mathematics

Representation in mathematics

Semigroups "A semigroup is defined to be set equipped with an associative binary operation. A good example of a semigroup is provided by the set of all binary strings; any two such strings can be composed by concatenation to form a third binary string, an operation which is clearly associative. This example also illustrates an important feature of modern semigroup theory. Binary strings form the input to computers: any program can be regarded as an, albeit extremely lengthy, binary string. The collection of all syntactically correct programs is then a subset of the set of all binary strings. In mathematical terms, the semigroup of all binary strings is the free semigroup on two generators, subsets of the free monoid are languages, and the computer is an example of a finite state machine. The relationship between semigroups, languages and automata is one of the most important aspects of contemporary semigroup theory."

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Created 20/9/98