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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 ...
In computational complexity theory, a log-space computable function is a function : that requires only () memory to be computed (this restriction does not apply to the size of the output). The computation is generally done by means of a log-space transducer .
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 ...
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.
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 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 ]
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.
In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t connectivity), which is the problem of determining whether there exists a path between two vertices in an undirected graph, otherwise described as the problem of determining whether two vertices are in the same connected component.