Words

Definition

Words are strings belonging to some language.

Example

If Σ= {x} then a language L can be defined as

L={xⁿ : n=1,2,3,…..} or L={x,xx,xxx,….}

Here x,xx,… are the words of L

Note

All words are strings, but not all strings are words.

Valid/In-valid alphabets

While defining an alphabet, an alphabet may contain letters consisting of group of symbols for example Σ₁= {B, aB, bab, d}.

Now  consider an alphabet

Σ₂= {B, Ba, bab, d} and a string BababB.

This string can be tokenized in two different ways

(Ba), (bab), (B)

(B), (abab), (B)

Which shows that the second group cannot be identified as a string, defined over

Σ = {a, b}.

As when this string is scanned by the compiler (Lexical Analyzer), first symbol B is identified as a letter belonging to Σ, while for the second letter the lexical analyzer would not be able to identify, so while defining an alphabet it should be kept in mind that ambiguity should not be created.

Remarks

While defining an alphabet of letters consisting of more than one symbols, no letter should be started with the letter of the same alphabet i.e. one letter should not be the prefix of another. However, a letter may be ended in a letter of same alphabet.

Conclusion

Σ₁= {B, aB, bab, d}

Σ₂= {B, Ba, bab, d}

Σ₁ is a valid alphabet while Σ₂ is an in-valid alphabet.

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