evaluation
Computational problem
The circuit value problem (or circuit evaluation problem) is the computational problem of computing the output of a given Boolean circuit on a given input
Circuit_value_problem
Model of computational complexity
In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according
Circuit_complexity
Mathematical topics based on the works of George Boole
digital logical circuits. Boolean expression, an expression in a programming language that produces a Boolean value when evaluated Boolean function, a function
Boolean
Branch of computational complexity theory
weighted Boolean circuit problems: Input: a Boolean circuit Parameter: k Output: Whether there exists a weight-k input such that the circuit outputs True
Parameterized_complexity
Function returning one of only two values
function Boolean formulas can also be displayed as a graph: Propositional directed acyclic graph Digital circuit diagram of logic gates, a Boolean circuit And-inverter
Boolean_function
Model of computation
this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates they contain
Circuit_(computer_science)
Expression in a computer program
propositional formulas in logic and are associated to Boolean circuits. Most programming languages have the Boolean operators OR, AND and NOT; in C and some languages
Boolean_expression
Classic NP-complete problem in computer science
the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit
Circuit satisfiability problem
Circuit_satisfiability_problem
Algebraic manipulation of "true" and "false"
algebra as the two-element Boolean algebra. In modern circuit engineering settings, there is little need to consider other Boolean algebras, thus "switching
Boolean_algebra
Process in digital electronics and integrated circuit design
metallic structures on an integrated circuit. In terms of Boolean algebra, the optimization of a complex Boolean expression is a process of finding a
Logic_optimization
Type of digital logic implemented by Boolean circuits
time-independent logic) is a type of digital logic that is implemented by Boolean circuits, where the output is a pure function of the present input only. This
Combinational_logic
Cryptographic protocol for two-party computation
party. In the garbled circuit protocol, the function has to be described as a Boolean circuit. The history of garbled circuits is complicated. The invention
Garbled_circuit
Class in computational complexity theory
by a uniform Boolean circuit (which can be calculated from the length of the input, for NC, we suppose we can compute the Boolean circuit of size n in
NC_(complexity)
Testing method for testing the randomness of pseudo-random number generators
i } {\displaystyle C=\{C_{k}^{i}\}} is a collection of boolean circuits, such that each circuit C k i {\displaystyle C_{k}^{i}} has less than P C ( k )
Next-bit_test
Set of problems in computational complexity theory
computation (e.g. probabilistic Turing machines, interactive proof systems, Boolean circuits, and quantum computers). The study of the relationships between complexity
Complexity_class
Algorithmic complexity class
example, some graphs can be succinctly described by a small Boolean circuit. The circuit has 2 n {\displaystyle 2n} inputs, 1 output and p o l y ( n )
EXPTIME
Subfield of cryptography
evaluated. The function is viewed as a Boolean circuit, with inputs in binary of fixed length. A Boolean circuit is a collection of gates connected with
Secure multi-party computation
Secure_multi-party_computation
System with multiple networked computers
executed by each computer. Models such as Boolean circuits and sorting networks are used. A Boolean circuit can be seen as a computer network: each gate
Distributed_computing
Topics referred to by the same term
paths Boolean circuit, a mathematical model for digital logic circuits Integer circuit, a mathematical object of computational complexity Circuit complexity
Circuit
Operation in Boolean circuit theory
transformation, takes as input an arbitrary combinatorial logic circuit and produces an equisatisfiable boolean formula in conjunctive normal form (CNF). The length
Tseytin_transformation
Complexity class used in circuit complexity
hierarchy of TC classes. TC0 contains all languages which are decided by Boolean circuits with constant depth and polynomial size, containing only unbounded
TC0
Ordering of binary values, used for positioning and error correction
n-ary Gray code, also known as a non-Boolean Gray code. As the name implies, this type of Gray code uses non-Boolean values in its encodings. For example
Gray_code
Mathematical study of switched networks
Number One Electronic Switching System Boolean circuit Boolean differential calculus C-element Circuit complexity Circuit minimization Karnaugh map Logic design
Switching_circuit_theory
Boolean function
A majority gate is a logical gate used in circuit complexity and other applications of Boolean circuits. A majority gate returns true if and only if
Majority_function
Algebraic structure modeling logical operations
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties
Boolean_algebra_(structure)
Puzzle video game
constructive, a method to quickly convert any Boolean circuit into such a grid that is possible if and only if the circuit is satisfiable; membership in NP is established
Minesweeper_(video_game)
Russian mathematician (1932–2006)
finite-state automata, Boolean circuits and multi-valued logic circuits. Ingo Wegener, in his book The Complexity of Boolean Functions, credits O. B
Oleg_Lupanov
Device performing a Boolean function
of the algorithms and mathematics that can be described with Boolean logic. Logic circuits include such devices as multiplexers, registers, arithmetic
Logic_gate
Cirquent calculus (circuit sequent calculus) is a proof calculus that combines aspects of sequent calculus and boolean circuits. Its proof-objects are
Cirquent_calculus
Standard model in theoretical computer science
the differences between the study of arithmetic circuits and the study of Boolean circuits. In Boolean complexity, one is mostly interested in computing
Arithmetic_circuit_complexity
Graphical representation of an electrical circuit
equipment. In computer science, circuit diagrams are useful when visualizing expressions using Boolean algebra. Circuit diagrams are pictures with symbols
Circuit_diagram
on the size of constant-depth Boolean circuits. It was first introduced by Johan Håstad to prove that AC0 Boolean circuits of depth k require size exp
Switching_lemma
(AOI) gate, it reduces the boolean expression ABCD + EFGH + EXPAND. When configured as AND-OR (AO) gate, it reduces the boolean expression ABCD + EFGH +
List of 4000-series integrated circuits
List_of_4000-series_integrated_circuits
Electronic circuit formed on a small, flat piece of semiconductor material
and microcontrollers, use boolean algebra to process "one" and "zero" signals. Among the most advanced integrated circuits are the microprocessors or
Integrated_circuit
Computational input that relies on the length but not content of the input
polynomial size Boolean circuit A(n) deciding the problem, we can use a Turing machine that interprets the advice string as a description of the circuit. Then,
Advice_(complexity)
Measure of complexity of a Boolean circuit
complexity theory, especially circuit complexity theory, the weft of a Boolean circuit is a measure of its complexity. A Boolean circuit is a directed acyclic
Weft_(circuit)
Difficulty measures for computer science problems
hierarchy can be described as the class of Boolean circuits over NP predicates. A collapse of the Boolean hierarchy would imply a collapse of the polynomial
Boolean_hierarchy
Two-dimensional Turing machine with emergent behavior
In 2000, Gajardo et al. showed a construction that calculates any boolean circuit using the trajectory of a single instance of Langton's ant. Greg Turk
Langton's_ant
Function in Boolean algebra
function is notable for its role in theoretical investigation of circuit complexity of Boolean functions. The output of the parity function is the parity bit
Parity_function
Formal concept in theoretical computer science and cryptography
(unproven) circuit lower bounds in computational complexity theory. Hence the construction of pseudorandom generators for the class of Boolean circuits of a
Pseudorandom_generator
Cryptographic software library
(FHEW) scheme for Boolean circuit evaluation with optimizations Chillotti–Gama–Georgieva–Izabachene (TFHE) scheme for Boolean circuit evaluation with extensions
OpenFHE
Problem of determining if a Boolean formula could be made true
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY
Boolean satisfiability problem
Boolean_satisfiability_problem
English mathematician and philosopher (1815–1864)
with operations resembling logical ones Boolean circuit, a mathematical model for digital logical circuits. Boolean data type is a data type, having two
George_Boole
On collapse of the polynomial hierarchy if NP is in non-uniform polynomial time class
Karp–Lipton theorem states that if the Boolean satisfiability problem (SAT) can be solved by Boolean circuits with a polynomial number of logic gates
Karp–Lipton_theorem
Unsolved problem in computer science
in NP can be transformed mechanically into a Boolean satisfiability problem in polynomial time. The Boolean satisfiability problem is one of many NP-complete
P_versus_NP_problem
avoid trivial failures. DLOGTIME-uniformity is used in circuit complexity. A Boolean circuit family C 0 , C 1 , … {\displaystyle C_{0},C_{1},\dots }
DLOGTIME
Logic gate implementing negation
1s. The NOT gate is one of three basic logic gates from which any Boolean circuit may be built up. Together with the AND gate and the OR gate, any function
Inverter_(logic_gate)
Digital logic gate type
gate, the OR gate is one of three basic logic gates from which any Boolean circuit may be constructed. All other logic gates may be made from these three
OR_gate
(FHEW) scheme for Boolean circuit evaluation with optimizations Chillotti-Gama-Georgieva-Izabachene (TFHE) scheme for Boolean circuit evaluation with extensions
PALISADE_(software)
Type of geometry processing
Boolean operations on polygons are a set of Boolean operations (AND, OR, NOT, XOR, ...) operating on one or more sets of polygons in computer graphics
Boolean operations on polygons
Boolean_operations_on_polygons
Electrical circuit with active components
binary '0'. Digital circuits make extensive use of transistors, interconnected to create logic gates that provide the functions of Boolean logic: AND, NAND
Electronic_circuit
Standard forms of Boolean functions
simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.
Canonical_normal_form
Cryptographic primitive
proofs is relatively small; however, transforming a statement into a boolean circuit incurs considerable overhead. Proof systems under the sub-group hiding
Non-interactive zero-knowledge proof
Non-interactive_zero-knowledge_proof
Inherent difficulty of computational problems
based on non-deterministic Turing machines, Boolean circuits, quantum Turing machines, monotone circuits, etc. The resource (or resources) that is being
Computational complexity theory
Computational_complexity_theory
Computing by new or unusual methods
billiard balls to perform computations. In this model, the wires of a Boolean circuit are represented by paths for the balls to travel on, the presence or
Unconventional_computing
Subject field of Boolean algebra discussing changes of Boolean variables and functions
Boolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of Boolean algebra discussing changes of Boolean
Boolean_differential_calculus
Type of conservative logic circuit
processes in physics. This model can be used to simulate Boolean circuits in which the wires of the circuit correspond to paths on which one of the balls may
Billiard-ball_computer
, there is a Boolean circuit of size polynomial in n {\displaystyle n} that implements a verifier for the problem. That is, the circuit computes a function
NP/poly
Unproven computational hardness assumption
by Impagliazzo & Paturi (1999). It states that satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved in subexponential time, 2 o ( n ) {\displaystyle
Exponential_time_hypothesis
Computer science concept
_{2}^{\mathrm {P} }} is circuit minimization: given a number k and a circuit A computing a Boolean function f, determine if there is a circuit with at most k gates
Polynomial_hierarchy
Formal language concept
( ℓ ) ) {\displaystyle O(\ell ^{2}\log(\ell ))} , and by a uniform Boolean circuit of depth O ( log ℓ ) {\displaystyle O(\log \ell )} . For two nondeterministic
Nested_word
Boolean circuit on which the key generation algorithm would be applied. The key generation algorithm runs Yao's garbling procedure over this Boolean circuit
Verifiable_computing
circuit complexity, TC (Threshold Circuit) is a complexity class of decision problems that can be recognized by threshold circuits, which are Boolean
TC_(complexity)
Electronic circuits that utilize digital signals
are often packaged into integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions. The binary number
Digital_electronics
Class of problems solvable in polynomial time
uniform family of Boolean circuits. A language L is in P if and only if there exists a polynomial-time uniform family of Boolean circuits { C n : n ∈ N }
P_(complexity)
Set of problems solved by small circuits
description of a Boolean circuit having n inputs, and that a Turing Machine for the language merely evaluates the given Boolean circuit on inputs of length
P/poly
Cryptographical test for pseudo-randomness
collection C = { C k } {\displaystyle C=\{C_{k}\}} is a collection of boolean circuits of size less than P C ( k ) {\displaystyle P_{C}(k)} . Let p k , S
Yao's_test
Swedish computer scientist
bounds on the size of constant-depth Boolean circuits for the parity function. After Andrew Yao proved that such circuits require exponential size, Håstad
Johan_Håstad
Topics referred to by the same term
Short-circuit evaluation, a form of Boolean evaluation in programming Short-circuit test Short (disambiguation) Circuit (disambiguation) Open circuit (disambiguation)
Short circuit (disambiguation)
Short_circuit_(disambiguation)
Concept in mathematical logic
In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic
Boolean_domain
Master's thesis by C. E. Shannon
arrangements of relays to solve Boolean algebra problems. His thesis laid the foundations for all digital computing and digital circuits. The utilization of the
A Symbolic Analysis of Relay and Switching Circuits
A_Symbolic_Analysis_of_Relay_and_Switching_Circuits
Logic constructed only from NAND gates
NAND(x,x). In the field of digital electronic circuits, this implies that it is possible to implement any Boolean function using just NAND gates. The mathematical
NAND_logic
Form of encryption that allows computation on ciphertexts
encrypted data. The computations are represented as either Boolean or arithmetic circuits. Some common types of homomorphic encryption are partially homomorphic
Homomorphic_encryption
In circuit complexity, AC is a complexity class hierarchy. Each class, ACi, consists of the languages recognized by Boolean circuits with depth O ( log
AC_(complexity)
Collection of molecular regulators
the functionalities of feedback circuits is determinant for the attractors' number and size in pathway-like Boolean networks". Scientific Reports. 7
Gene_regulatory_network
Type of cryptographic software obfuscation
the following two statements: Completeness or Functionality: For any Boolean circuit C of input length n and input x ∈ { 0 , 1 } n {\displaystyle x\in \{0
Indistinguishability obfuscation
Indistinguishability_obfuscation
simple circuit like this can be used: In digital electronics a diode-OR circuit is used to derive a simple Boolean logic function. This kind of circuit was
Diode-or_circuit
Graphical method to simplify Boolean expressions
Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 as
Karnaugh_map
Determining all voltages and currents within an electrical network
analysed using Boolean algebra by assigning the two states ("on"/"off", "positive"/"negative" or whatever states are being used) to the Boolean constants "0"
Network analysis (electrical circuits)
Network_analysis_(electrical_circuits)
Logical gate whose output is false if all its inputs are true
NOR logic. Boolean algebra Flash memory Functional completeness Logic gate symbols NAND logic Sheffer stroke Smith, J.S. "Digital circuits, sizing, output
NAND_gate
results, so-called circuit lower bounds, can be proved. Informally, ACC0 models the class of computations realised by Boolean circuits of constant depth
ACC0
Class in computational complexity theory
_{m}^{{\mathsf {NC}}^{k}}L'} if and only if there exists a L-uniform NCk Boolean circuit family that together computes a function f : { 0 , 1 } ∗ → { 0 , 1
P-complete
Russian mathematician
Prize (1990) for introducing the "approximation method" in proving Boolean circuit lower bounds of some essential algorithmic problems, Erdős Lecturer
Alexander_Razborov
Pair of logical equivalences
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid
De_Morgan's_laws
Provides lower bounds on the circuit complexity of boolean functions
lower bounds on the circuit complexity of boolean functions. A natural proof shows, either directly or indirectly, that a boolean function has a certain
Natural_proof
Complexity class
polynomial-time reduction to the PIGEON problem, defined as follows: Given a Boolean circuit C {\displaystyle C} having the same number n {\displaystyle n} of input
PPP_(complexity)
Sequence in computer science
parallel prefix sum algorithms was in the design of binary adders, Boolean circuits that can add two n-bit binary numbers. In this application, the sequence
Prefix_sum
1969 non-fiction book by G. Spencer-Brown
Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean
Laws_of_Form
Soviet and Russian mathematician
Russia for a generalization of finite-state automata, Boolean circuits and multi-valued logic circuits. Yablonsky is credited for helping to overcome the
Sergey_Yablonsky
American mathematician
the Karp–Lipton theorem (which proves that if SAT can be solved by Boolean circuits with a polynomial number of logic gates, then the polynomial hierarchy
Richard_M._Karp
Logical connective OR
will come.' Affirming a disjunct Boolean algebra (logic) Boolean algebra topics Boolean domain Boolean function Boolean-valued function Conjunction/disjunction
Logical_disjunction
2D cellular automaton similar to Conway's Game of Life
simulate arbitrary Boolean circuits: the presence or absence of a ladder in a certain position may be used to represent a Boolean signal, and different
Life_without_Death
Class of problems in computer science
includes uniform TC0, the class of constant-depth, unbounded-fan-in boolean circuits with majority gates that are uniform (generated by a polynomial-time
PP_(complexity)
Algorithm that outputs all solutions to a problem
disjunctive normal form, a binary decision diagram such as an OBDD, or a Boolean circuit in restricted classes studied in knowledge compilation, e.g., NNF.
Enumeration_algorithm
graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic graph
Propositional directed acyclic graph
Propositional_directed_acyclic_graph
Models replicating electronic behavior
use the actual transistor topology of the integrated circuit, and finally, with inline Boolean logic expressions. Exact representations are used mainly
Electronic_circuit_simulation
Electrically operated switch
of Boolean algebra to relay circuit design in A Symbolic Analysis of Relay and Switching Circuits. Relays can perform the basic operations of Boolean combinatorial
Relay
1991 Anna Gal (Chicago) "Lower bounds for the complexity of reliable Boolean circuits with noisy gates" Jaikumar Radhakrishnan (Rutgers) "Better Bounds for
Machtey_Award
BOOLEAN CIRCUIT
BOOLEAN CIRCUIT
Boy/Male
American, British, English
Lives at the Buck Meadow
Boy/Male
Irish
Puppy.
Surname or Lastname
Irish
Irish : Anglicized form of Gaelic Ó Baoighealláin. It was the name of a sept of Dartry, County Monaghan.English : variant of Boyland.
Boy/Male
English American German
Cuts the nap of woolen cloth. 'Shireman' In medieval times the shireman served as governor-judge...
Surname or Lastname
Czech
Czech : from a pet form of the personal names Boleslav or Bolebor.Polish (Boleń) : from a pet form of the personal name Bolesław.Variant spelling of German Bohlen.Swedish (Bolén) : ornamental name composed of an unexplained first element + the common surname suffix -én, a derivative of Latin -enius ‘descendant of’.English : variant of Bullen.
Boy/Male
Indian, Punjabi, Sikh
God's Spoken Word
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Telugu, Traditional
Flowering
Surname or Lastname
English
English : variant of Bullen.
Girl/Female
Tamil
Foolan | பூலந, பூலà®
Flowering, Blooming, Flower
Foolan | பூலந, பூலà®
Surname or Lastname
English
English : possibly a variant of Woolen.
Surname or Lastname
English
English : variant of Bowerman.
Surname or Lastname
English
English : variant of Boland.Irish : Anglicized form of Gaelic Ó Beólláin, ‘descendant of Bjolan’, a Norse personal name.
Girl/Female
Indian
Flowering, Blooming, Flower
Surname or Lastname
English
English : variant spelling of Woolen.
Surname or Lastname
English
English : variant of Wool.Americanized form of Jewish Wollman or German Wollmann (see Wollman).
Surname or Lastname
English
English : variant of Bullen.
Surname or Lastname
English
English : habitational name from places in Devon and Norfolk named Boyland. The Norfolk place name is derived from the Old English personal name Boia + lund ‘grove’ (Old Norse lundr).Irish : variant of Boylan.
Surname or Lastname
English
English : topographic name for someone who lived on a curved or irregularly shaped piece of land, from Old English wÅh ‘curved’, ‘crooked’ + land ‘land’, ‘estate’, or a habitational name from Woolland in Dorset, named from an Old English winn, wynn ‘meadow’, ‘pasture’ + land ‘land’, ‘estate’.
Surname or Lastname
English
English : metonymic occupational name for a maker and seller of woolen cloth, from Old French drap ‘cloth’.
Surname or Lastname
North German form of Fries 1.Dutch
North German form of Fries 1.Dutch : variant of Frese.English : metonymic occupational name for a weaver of frieze, a coarse woolen cloth with a thick nap, Old French frise.
BOOLEAN CIRCUIT
BOOLEAN CIRCUIT
Boy/Male
British, English
From the Deer Spring
Boy/Male
Indian
Lord Vinayaka
Boy/Male
Hindu, Indian
Lord Shiva
Girl/Female
Arabic, French, Indian, Muslim
Arabian Jasmine
Girl/Female
Arabic, Chinese
Protected
Surname or Lastname
English
English : topographic name from Old French plasquet, a diminutive of plascq ‘damp meadow’.
Boy/Male
Indian
Blood, Old Arabic name
Girl/Female
American, British, English, Greek, Latin
Divine
Female
Spanish
Feminine form of Spanish Manuel, MANUELA means "God is with us."
Girl/Female
Sikh
Body, Elder sister
BOOLEAN CIRCUIT
BOOLEAN CIRCUIT
BOOLEAN CIRCUIT
BOOLEAN CIRCUIT
BOOLEAN CIRCUIT
n.
A kind of woolen.
a.
Made of wool; consisting of wool; as, woolen goods.
n.
A studious man; a scholar.
a.
Swollen; puffed out.
n.
A woolen stuff thinner than ratteen.
n.
One who deals in wool.
n.
A soft and delicate woolen, or woolen and silk, fabric, for ladies' dresses.
a.
Alt. of Bollen
n.
A kind of woolen cloth.
a.
Of or pertaining to wool or woolen cloths; as, woolen manufactures; a woolen mill; a woolen draper.
a.
Having the characteristic of Zoilus, a bitter, envious, unjust critic, who lived about 270 years before Christ.
n.
A kind of woolen cloth; tammy.
n.
Cloth, or woolen stuffs in general.
a.
Of or pertaining to Sir Thomas Bodley, or to the celebrated library at Oxford, founded by him in the sixteenth century.
n.
A kind of woolen stuff.
a.
See Boln, a.
pl.
of Woolman
pl.
of Bookman
n.
Cloth made of wool; woollen goods.