There is an extended grammar notation in common use. In this notation, square and curly braces in…

Need your ASSIGNMENT done? Use our paper writing service to score better and meet your deadline.


Order a Similar Paper Order a Different Paper

There is an extended grammar notation in common use. In this notation, square and curly braces in production bodies are meta symbols (like → or |) with the following meanings:

i) Square braces around a grammar symbol or symbols denotes that these constructs are optional. Thus, production A→ X [Y] Z has the same effect as the two productions A → X Y Z and A →X Z.

ii) Curly braces around a grammar symbol or symbols says that these symbols may be repeated any number of times, including zero times. Thus, A → X {Y Z) has the same effect as the infinite sequence of productions A→X, A→X Y Z, A→X Y Z Y Z, and so on.

Show that these two extensions do not add power to grammars; that is, any language that can be generated by a grammar with these extensions can be generated by a grammar without the extensions.