Recall the definition of alphabet E and string over an alphabet. Let ɛ be the empty string. The following rules recursively define a set S of strings over the alphabet E = {0, 1}: Basis step : the empty string in S, i.e., e S. Inductive step : if x E S is a string in S, then Ox1 is a string in S, i.e., Ox1 E S. Describe without using recursion, the set of strings in S. The suggested way is to first give a few examples of strings in S, and then describe in plain English the structure of all and only the strings in S. Important: your description must separate the strings in S from the strings not in S. If you say something like, “S is a set of strings made of Os and 1s," you are not making an incorrect statement, but the answer is not acceptable because there are many strings made of Os and 1s that are not in S.
Recall the definition of alphabet E and string over an alphabet. Let ɛ be the empty string. The following rules recursively define a set S of strings over the alphabet E = {0, 1}: Basis step : the empty string in S, i.e., e S. Inductive step : if x E S is a string in S, then Ox1 is a string in S, i.e., Ox1 E S. Describe without using recursion, the set of strings in S. The suggested way is to first give a few examples of strings in S, and then describe in plain English the structure of all and only the strings in S. Important: your description must separate the strings in S from the strings not in S. If you say something like, “S is a set of strings made of Os and 1s," you are not making an incorrect statement, but the answer is not acceptable because there are many strings made of Os and 1s that are not in S.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Recall the definition of alphabet Σ and string over an alphabet. Let ε be the empty string. The following rules recursively define a set S of strings over the alphabet Σ = {0, 1}:
**Basis step**: the empty string in S, i.e., ε ∈ S.
**Inductive step**: if x ∈ S is a string in S, then 0x1 is a string in S, i.e., 0x1 ∈ S.
Describe without using recursion, the set of strings in S. The suggested way is to first give a few examples of strings in S, and then describe in plain English the structure of all and only the strings in S.
Important: your description must separate the strings in S from the strings not in S. If you say something like, “S is a set of strings made of 0s and 1s,” you are not making an incorrect statement, but the answer is not acceptable because there are many strings made of 0s and 1s that are not in S.
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