III.3 Semantic Preliminaries

Interval and Length [Slide 92]

An interval σ is a finite sequence of states

σ : σ₀σ₁σ₂…

Let Σ⁺ denote the set of all finite intervals with at least 1 state.

The length of an interval σ is denoted by |σ| and is the number of states minus 1.

Prefix, Suffix and Sub Interval [Slide 93]

Let σ = σ₀σ₁σ₂…σ_|σ| be an interval then

• σ₀…σ_k (where 0 ≤ k ≤|σ|) denotes a prefix interval of σ
• σ_k…σ_|σ| (where 0 ≤ k ≤|σ|) denotes a suffix interval of σ
• σ_k…σ_l (where 0 ≤ k ≤ l ≤|σ|) denotes a sub interval of σ