Complexity Results
In computational complexity theory, the complexity class of all regular languages is sometimes referred to as REGULAR or REG and equals DSPACE(O(1)), the decision problems that can be solved in constant space (the space used is independent of the input size). REGULAR ≠ AC0, since it (trivially) contains the parity problem of determining whether the number of 1 bits in the input is even or odd and this problem is not in AC0. On the other hand, REGULAR does not contain AC0, because the nonregular language of palindromes, or the nonregular language can both be recognized in AC0.
If a language is not regular, it requires a machine with at least Ω(log log n) space to recognize (where n is the input size). In other words, DSPACE(o(log log n)) equals the class of regular languages. In practice, most nonregular problems are solved by machines taking at least logarithmic space.
Read more about this topic: Regular Language
Famous quotes containing the words complexity and/or results:
“In times like ours, where the growing complexity of life leaves us barely the time to read the newspapers, where the map of Europe has endured profound rearrangements and is perhaps on the brink of enduring yet others, where so many threatening and new problems appear everywhere, you will admit it may be demanded of a writer that he be more than a fine wit who makes us forget in idle and byzantine discussions on the merits of pure form ...”
—Marcel Proust (1871–1922)
“Silence is to all creatures thus attacked the only means of salvation; it fatigues the Cossack charges of the envious, the enemy’s savage ruses; it results in a cruising and complete victory.”
—Honoré De Balzac (1799–1850)