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13 February, 06:43

For a string w, recall that wR denotes the reverse of w, i. e., the string obtained by reversing the order of the symbols of w. For a language L, define S (L) = {w∈L:wR∈L}. If L is regular, is S (L) also regular? Prove your claim.

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  1. 13 February, 09:47
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    One arrangement is recursively (or inductively) characterize a turning around procedure on regular articulations, and apply that procedure on the regular articulation for L. Specifically, given a regular articulation R, reverse (R) is

    • a for some a ∈ Σ,

    • Σ if R = Σ,

    • ∅ if R = ∅,

    • (reverse (R1) ∪ reverse (R2)), if R = R1 ∪ R2,

    • (reverse (R2) ◦ reverse (R1)) if R = R1◦ R2, or

    • (reverse (R1) ∗), if R = (R∗1)
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