Theory: Difference between revisions
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* Type 3 of the Chomsky Hierarchy | * Type 3 of the Chomsky Hierarchy | ||
* Recognized by finite state machines. Equivalent to [http://qwiki.stanford.edu/wiki/Complexity_Zoo:D#dspace DSPACE(1)]. | * Recognized by finite state machines. Equivalent to [http://qwiki.stanford.edu/wiki/Complexity_Zoo:D#dspace DSPACE(1)]. | ||
* Closed under union, concatenation, Kleene, intersection, difference, complement, reverse | * Closed under union, concatenation, Kleene, intersection, difference, complement, reverse, right-quotient, homomorphism | ||
* Pumping lemma: A language '''L''' is regular if and only if there exists a positive integer ''m'' such that for any ''w'' ∈ '''L''' with |''w''| ≥ ''m'' there exist strings ''x'', ''y'' and ''z'' such that: | |||
** ''w'' = ''xyz'', | |||
** |''xy''| ≤ ''m'', | |||
** |''y''| ≥ 1, and | |||
** ''xy<sup>i</sup>z'' ∈ '''L''' for all ''i'' ≥ 0 | |||
===Context-Free Languages (CFLs) / Grammars (CFGs)=== | ===Context-Free Languages (CFLs) / Grammars (CFGs)=== | ||
* Type 2 of the Chomsky Hierarchy, a proper superset of RL's | * Type 2 of the Chomsky Hierarchy, a proper superset of RL's | ||