Semantics of the Requirement Specification Language

In the following we give a pseudo-formal semantics for the requirement specification language of UPPAAL. We assume the existens of a timed transition system (S, s0, ->) as defined in the semantics of UPPAAL.

The UPPAAL requirement specification language supports five types of properties, which can be reduced to two types as illustrated by the following table (here p is a state property).

Name Property Equivalent to
Possibly E<> p
Invariantly A[] p not E<> not p
Potentially alwaysE[] p
Eventually A<> p not E[] not p
Leads to p --> q A[] (p imply A<> q)

Thus in the following we will define the Possibly and Potentially always operators.

Possibly

The property E<> p evaluates to true for a timed transition system if and only if there is a sequence of alternating delay transitions and action transitions s0-->s1-->...-->sn, where s0 is the initial state and sn satisfies p.

Potentially always

The property E[] p evaluates to true for a timed transition system if and only if there is a sequence of alternating delay or action transitions s0-->s1-->...-->si-->... for which p holds in all states si and which either:

State Properties

Any side-effect free expression is a valid state property. In addition it is possible to test whether a process is in a particular location and whether a state is a deadlock.

Locations

Expressions on the form P.l, where P is a process and l is a location, evaluate to true in a state (L, v) if and only if P.l is in L.

Deadlocks

The state property deadlock evaluates to true for a state (L, v) if and only if for all d >= 0 there is no action successor of (L, v + d).