Computational tree logic

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Computational tree logic (CTL) is a temporal logic. It is often used to express properties of a system in the context of formal verification or model checking.

It uses atomic propositions as its building blocks to make statements about the states of a system. CTL then combines theses propositions into formulas using logical operators and temporal operators.

Table of contents

1 Operators 1.1 Logical operators 1.2 Temporal operators 1.2.1 State operators 1.2.2 Path operators 2 Relations with other logics 3 See also

Operators

Logical operators

The logical operators are the usual ones: <math>\neg,\or,\and,\rightarrow<math> and <math>\leftrightarrow<math>. Along with these operators CTL formulas can also make use of the boolean constants true and false.

Temporal operators

The temporal operators are the following:

State operators

These operators "select" states.

Unary operators

• N <math>\phi<math> - Next: <math>\phi<math> has to hold at the next state (this operator is sometimes noted X instead of N).
• G <math>\phi<math> - Globally: <math>\phi<math> has to hold on the entire subsequent path.
• F <math>\phi<math> - Finally: <math>\phi<math> eventually has to hold (somewhere on the subsequent path).

Binary operators:

• <math>\phi<math> U <math>\psi<math> - Until: <math>\phi<math> has to hold until at some position <math>\psi<math> holds. This implies that <math>\psi<math> will be verified in the future.
• <math>\phi<math> W <math>\psi<math> - Weak until: <math>\phi<math> has to hold until <math>\psi<math> holds. The difference with U is that there is no guarantee that <math>\psi<math> will ever be verified. The W operator is sometimes called "unless".

Path operators

These operators "select" paths.

• A <math>\phi<math> - All: <math>\phi<math> has to hold on all paths starting from the current state.
• E <math>\phi<math> - Exists: there exists at least one path starting from the current state where <math>\phi<math> holds.

Relations with other logics

Linear temporal logic (LTL) is a subset of CTL*.

See also

• Linear temporal logic

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