CTL*

CTL*

CTL* (Computation Tree Logic Star) is a temporal logic used in formal verification of computer systems. It is an extension of CTL (Computation Tree Logic) and is widely used in the field of model checking.

Overview

CTL* is a temporal logic that allows the specification and verification of properties of concurrent and reactive systems. It is based on the notion of computation trees, which represent the possible behaviors of a system. CTL* provides a rich set of operators to express temporal properties, such as "eventually," "always," "until," and "next."

Syntax

The syntax of CTL* is defined by a set of logical operators and quantifiers. These operators can be combined to form complex formulas that express temporal properties. Some of the key operators in CTL* include:

- `AG`: Universal "Globally" operator, which asserts that a property holds in all possible computation paths. - `AF`: Universal "Eventually" operator, which asserts that a property will eventually hold in some computation path. - `EX`: Existential "Next" operator, which asserts that a property holds in the next state. - `EU`: Existential "Until" operator, which asserts that a property holds until another property becomes true. - `AX`: Universal "Next" operator, which asserts that a property holds in all next states. - `AU`: Universal "Until" operator, which asserts that a property holds until another property becomes true in all computation paths.

Example

Let's consider a simple example to illustrate the usage of CTL* in formal verification. Suppose we have a concurrent system with two processes, P1 and P2. We want to verify the property that "eventually, both P1 and P2 will reach a state where they are idle."

We can express this property in CTL* as follows:

``` AF (P1_idle && P2_idle) ```

Here, `P1_idle` and `P2_idle` are atomic propositions representing the idle state of processes P1 and P2, respectively. The `AF` operator ensures that eventually, both P1 and P2 will reach the idle state.

Applications

CTL* is widely used in the field of model checking for the formal verification of hardware and software systems. It allows engineers to specify and verify complex temporal properties, such as safety and liveness properties, in a rigorous and systematic manner.

See Also

- CTL (Computation Tree Logic) - Model Checking - Temporal Logic

References

1. Clarke, E. M., Grumberg, O., & Peled, D. A. (1999). Model Checking. MIT Press. 2. Baier, C., & Katoen, J. P. (2008). Principles of Model Checking. MIT Press.