Editing Automata theory (section)

== Applications ==
Each model in automata theory plays important roles in several applied areas. [[Finite automata]] are used in [[text processing]], compilers, and [[hardware design]]. [[Context-free grammar]] (CFGs) are used in [[programming language specification|programming language]]s and artificial intelligence. Originally, CFGs were used in the study of [[natural language|human language]]s. [[Cellular automata]] are used in the field of [[artificial life]], the most famous example being [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]]. Some other examples which could be explained using automata theory in biology include mollusk and pine cone growth and pigmentation patterns. Going further, a theory suggesting that the whole universe is computed by some sort of a discrete automaton, is advocated by some scientists. The idea originated in the work of [[Konrad Zuse]], and was popularized in America by [[Edward Fredkin]]. Automata also appear in the theory of [[finite field]]s: the set of [[irreducible polynomial]]s that can be written as composition of degree two polynomials is in fact a regular language.<ref>{{Citation
  | last1 = Ferraguti
  | first1 = A.
  | last2 = Micheli
  | first2 = G.
  | last3 = Schnyder
  | first3 = R.
  | title = Irreducible compositions of degree two polynomials over finite fields have regular structure
  | volume = 69
  | issue = 3
  | pages = 1089–1099
  | series = The Quarterly Journal of Mathematics
  | publisher = Oxford University Press
  | doi = 10.1093/qmath/hay015
  | year = 2018
  | arxiv = 1701.06040
  | s2cid = 3962424
 }}</ref>
Another problem for which automata can be used is the [[induction of regular languages]].