|
GapP
GapP is a counting complexity class, consisting of all of the functions ''f'' such that there exists a polynomial-time non-deterministic Turing machine ''M'' where, for any input ''x'', ''f(x)'' is equal to the number of accepting paths of ''M'' minus the number of rejecting paths of ''M''. GapP is exactly the closure of #P under subtraction. It also has all the other closure properties of #P, such as addition, multiplication, and binomial coefficients. The counting class AWPP is defined in terms of GapP functions. References * S. Fenner, L. Fortnow, and S. KurtzGap-definable counting classes ''Journal of Computer and System Sciences'' 48(1):116-148, 1994. * {{Comp-sci-theory-stub Complexity classes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counting Complexity Class
In computational complexity theory and computability theory, a counting problem is a type of computational problem. If ''R'' is a search problem then :c_R(x)=\vert\\vert \, is the corresponding counting function and :\#R=\ denotes the corresponding decision problem. Note that ''cR'' is a search problem while #''R'' is a decision problem, however ''cR'' can be ''C'' Cook-reduced to #''R'' (for appropriate ''C'') using a binary search (the reason #''R'' is defined the way it is, rather than being the graph of ''cR'', is to make this binary search possible). Counting complexity class If ''NX'' is a complexity class associated with non-deterministic machines then ''#X'' = is the set of counting problems associated with each search problem in ''NX''. In particular, #P is the class of counting problems associated with NP search problems. Just as NP has NP-complete problems via many-one reductions, #P has complete problems via parsimonious reductions, problem transformations t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almost Wide Probabilistic Polynomial-Time
In theoretical computer science, almost wide probabilistic polynomial-time (AWPP) is a complexity class contained in PP defined via GapP functions. The class often arises in the context of quantum computing. AWPP contains the complexity class BQP (bounded-error quantum polynomial time), which contains the decision problems solvable by a quantum computer in polynomial time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ..., with an error probability of at most 1/3 for all instances. In fact, it is the smallest classical complexity class that upper bounds BQP. Furthermore, it is contained in the APP class. References General * Provides information on the connection between various complexity classes. * Definition of AWPP and connection to APP and PP. * Proof of BPQ in AWPP. * " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-deterministic Turing Machine
In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is ''not'' completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine. NTMs are sometimes used in thought experiments to examine the abilities and limits of computers. One of the most important open problems in theoretical computer science is the P versus NP problem, which (among other equivalent formulations) concerns the question of how difficult it is to simulate nondeterministic computation with a deterministic computer. Background In essence, a Turing machine is imagined to be a simple computer that reads and writes symbols one at a time on an endless tape by strictly following a set of rules. It determines what action it should perform next according to its internal ''state'' and ''what symbol it curr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
