Linear temporal logic Guide, Meaning , Facts, Information and Description

Linear temporal logic (LTL) is a field of mathematical logic that is able to talk about the future of paths. LTL is build up from proposition variables , the usual logic connectives and the following temporal operators. LTL formulas are generally evaluated over paths and a position on that path. A LTL formula as such is satisfied if and only if it is satisfied for position 0 on that path.

Unary operators:

• N - Next: has to hold at the next state.
• G - Globally: has to hold on the entire subsequent path.
• F - Finally: eventually has to hold (somewhere on the subsequent path).

Binary operator:

• U - Until: has to hold until at some position holds. At that position does not have to hold any more.

However one can reduce to two of those operators since the following is always satisfied:

• F = true U
• G = F

LTL can be shown to be equivalent to the first-order logic over one successor and the smaller relation, FO[S,<] as well as star-free regular expressions or deterministic finite automata with loop complexity 0.

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