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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 ...
Equally spaced values on a logarithmic scale have exponents that increment uniformly. Examples of equally spaced values are 10, 100, 1000, 10000, and 100000 (i.e., 10 1, 10 2, 10 3, 10 4, 10 5) and 2, 4, 8, 16, and 32 (i.e., 2 1, 2 2, 2 3, 2 4, 2 5). Exponential growth curves are often depicted on a logarithmic scale graph.
L or LOGSPACE is the set of problems that can be solved by a deterministic Turing machine using only () memory space with regards to input size. Even a single counter that can index the entire n {\displaystyle n} -bit input requires log n {\displaystyle \log n} space, so LOGSPACE algorithms can maintain only a constant number of counters ...
This was the strongest deterministic-space inclusion known in 1994 (Papadimitriou 1994 Problem 16.4.10, "Symmetric space"). Since larger space classes are not affected by quadratic increases, the nondeterministic and deterministic classes are known to be equal, so that for example we have PSPACE = NPSPACE.
If an NL-complete language X could belong to L, then so would every other language Y in NL.For, suppose (by NL-completeness) that there existed a deterministic logspace reduction r that maps an instance y of problem Y to an instance x of problem X, and also (by the assumption that X is in L) that there exists a deterministic logspace algorithm A for solving problem X.
In probability theory and computer science, a log probability is simply a logarithm of a probability. [1] The use of log probabilities means representing probabilities on a logarithmic scale (,], instead of the standard [,] unit interval.
In computational complexity theory, a log space transducer (LST) is a type of Turing machine used for log-space reductions. A log space transducer, , has three tapes: A read-only input tape. A read/write work tape (bounded to at most () symbols). A write-only, write-once output tape.
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 ]