Exercise 9:

Context-free description for {w1aw2aw3w1,w2,w3{0,1}    w1=w20+w31    w1w21111}\{ w_1aw_2aw_3 \mid w_1,w_2,w_3\in\{0,1\}^*\;\wedge\;|w_1|=|w_2|_0+|w_3|_1\;\wedge\;|w_1w_2|_{111}\geq 1 \}
Give a context-free description for the set of words of the form w1aw2aw3w_1aw_2aw_3 such that w1,w2,w3w_1,w_2,w_3 are constructed over the alphabet {0,1}\{0,1\}, the size w1w_1 coincides with the number of 00’s of w2w_2 plus the number of 11’s of w3w_3, and w1w2w_1w_2 has at least one occurrence of 111111.
Authors: Guillem Godoy / Documentation:
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