# lec0411 - Strings and Languages A string is simply the...

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Strings and Languages A string is simply the concatenation of several letters in an alphabet. Typically, we will define an alphabet as a set Σ . So, for example, we could have Σ = {a,b}. Then, a string over this alphabet Σ , would be any “word” formed with only the letters or characters a and b. There is no limit on the length of a string. It must simply be a non negative integer. This means there is a string of length of length 0. This is known as the empty string. The empty string is typically denoted by λ . In particular, if you concatenate the empty string with any other string, you get back that string. It seems silly to have an empty string, but it will help out in certain situations. Make sure you do not confuse the empty string with the empty set. Also, recognize that λ can never be a letter of an alphabet. In the book, they define non-empty strings in the following manner : Σ n is a string of length n over the alphabet Σ , and is defined as below: 1) Σ 1 = Σ . 2) Σ n+1 = {xy | x ∈Σ , y ∈Σ n } And any string is simply a subset of Σ n , where n is a positive integer.

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Using the book’s definition, we can define the following two sets: Σ + = n=1 to Σ n , or in English, Σ + is the set of all strings of positive length over an alphabet Σ . Σ
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## lec0411 - Strings and Languages A string is simply the...

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