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the logarithmic cost model, also called logarithmic-cost measurement (and similar variations), assigns a cost to every machine operation proportional to the number of bits involved The latter is more cumbersome to use, so it is only employed when necessary, for example in the analysis of arbitrary-precision arithmetic algorithms, like those ...
L is a subclass of NL, which is the class of languages decidable in logarithmic space on a nondeterministic Turing machine.A problem in NL may be transformed into a problem of reachability in a directed graph representing states and state transitions of the nondeterministic machine, and the logarithmic space bound implies that this graph has a polynomial number of vertices and edges, from ...
In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space. NL is a generalization of L, the class for logspace problems on a deterministic Turing machine.
For a precise definition of what it means to solve a problem using a given amount of time and space, a computational model such as the deterministic Turing machine is used. The time required by a deterministic Turing machine M {\displaystyle M} on input x {\displaystyle x} is the total number of state transitions, or steps, the machine makes ...
Here we consider operations over polynomials and n denotes their degree; for the coefficients we use a unit-cost model, ignoring the number of bits in a number. In ...
In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into the input, along with a logarithmic number of fixed-size integers . [ 1 ]
The space hierarchy theorem is stronger than the analogous time hierarchy theorems in several ways: It only requires s(n) to be at least log n instead of at least n. It can separate classes with any asymptotic difference, whereas the time hierarchy theorem requires them to be separated by a logarithmic factor.
SC is the class of problems solvable in polynomial time and polylogarithmic space on a deterministic Turing machine; in other words, this result shows that, given polylogarithmic space, a deterministic machine can simulate logarithmic space probabilistic algorithms. BPL is contained in NC and in L/poly.