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The π-calculus belongs to the family of process calculi, mathematical formalisms for describing and analyzing properties of concurrent computation.In fact, the π-calculus, like the λ-calculus, is so minimal that it does not contain primitives such as numbers, booleans, data structures, variables, functions, or even the usual control flow statements (such as if-then-else, while).
The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π . However, it has some drawbacks (for example, it is computer memory -intensive) and therefore all record-breaking calculations for many years have used other ...
The search procedure consists of choosing a range of parameter values for s, b, and m, evaluating the sums out to many digits, and then using an integer relation-finding algorithm (typically Helaman Ferguson's PSLQ algorithm) to find a sequence A that adds up those intermediate sums to a well-known constant or perhaps to zero.
In computer science, communicating sequential processes (CSP) is a formal language for describing patterns of interaction in concurrent systems. [1] It is a member of the family of mathematical theories of concurrency known as process algebras, or process calculi, based on message passing via channels.
Once the message has been sent, becomes the process , while () becomes the process [/], which is with the place-holder substituted by , the data received on . The class of processes that P {\displaystyle {\mathit {P}}} is allowed to range over as the continuation of the output operation substantially influences the properties of the calculus.
The algorithm uses a message called probe(i,j,k) to transfer a message from controller of process P j to controller of process P k. It specifies a message started by process P i to find whether a deadlock has occurred or not. Every process P j maintains a boolean array dependent which contains the information about the processes that depend on ...
Borwein's algorithm was devised by Jonathan and Peter Borwein to calculate the value of /. This and other algorithms can be found in the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity .