Definition:Balanced String/Definition 1

Definition

Let $S$ be a string in an alphabet containing brackets.

$S$ is said to be balanced if and only if:

$(1): \quad S$ contains equally many left and right brackets.

$(2): \quad$ Every prefix of $S$ contains at least as many left brackets as it does right brackets.

Also see

• Equivalence of Definitions of Balanced String

Sources

• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: Exercises: $1.4$