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Copy file name to clipboardExpand all lines: ch02/2.2/2.2.md
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@@ -95,16 +95,16 @@ the following languages. In each case show that your grammar is correct.
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#### Answer
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1.proof
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1.Proof
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any string derived from the grammar can be considered to be a sequence consisting of 11 and 1001, where each sequence element is possibly suffixed with a 0.
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Any string derived from the grammar can be considered to be a sequence consisting of 11 and 1001, where each sequence element is possibly suffixed with a 0.
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let`n` be the set of positions where `11` is placed. `11` is said to be at position `i` if the first `1` in `11` is at position `i`, where `i` starts at 0 and
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Let`n` be the set of positions where `11` is placed. `11` is said to be at position `i` if the first `1` in `11` is at position `i`, where `i` starts at 0 and
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grows from least significant to most significant bit.
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let`m` be the equivalent set for `1001`.
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Let`m` be the equivalent set for `1001`.
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the sum of any string produced by the grammar is:
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The sum of any string produced by the grammar is:
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sum
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This is clearly divisible by 3.
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2. No. Consider string "10101", it is divisible by 3, but cannot derived from the grammar.
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2. No. Consider the string "10101", which is divisible by 3, but cannot be
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derived from the grammar.
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Readers seeking a more formal proof can read about it below:
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