### 10 Semantic Preliminaries

An interval is a (in)finite sequence of states

Let denote the set of all possible non-empty finite intervals. Let denote the set of infinite intervals. [2mm] The length of an interval is denoted by and is the number of states minus 1.

Example 5

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Static vs State Variables

• Static variables don’t change their values within an interval.
• State variables can change their values within an interval.

State variables are denoted by capital first symbols and static variables are denoted by small symbols.

Example 6 Let be an interval where

is a state variable and is a static variable.

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Let be an interval then

• denotes a prefix interval of
• denotes a suffix interval of
• denotes a sub interval of

Example 7 Let be an interval then

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