CFL_closures - PBL on closure properties of (D)CFL  CISC...

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Unformatted text preview: PBL on closure properties of (D)CFL  CISC 303 Timo Kötzing (tkoe@udel.edu) The following table gives closure properties for various collections of languages. closure under reg DCFL CFL ∪ ∩ complement set dierence ? dot product × × Kleene-∗ (HW5) We dene the following languages. L0 L1 L2 = = = {al bm cn | l = m}; (2) lmn (3) {a b c | m = n}; {a b c | l = n}. The goal of this in-class assignment is to complete the above table, putting a whereever closure doesn't hold. (1) lmn wherever closure holds, and a The following is to guide you through this assignment. × If you ever get stuck, use the instructor and/or the lecture notes as resources. In particular, you might want to check how we have shown the closure properties for regular languages. Each of you should have an answer to the following questions written down by the end of this in-class assignment. (1) Write one (grammatically correct) sentence explaining how you can justify a language to be a DCFL. (2) Write one (grammatically correct) sentence explaining how you can justify a language to be a CFL. (3) Write one (grammatically correct) sentence explaining how you can justify a language (4) Which of L0 , L1 and L2 not to be a CFL. are DCFLs, which are CFLs and which are neither? Justify your answer. (5) Write one (grammatically correct) paragraph answering What do you need to show to justify putting a into one of the empty cells? (6) Write one (grammatically correct) paragraph answering What do you need to show to justify putting a one of the empty cells? (7) Fill in the cell about CFL-closure under ∩. (8) Fill in the cell about DCFL-closure under ∩. (9) Fill in the cell about CFL-closure under complement. (10) Fill in the cell about DCFL-closure under ∪. (11) Fill in the cell about CFL-closure under set dierence. (12) Fill in the cell about CFL-closure under Kleene-∗. 1 × into ...
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