Probabilistic Computation Tree Logic (PCTL) is an extension of computation tree logic (CTL) that allows for probabilistic quantification of described properties. It has been defined in the paper by Hansson and Jonsson.

PCTL is a useful logic for stating soft deadline properties, e.g. "after a request for a service, there is at least a 98% probability that the service will be carried out within 2 seconds". Akin CTL suitability for model-checking PCTL extension is widely used as a property specification language for probabilistic model checkers.

PCTL syntax

A possible syntax of PCTL can be defined as follows: is a probability threshold. Formulas of PCTL are interpreted over discrete Markov chains, where

• is a finite set of states,

• is an initial state,

• , and

• , assigning atomic propositions to states.

.

Probability measure

is given by the product of transition probabilities along the prefix of the path: .

Satisfaction relation

is inductively defined as follows:

• ,

• if and only if,

• ,

• ,

• , and

• .

See also

• Computation tree logic

• Temporal logic

References