# Lec04PL - Macpherson Delva Sean Morgan Section 1.4...

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Macpherson Delva Sean Morgan Section 1.4 - Nonregular Languages Not all languages can be represented by a regular expression or recognized by a NFA. These languages are said to be nonregular. Nonregular languages can be very simple such as L = { 0 n 1 n | n ` N}, to recognize this language a machine would have to keep track of the number of 0’s and 1’s and a NFA has no way of counting. We can proof that L is a nonregular language formally by proving that there is no NFA which accepts it. Proof by contradiction that L is irregular 1 Assume a DFA exist that accepts L, the number of states within this DFA is denoted by k 2 Take a case with k zeros. To accept k zeros there must be at least k+1 transition, so at least one repeated transition. Call the repeated transition q. 3. Assume it take it takes ii zeros to get to q the first time ( 0 i ) and that it takes j zeros to get to q the second time. Where i<j 4.) Therefore 0 i 1 i and 0 j 1 i go to the same place since they start at the same place and follow the same transition when they start processing the ones. Since 0

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