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- Circuit_complexity abstract "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. One speaks of the circuit complexity of a Boolean circuit. A related notion is the circuit complexity of a recursive language that is decided by a family of circuits (see below).A Boolean circuit with input bits is a directed acyclic graph in which every node (usually called gates in this context) is either an input node of in-degree 0 labeled by one of the input bits, an AND gate, an OR or a NOT gate. One of these gates is designated as the output gate. Such a circuit naturally computes a function of its inputs. The size of a circuit is the number of gates it contains and its depth is the maximal length of a path from an input gate to the output gate.There are two major notions of circuit complexity (these are outlined in Sipser (1997)). The circuit-size complexity of a Boolean function is the minimal size of any circuit computing . The circuit-depth complexity of a Boolean function is the minimal depth of any circuit computing .These notions generalize when one considers the circuit complexity of a recursive language: A formal language may contain strings with many different bit lengths. Boolean circuits, however, only allow a fixed number of input bits. Thus no single Boolean circuit is capable of deciding such a language. To account for this possibility, one considers families of circuits where each accepts inputs of size . Each circuit family will naturally generate a recursive language by outputting when a string is a member of the family, and otherwise. We say that a family of circuits is size minimal if there is no other family that decides on inputs of any size, , with a circuit of smaller size than (respectively for depth minimal families).Hence, the circuit-size complexity of a recursive language is defined as the function , that relates a bit length of an input, , to the circuit-size complexity of a minimal circuit that decides whether inputs of that length are in . The circuit-depth complexity is defined similarly.Complexity classes defined in terms of Boolean circuits include AC0, AC, TC0 and NC.".
- Circuit_complexity wikiPageExternalLink The_Complexity_of_Boolean_Functions.
- Circuit_complexity wikiPageExternalLink fsttcs.96.slides.ps.
- Circuit_complexity wikiPageExternalLink fsttcs.pdf.
- Circuit_complexity wikiPageExternalLink scribe-boolean.html.
- Circuit_complexity wikiPageID "7641969".
- Circuit_complexity wikiPageRevisionID "604665868".
- Circuit_complexity b "2".
- Circuit_complexity hasPhotoCollection Circuit_complexity.
- Circuit_complexity p "P".
- Circuit_complexity subject Category:Circuit_complexity.
- Circuit_complexity subject Category:Computational_complexity_theory.
- Circuit_complexity comment "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. One speaks of the circuit complexity of a Boolean circuit.".
- Circuit_complexity label "Circuit complexity".
- Circuit_complexity label "Complessità dei circuiti".
- Circuit_complexity label "回路計算量".
- Circuit_complexity label "电路复杂性".
- Circuit_complexity sameAs Complessità_dei_circuiti.
- Circuit_complexity sameAs 回路計算量.
- Circuit_complexity sameAs m.0267lqh.
- Circuit_complexity sameAs Q1055112.
- Circuit_complexity sameAs Q1055112.
- Circuit_complexity wasDerivedFrom Circuit_complexity?oldid=604665868.
- Circuit_complexity isPrimaryTopicOf Circuit_complexity.