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The top left graph is linear in the X- and Y-axes, and the Y-axis ranges from 0 to 10. A base-10 log scale is used for the Y-axis of the bottom left graph, and the Y-axis ranges from 0.1 to 1000. The top right graph uses a log-10 scale for just the X-axis, and the bottom right graph uses a log-10 scale for both the X axis and the Y-axis.
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 ...
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 ...
NL is a generalization of L, the class for logspace problems on a deterministic Turing machine. Since any deterministic Turing machine is also a nondeterministic Turing machine, we have that L is contained in NL. NL can be formally defined in terms of the computational resource nondeterministic space (or NSPACE) as NL = NSPACE(log n).
The logarithmic scale is usually labeled in base 10; occasionally in base 2: = ( ()) + (). A log–linear (sometimes log–lin) plot has the logarithmic scale on the y-axis, and a linear scale on the x-axis; a linear–log (sometimes lin–log) is the opposite.
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.
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Logspace hierarchy [ edit ] As a corollary, in the same article, Immerman proved that, using descriptive complexity 's equality between NL and FO(Transitive Closure) , the logarithmic hierarchy, i.e. the languages decided by an alternating Turing machine in logarithmic space with a bounded number of alternations, is the same class as NL.