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Unformatted text preview: 1 Module 17 Closure Properties of Language class LFSA Remember ideas used in solvable languages unit Set complement Set intersection, union, difference, symmetric difference 2 LFSA is closed under set complement If L is in LFSA, then L c is in LFSA Proof Let L be an arbitrary language in LFSA Let M be the FSA such that L(M) = L M exists by definition of L in LFSA Construct FSA M from M Argue L(M) = L c There exists an FSA M such that L(M) = L c L c is in LFSA 3 Visualization Let L be an arbitrary language in LFSA Let M be the FSA such that L(M) = L M exists by definition of L in LFSA Construct FSA M from M Argue L(M) = L c L c is in LFSA L c L LFSA FSAs M M 4 Construct FSA M from M What did we do when we proved that REC, the set of solvable languages, is closed under set complement? Construct program P from program P Can we translate this to the FSA setting? 5 Construct FSA M from M M = (Q, , q , A, ) M = (Q, , q, A, ) M should say yes when M says no M should say no when M says yes How? Q = Q = q = q = A = QA 6 Example 1 2 3 a a a b b b FSA M 1 2 3 a a a b b b FSA M Q = Q = q = q = A = QA 7 Construction is an algorithm * Set Complement Construction Algorithm Specification Input: FSA M Output: FSA M such that L(M) = L(M) c Comments This algorithm can be in any computational model....
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This note was uploaded on 07/25/2008 for the course CSE 460 taught by Professor Torng during the Fall '07 term at Michigan State University.
 Fall '07
 TORNG

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