13 H.W questions in Theory of Computing

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13 H.W questions in Theory of Computing. Questions are attached in file. ......................................................................

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HW4 1. (1 pt) Construct the complement FA of the following FA 2. (1 pt) Find the regular expression for the following TG 3. (1 pts) Build the intersection machine for the two following languages described by the two following FAs 4. (1 pt) Prove that the language L={anb2n} is non-regular. 5. Determine if the following words can be generated by the following CFG and if so draw the parse tree. (1 point) The CFG: S → aS | bS | a The words to consider are aaaa and aabb 6. What is the language generated by the following CFG ( 1 point) S → AA A → AAA A → bA | Ab | a 7. Find a CFG that generates the language of all words that have at least two a’s or at least three b’s. (1 point) 8. Show the following grammar is ambiguous by finding a word with two distinct parse trees. (1 point) S → aaS | aaaS | a 9. Draw the total language tree for the following CFG until we can be sure that we have found all words in these language with one, two, three or four letters. (1 point) S → aSb | bX X → bX | b 10. Draw the TG for the following regular grammar and infer the regular expression defining the language generated by the CFG. (1 point) S → aX | bS | a | b X → aX | a 11. Find the CFG after removing the Λ-productions. (1 point) S → aX | bX X→a|b|Λ 12. Convert the following CFG into CNF. (1 point) S → aXX X → aS | bS | a 13. Convert the following FA into a PDA. (1 point)
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