Property Pattern Mappings for ACTL

This page describes mappings for property patterns in ACTL (Action Computation Tree Logic). For other information about the patterns click on the pattern links.

These pattern mappings can be used with the EVALUATOR 3.5 model-checker of CADP, whose input specification language allows to encode the operators of ACTL.

Information about the entire pattern system is available at the Specification Patterns Home Page.


Pattern Mappings

The patterns written in ACTL are adequate for action-based systems (the symbols P, Q, R, etc. denote action predicates). For simplicity, we assume there is no clash between action predicates, i.e., every action of the system satisfies at most one predicate P, Q, R, etc. This restriction can be removed by changing the pattern mappings appropriately.

Absence

P is false:
Globally AG{true} [P] false
Before R AG{not R} [P] AG{not R} [R] false
After Q AG{not Q} [Q] AG{true} [P] false
Between Q and R AG{true} [Q] AG{not R} [P] AG{not R} [R] false
After Q until R AG{true} [Q] AG{not R} [P] false

Existence

P occurs:
Globally A [true{true} U{P} true]
Before R AG{not P} [R] false
After Q AG{not Q} [Q] A [true{true} U{P} true]
Between Q and R AG{true} [Q] AG{not (P or R)} [R] false
After Q until R AG{true} [Q] A [true{not R} U{P} true]

Bounded Existence

In these mappings we illustrate one instance of the bounded existence pattern, where the bound is at most 2 designated actions. Other bounds can be specified by variations on this mapping.
P occurs at most 2 times:
Globally AG{not P} [P] AG{not P} [P] AG{not P} [P] false
Before R AG{not R} [P] AG{not R} [P] AG{not R} [P] AG{not R} [R] false
After Q AG{not Q} [Q] AG{not P} [P] AG{not P} [P] AG{not P} [P] false
Between Q and R AG{true} [Q] AG{not R} [P] AG{not R} [P] AG{not R} [P]
AG{not R} [R] false
After Q until R AG{true} [Q] AG{not R} [P] AG{not R} [P] AG{not R} [P] false

Universality

P is true:
Globally AG{true} [not P] false
Before R AG{not R} [not (P or R)] AG{not R} [R] false
After Q AG{not Q} [Q] AG{true} [not P] false
Between Q and R AG{true} [Q] AG{not R} [not (P or R)] AG{not R} [R] false
After Q until R AG{true} [Q] AG{not R} [not (P or R)] false

Precedence

S precedes P:
Globally AG{not S} [P] false
Before R AG{not (S or R)} [P] AG{not R} [R] false
After Q AG{not Q} [Q] AG{not S} [P] false
Between Q and R AG{true} [Q] AG{not (S or R)} [P] AG{not R} [R] false
After Q until R AG{true} [Q] AG{not (S or R)} [P] false

Response

S responds to P:
Globally AG{true} [P] A [true{true} U{S} true]
Before R AG{not R} [P] AG{not (S or R)} [R] false
After Q AG{not Q} [Q] AG{true} [P] A [true{true} U{S} true]
Between Q and R AG{true} [Q] AG{not R} [P] AG{not (S or R)} [R] false
After Q until R AG{true} [Q] AG{not R} [P] A [true{not R} U{S} true]

Precedence Chain

This is the 2 cause-1 effect mapping.

S, T precede P:

Globally AG{not S} ([P] false and [S] AG{not T} [P] false)
Before R AG{not (S or R)} ([P] AG{not R} [R] false and
[S] AG{not (T or R)} [P] AG{not R} [R] false)
After Q AG{not Q} [Q] AG{not S} ([P] false and [S] AG{not T} [P] false)
Between Q and R AG{true} [Q] AG{not (S or R)} ([P] AG{not R} [R] false and
[S] AG{not (T or R)} [P] AG{not R} [R] false)
After Q until R AG{true} [Q] AG{not (S or R)} ([P] false and
[S] AG{not (T or R)} [P] false)

This is the 1 cause-2 effect mapping.

P precedes S, T:

Globally AG{not P} [S] AG{not T} [T] false
Before R AG{not (P or R)} [S] AG{not (T or R)} [T] AG{not R} [R] false
After Q AG{not Q} [Q] AG{not P} [S] AG{not T} [T] false
Between Q and R AG{true} [Q] AG{not (P or R)} [S] AG{not (T or R)} [T]
AG{not R} [R] false
After Q until R AG{true} [Q] AG{not (P or R)} [S] AG{not (T or R)} [T] false

Response Chain

This is the 2 stimulus-1 response mapping.

P responds to S, T:

Globally AG{true} [S] AG{not T} [T] A [true{true} U{P} true]
Before R AG{true} [S] AG{not T} [T] AG{not P} [R] false
After Q AG{not Q} [Q] AG{true} [S] AG{not T} [T] A [true{true} U{P} true]
Between Q and R AG{true} [Q] AG{not (S or R)} [S] AG{not (T or R)} [T]
AG{not (P or R)} [R] false
After Q until R AG{true} [Q] AG{not (S or R)} [S] AG{not (T or R)} [T]
A [true{not R} U{P} true]

This is the 1 stimulus-2 response mapping.

S, T respond to P:

Globally AG{true} [P] A [true{true} U{S} A [true{true} U{T} true]]
Before R AG{not R} [P] AG{not (S or R)}
([R] false and [S] AG{not (T or R)} [R] false)
After Q AG{not Q} [Q] AG{true} [P] A [true{true} U{S} A [true{true} U{T} true]]
Between Q and R AG{true} [Q] AG{not R} [P] AG{not (S or R)}
([R] false and [S] AG{not (T or R)} [R] false)
After Q until R AG{true} [Q] AG{not R} [P]
A [true{not R} U{S} A [true{not R} U{T} true]]

Constrained Chain Patterns

This is the 1-2 response chain constrained with a single event.

S, T without Z respond to P:

Globally AG{true} [P] A [true{true} U{S} A [true{not Z} U{T} true]]
Before R AG{not R} [P] AG{not (S or R)} ([R] false and
[S] (AG{not (T or R)} [R] false and
AG{not (T or R)} [Z] AG{not (T or R)} [R] false))
After Q AG{not Q} [Q] AG{true} [P] A [true{true} U{S} A [true{not Z} U{T} true]]
Between Q and R AG{true} [Q] AG{not R} [P] AG{not (S or R)} ([R] false and
[S] (AG{not (T or R)} [R] false and
AG{not (T or R)} [Z] AG{not (T or R)} [R] false))
After Q until R AG{true} [Q] AG{not R} [P]
A [true{not R} U{S} A [true{not (Z or R)} U{T} true]]

Authors: Radu Mateescu and Mihaela Sighireanu (INRIA/VASY team). Last updated 2011/11/24 14:42:56.