Theory: Difference between revisions

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==Formal Languages==
==Formal Languages==
===Regular Languages (Class [http://qwiki.stanford.edu/wiki/Complexity_Zoo:R#reg REG])===
===Regular Languages (Class [http://qwiki.stanford.edu/wiki/Complexity_Zoo:R#reg REG])===
* 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, right-quotient, homomorphism
* Closed under union, concatenation, Kleene, intersection, difference, complement, reverse, right-quotient, homomorphism
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===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
* Recognized by nondeterministic pushdown automata
* Recognized by nondeterministic pushdown automata
** Deterministic pushdown automata cannot recognize all CFL's!
** Deterministic pushdown automata cannot recognize all CFL's!
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* LR(''n'') (Knuth, 1965):
* LR(''n'') (Knuth, 1965):
===Context-Sensitive Languages===
===Context-Sensitive Languages===
* Type 1 of the Chomsky Hierarchy, a proper superset of CFL's
* Type 1 of the [[Chomsky Hierarchy]], a proper superset of CFL's
* Recognized by linear bounded automata
* Recognized by linear bounded automata
===Recursively-Enumerable Languages (Class [http://qwiki.stanford.edu/wiki/Complexity_Zoo:R#re RE])===
===Recursively-Enumerable Languages (Class [http://qwiki.stanford.edu/wiki/Complexity_Zoo:R#re RE])===
* Type 0 of the Chomsky Hierarchy, a proper superset of CSL's
* Type 0 of the [[Chomsky Hierarchy]], a proper superset of CSL's
* Recognized by Turing Machines
* Recognized by [[Turing Machines]]
===Recursive Languages (Class [http://qwiki.stanford.edu/wiki/Complexity_Zoo:R#r R])===
* Decided by [[Turing Machines]]


[[Category: CS GRE Prep]]
[[Category: CS GRE Prep]]