In the 17th century, Gottfried Leibniz imagined and described the characteristica universalis, a universal and formal language which utilised pictographs. Later, Carl … 展开

A formal language L over an alphabet Σ is a subset of Σ , that is, a set of words over that alphabet. Sometimes the sets of words are grouped into expressions, whereas rules and … 展开

Formal languages are used as tools in multiple disciplines. However, formal language theory rarely concerns itself with particular languages … 展开

Certain operations on languages are common. This includes the standard set operations, such as union, intersection, and complement. Another class of operation is the element-wise application of string operations.
Examples: suppose 展开

An alphabet, in the context of formal languages, can be any set; its elements are called letters. An alphabet may contain an infinite number of elements; however, most definitions in formal … 展开

The following rules describe a formal language L over the alphabet Σ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, =}:
• Every nonempty string that does not contain "+" or "=" and does not start with "0" is in L.
• The string … 展开

Programming languages
A compiler usually has two distinct components. A lexical analyzer, sometimes generated by a … 展开