Hw3 - Homework 3 CISC 303 Timo Kötzing([email protected]

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Unformatted text preview: Homework 3 CISC 303 Timo Kötzing ([email protected]) Handed out: Friday, February 27. Due Date: Friday, March 6. Problem 1. (8 points) Let A = { a } be our alphabet. (i) Give an NFA M in graphical notation only such that L ( M ) = { w | | w | is divisible by 3 or by 5 } . (ii) Convert your NFA from (i) into a DFA by using the multi-state-machine construction . Make sure to give inter- mediate steps. Problem 2. (8 points) Let A = { a,b } be our alphabet. (i) Give an ε-NFA M in graphical notation only such that L ( M ) = { a n | n ≥ } ∪ { ( ba ) n | n ≥ } . (ii) Convert your ε-NFA from (i) into an NFA using the algorithm from class. Make sure to give intermediate steps. (iii) Convert your NFA from (ii) into a DFA using the algorithm from class (multi-state-machine). Make sure to give intermediate steps. Problem 3. (8 points) Let L ⊆ A * be any language. Two strings v,w ∈ A * are called L-equivalent (written v ≡ L w ), i ∀ u ∈ A * : vu ∈ L ⇔ wu ∈ L. (1) (a) Prove that...
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  • Spring '08
  • Carberry,M
  • Equivalence relation, equivalence class, Congruence relation, Partition of a set, di1Berent equivalence classes

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