Q4real09sol

# Q4real09sol - CSE303 Q4 SOLUTIONS Summer 2009 YES/NO...

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Q4 SOLUTIONS Summer 2009 YES/NO questions 1. The set of terminals is always non- empty Justify : Finite set can be empty n 2. L ( G ) = { w V : S * G w } Justify : w Σ * n 3. Any regular language is context-free Justify : 1. Any Finite Automata is a PDF automata 2.Regular languages are generated by regular grammars, that are also CF. y 4. Language is regular if and only if is generated by a regular grammar (right- linear) Justify : proof in class y 5. The stack alphabet of a pushdown automaton is always non- empty Justify : ﬁnite set can be empty n 6. Δ ( K × Σ * × Γ * ) × ( K × Γ * is a transition relation of a pushdown automaton (lecture deﬁnition) Justify : Δ must be ﬁnite n 7. L ( M ) = { w Σ * : ( s,w,e ) | = * M ( f,e,e ) } Justify : f F n 8. Any regular language is accepted by a pushdown automaton Justify : Any ﬁnite automata is a pushdown automata operating on an empty stock. y 9. Context-free languages are closed under intersection Justify : Take L 1 = a n b n c m ,L 2 = a m b n c n , both CF and we get that L 1 L 2 = a n b n c n is not CF n 10. The union of a context-free language and regular language is a context- free language Justify : regular language is also a context free language and context free languages are closed under union y PROBLEMS QUESTION 1 Consider a grammar G = ( V, Σ ,R,S ), where V = { a,b,S,A

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## This note was uploaded on 06/03/2011 for the course CSE 303 taught by Professor Ko,k during the Spring '08 term at SUNY Stony Brook.

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Q4real09sol - CSE303 Q4 SOLUTIONS Summer 2009 YES/NO...

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