Examples of using Boolean circuits in English and their translations into Portuguese
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The classes AC andNC are defined using Boolean circuits.
Boolean circuits are defined in terms of the logic gates they contain.
Complexity classes defined in terms of Boolean circuits include AC0, AC, TC0 and NC.
Boolean circuits, however, only allow a fixed number of input bits.
The aim of this project is to study average-case lower bounds in restricted classes of Boolean circuits, such as monotone….
Boolean circuits are also used as a formal model for combinational logic in digital electronics.
A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length.
A common basis for Boolean circuits is the set{AND, OR, NOT}, which is functionally complete, i. e. from which all other Boolean functions can be constructed.
He did important early work on parallel algorithms for prefix sums andtheir application in the design of Boolean circuits for addition.
Boolean circuits provide a model for many digital components used in computer engineering, including multiplexers, adders, and arithmetic logic units.
NC is defined to be the set of Boolean functions that can be decided by uniform Boolean circuits of polynomial size and polylogarithmic depth.
In giving a formal definition of Boolean circuits, Vollmer starts by defining a basis as set B of Boolean functions, corresponding to the gates allowable in the circuit model.
Adleman's theorem states that membership in any language in BPP can be determined by a family of polynomial-size Boolean circuits, which means BPP is contained in P/poly.
Several important complexity measures can be defined on Boolean circuits, including circuit depth,circuit size, and number of alternations between AND gates and OR gates.
In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of Boolean circuits that compute them.
An individual computational problem is thus associated with a particular"family" of Boolean circuits formula_21 where each formula_15 is the circuit handling inputs of"n" bits.
Boolean circuits are one of the prime examples of so-called non-uniform models of computation in the sense that inputs of different lengths are processed by different circuits, in contrast with uniform models such as Turing machines where the same computational device is used for all possible input lengths.
An individual computational problem is thus associated with a particular family of Boolean circuits C 1, C 2,…{\displaystyle C_{1}, C_{2},\dots} where each C n{\displaystyle C_{n}} is the circuit handling inputs of n bits.
The model of computation: The most common model of computation is the deterministic Turing machine, butmany complexity classes are based on nondeterministic Turing machines, boolean circuits, quantum Turing machines, monotone circuits, etc.
Informally, ACC0 models the class of computations realised by Boolean circuits of constant depth and polynomial size, where the circuit gates includes"modular counting gates" that compute the number of true inputs modulo some fixed constant.
Other important complexity classes include BPP, ZPP and RP, which are defined using probabilistic Turing machines; AC and NC,which are defined using boolean circuits and BQP and QMA, which are defined using quantum Turing machines.
NCi is the class of decision problems decidable by uniform boolean circuits with a polynomial number of gates of at most two inputs and depth O(logi n), or the class of decision problems solvable in time O(logi n) on a parallel computer with a polynomial number of processors.
The model of computation: The most common model of computation is the deterministic Turing machine, butmany complexity classes are based on non-deterministic Turing machines, Boolean circuits, quantum Turing machines, monotone circuits, etc.
In 1980, along with Richard J. Lipton, Karp proved 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 collapses to its second level.
Other important complexity classes include BPP, ZPP and RP, which are defined using probabilistic Turing machines; AC and NC,which are defined using Boolean circuits; and BQP and QMA, which are defined using quantum Turing machines. P is an important complexity class of counting problems not decision problems.
Thus no single Boolean circuit is capable of deciding such a language.
One speaks of the circuit complexity of a Boolean circuit.
A Boolean circuit over a basis B, with n inputs and m outputs, is then defined as a finite directed acyclic graph.
In 2000, Gajardo et al. showed a construction that calculates any boolean circuit using the trajectory of a single instance of Langton's ant.