Examples
While computing the star height of a regular expression is easy, determining the star height of a language can be sometimes tricky. For illustration, the regular expression
over the alphabet A = {a,b} has star height 2. However, the described language is just the set of all words ending in an a: thus the language can also be described by the expression
which is only of star height 1. To prove that this language indeed has star height 1, one still needs to rule out that it could be described by a regular expression of lower star height. For our example, this can be done by an indirect proof: One proves that a language of star height 0 contains only finitely many words. Since the language under consideration is infinite, it cannot be of star height 0.
The star height of a group language is computable: for example, the star height of the language over {a,b} in which the number of occurrences of a and b are congruent modulo 2n is n.
Read more about this topic: Star Height
Famous quotes containing the word examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)