Rational language
Encyclopedia
In computer science rational languages are a category of formal language
s. They are defined as the set of strings for which some rational series assigns non-zero values (also known as that series' support
). When the semiring
of the rational series is boolean
, the associated rational languages are simply the regular language
s.
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
s. They are defined as the set of strings for which some rational series assigns non-zero values (also known as that series' support
Support (mathematics)
In mathematics, the support of a function is the set of points where the function is not zero, or the closure of that set . This concept is used very widely in mathematical analysis...
). When the semiring
Semiring
In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse...
of the rational series is boolean
Boolean logic
Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...
, the associated rational languages are simply the regular language
Regular language
In theoretical computer science and formal language theory, a regular language is a formal language that can be expressed using regular expression....
s.