Assumption Generation

In the early stages of model development and analysis, properties of system components often fail to hold because the assumptions made about a component’s environment are insufficient to guarantee these properties, even when component’s behavior is correctly specified. When this happens, the system designer must study the counterexample provided by Kind 2, pinpoint the cause, and identify possible restrictions on the environment that the properties need in order to hold — which were perhaps assumed by the designer but were not made explicit.

For instance, consider the following Lustre program:

node Arbiter (s1,s2: bool; e1,e2:int) returns(o: int);
  guarantee "G1" s1 => o=e1;
  guarantee "G2" s2 => o=e2;
  if s1 and s2 then
    o = any { o:int | o = e1 or o = e2 };
  elsif s1 then
    o = e1;
    o = e2;

If we run Kind 2 to check guarantees G1 and G2, Kind 2 determines the properties are invalid, providing a counterexample for each of them. In the first counterexample, s1 and s2 are true initially, and the output is equal to the value of e2, which falsifies G1. In the second counterexample, s1 and s2 are true initially, and the output is equal to the value of e1, which falsifies G2.

From the description of the counterexamples, it is evident that one potential missing assumption is that s1 and s2 are never simultaneously true. If that is indeed the case, explicitly stating this assumption in the contract of the node, allows Kind 2 to prove both properties valid.

Generating the missing assumptions for straightforward examples like the one above is not very difficult. However, in more realistic scenarios, this task can become quite challenging. To help system designers in those situations, Kind 2 offers a post-analysis that can be enabled by passing the command-line option --assumption_gen true. When this option is enabled, Kind 2 will automatically generate assumptions that are strong enough to prove the set of falsified properties in the verification analysis while not being overly restrictive. Note that just finding sufficient assumptions is not challenging. The challenge is to find minimally restrictive assumptions which can then be recognized as realistic by the designer.

For the example above, Kind 2 generates the assumption: (not s2) or (not s1) or (e1 = e2). Notice that this assumption is a weaker version of the one mentioned above, as it considers a third case where the inputs e1 and e2 equal.

The functionality generates one-state constraints on a node’s environment, but it currently lacks the capability to generate two-state properties, which presents a significantly more complex challenge.