The Theory of computation

Computer Science

University of Nebraska at Omaha

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1. Define the following terms: (a) deterministic finite automaton (b) context free grammar (c) Turing machine 2. Is the language L1 = {anbn | n > 0} regular? Prove your answer. 3. Prove that the language L2 = {ambn | m,n > 0} is regular. 4. Is the language L3 = {ωωR | ω ∈ {a,b}∗} context free? Prove your answer. 5. Is the language L4 = {anbncn | n > 0} context free? Prove your answer. 6. Consider the following grammar G1: E⇒E+E E⇒E−E E⇒E×E E⇒E÷E E ⇒ 0 | ... | 9 Is G1 ambiguous? Prove your answer. 7. Consider the following G2: E⇒T+E E⇒T–E E⇒T T⇒F×T T⇒F÷T T⇒F F ⇒ (E) F ⇒ 0 | ... | 9 (a) Give the parse tree for the expression ω = (5 + 4)×(2 − 3). b) Convert G2 into Chomsky Normal Form. 8. Consider the following regular expression: a∗b∗c. Convert the regular expression into a nondeterministic finite automaton. 9. Convert the NFA you defined for Problem 8 into a deterministic finite automaton using the algorithm discussed in class. 10. Is it the case that every regular language is context free? Is every context free language also regular? Explain your answer. 11. Define a Turing machine which accepts the language L5 = {anbn | n > 0}. Show the derivation of the string ω = aabb. 12. Is it the case that every regular language is also Turing decidable? Prove your answer. 13. Is every Turing recognizable language also Turing decidable? Prove your answer. ...
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