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In other words, a problem with input size n is in NC if there exist constants c and k such that it can be solved in time O((log n) c) using O(n k) parallel processors. Stephen Cook [ 1 ] [ 2 ] coined the name "Nick's class" after Nick Pippenger , who had done extensive research [ 3 ] on circuits with polylogarithmic depth and polynomial size.
To show that NL is contained in C, we simply take an NL algorithm and choose a random computation path of length n, and execute this 2 n times. Because no computation path exceeds length n, and because there are 2 n computation paths in all, we have a good chance of hitting the accepting one (bounded below by a constant).
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 ...
For example, the amount of time it takes to solve problems in the complexity class P grows at a polynomial rate as the input size increases, which is comparatively slow compared to problems in the exponential complexity class EXPTIME (or more accurately, for problems in EXPTIME that are outside of P, since ).
In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space. The NL-complete languages are the most "difficult" or "expressive" problems in NL.
The analysis of the former and the latter algorithm shows that it takes at most log 2 n and n check steps, respectively, for a list of size n. In the depicted example list of size 33, searching for "Morin, Arthur" takes 5 and 28 steps with binary (shown in cyan) and linear (magenta) search, respectively. Graphs of functions commonly used in the ...
Created independently in 1977 by W. Eddy and in 1978 by A. Bykat. Just like the quicksort algorithm, it has the expected time complexity of O(n log n), but may degenerate to O(n 2) in the worst case. Divide and conquer, a.k.a. merge hull — O(n log n) Another O(n log n) algorithm, published in 1977 by Preparata and Hong. This algorithm is also ...
A single-tape deterministic Turing machine can solve the problem, for n elements of m ≥ log n bits each, in time O(n 2 m(m+2–log n)), while on a nondeterministic machine the time complexity is O(nm(n + log m)). [6]