Question

For strings w and t, write w $ t if the symbols of w are a permutation of the symbols of t. In other words, w $ t if t and w have the same symbols in the same quantities, but possibly in a different order. For any string w, define SCRAMBLE(w) = {t| t $ w}. For any language A, let SCRAMBLE(A) = {t| t ∈ SCRAMBLE(w) for some w ∈ A}. a. Show that if Σ = {0,1}, then the SCRAMBLE of a regular language is con- text free. b. What happens in part (a) if Σ contains three or more symbols? Prove your answer.

Name: for strings w and t write w t if the symbols of w are a permutation of the symbols of t in other words w t if t and w have the same symbols in the same quantities but possibly in a different 39993
Uploaded: 2020-02-13T20:25:47-08:00
Duration: 1 min 49 s
Channel: Danielle Leedy
Description: for strings w and t write w t if the symbols of w are a permutation of the symbols of t in other words w t if t and w have the same symbols in the same quantities but possibly in a different 39993

          For strings w and t, write w $ t if the symbols of w are a permutation of the
symbols of t. In other words, w $ t if t and w have the same symbols in the same
quantities, but possibly in a different order.
For any string w, define SCRAMBLE(w) = {t| t $ w}. For any language A, let
SCRAMBLE(A) = {t| t ∈ SCRAMBLE(w) for some w ∈ A}.
a. Show that if Σ = {0,1}, then the SCRAMBLE of a regular language is con-
text free.
b. What happens in part (a) if Σ contains three or more symbols? Prove your
answer.

Added by Tom-S B.

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