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Pairing, sometimes known as bonding, is a process used in computer networking that helps set up an initial linkage between computing devices to allow communications between them. The most common example is used in Bluetooth , [ 1 ] where the pairing process is used to link devices like a Bluetooth headset with a mobile phone .
PC—Personal Computer; PCB—Printed Circuit Board; PCB—Process Control Block; PC DOS—Personal Computer Disc Operating System; PCI—Peripheral Component Interconnect; PCIe—PCI Express; PCI-X—PCI Extended; PCL—Printer Command Language; PCMCIA—Personal Computer Memory Card International Association; PCM—Pulse-Code Modulation
After time t, thread 1 reaches barrier3 but it will have to wait for threads 2 and 3 and the correct data again. Thus, in barrier synchronization of multiple threads there will always be a few threads that will end up waiting for other threads as in the above example thread 1 keeps waiting for thread 2 and 3.
A pairing can be nondegenerate without being a perfect pairing, for instance Z × Z → Z via (x, y) ↦ 2xy is nondegenerate, but induces multiplication by 2 on the map Z → Z ∗. Terminology varies in coverage of bilinear forms. For example, F. Reese Harvey discusses "eight types of inner product". [6]
In most cases, a single input parameter or an interaction between two parameters is what causes a program's bugs. [2] Bugs involving interactions between three or more parameters are both progressively less common [3] and also progressively more expensive to find, such testing has as its limit the testing of all possible inputs. [4]
For example, in representation theory, one has a scalar product on the characters of complex representations of a finite group which is frequently called character pairing. See also [ edit ]
In 1990, Regan proposed the first known pairing function that is computable in linear time and with constant space (as the previously known examples can only be computed in linear time if multiplication can be too, which is doubtful). In fact, both this pairing function and its inverse can be computed with finite-state transducers that run in ...
The case n = 2 is the axiom of pairing with A = A 1 and B = A 2. The cases n > 2 can be proved using the axiom of pairing and the axiom of union multiple times. For example, to prove the case n = 3, use the axiom of pairing three times, to produce the pair {A 1,A 2}, the singleton {A 3}, and then the pair {{A 1,A 2},{A 3}}.