Definition:String

Definition

Let $\AA$ be an alphabet of symbols.

A string (in $\AA$) is a sequence of symbols from $\AA$.

There is no limit to the number of times a particular symbol may appear in a given string.

Finite String

A string $S$ in $\AA$ is a finite string if and only if the sequence of symbols of which it is composed is finite.

Infinite String

A string $S$ in $\AA$ is an infinite string if and only if the sequence of symbols of which it is composed is infinite.

Also defined as

Some sources use the word string to mean a finite string, that is, what is defined on $\mathsf{Pr} \infty \mathsf{fWiki}$ as a word.

Also see

• Definition:Substring
• Definition:Prefix
• Definition:Suffix
• Definition:Null String
• Definition:Word (Formal Systems)
• Definition:Concatenation (Formal Systems)

• Results about strings can be found here.

Sources

• 1988: Dominic Welsh: Codes and Cryptography ... (previous) ... (next): Notation: Alphabets and strings
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.2$: Syntax of Propositional Logic
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (next): $\S 2.2$