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as to what sort of transformation rules could be used, Chomsky was able to define four strictly nested transformational grammars, which he numbered from 0 to 3. As the grammar number increases, the generated language becomes simpler. As the grammar number decreases, parsing a sentence in that language becomes more difficult.
 
as to what sort of transformation rules could be used, Chomsky was able to define four strictly nested transformational grammars, which he numbered from 0 to 3. As the grammar number increases, the generated language becomes simpler. As the grammar number decreases, parsing a sentence in that language becomes more difficult.
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Other linguists have described formal grammars which fit in between the various Chomsky levels. This lecture
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Other linguists have described formal grammars which fit in between the various Chomsky levels.  
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<ref>{{cite web
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| url = http://www.google.co.uk/url?sa=t&rct=j&q=recursively+enumerable+languages+examples&source=web&cd=4&ved=0CF4QFjAD&url=http%3A%2F%2Fwww.cs.colostate.edu%2F~massey%2FTeaching%2Fcs301%2FRestrictedAccess%2FSlides%2F301lecture23.pdf&ei=6qelT4KMA6SA0AXIu7CQBA&usg=AFQjCNG3fc1mD7g5f-14vfDPdvyX2uScDg
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| title = Recursive and Recursively Enumerable Languages
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| accessdate = 2012-05-05
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}}</ref>
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shows that there exist languages which can not be described by any set of rules.
      
The following table provides a summary, which is then explained further in the subsequent subsections.
 
The following table provides a summary, which is then explained further in the subsequent subsections.
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