P class

P class or Class P may refer to:

Computing

Ships and yachts

Railway locomotives

P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(n^O(1)), is one of the most fundamental complexity classes. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time.

Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable"; in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb.

Definition

A language L is in P if and only if there exists a deterministic Turing machine M, such that

P can also be viewed as a uniform family of boolean circuits. A language L is in P if and only if there exists a polynomial-time uniform family of boolean circuits , such that

For all , takes n bits as input and outputs 1 bit

For all x in L,

For all x not in L,

NZR P class (1885)

The P class was a class of steam locomotives built to haul freight trains on the national rail network of New Zealand. The class consisted of ten individual locomotives ordered from the British company of Nasmyth, Wilson and Company in 1885, but miscommunications about the weight limitations imposed on the locomotives meant they did not start work until 1887. This debacle came at a time when the New Zealand Railways Department (NZR) was suffering from a lack of motive power to work on its rapidly expanding network and was part of what prompted a shift towards American and home-grown manufacturers.

The classification of this class as "P" was the first example of the re-use of a classification that had previously been used for an earlier class. The members of the P class of 1876 had been sold to private companies or the Public Works Department, leaving the classification unused. The Railways Department chose to assign it to this class, setting a pattern that was followed with other classes in years to come, with the most prominent example being the A class of 1906 re-using the classification of the A class of 1873.