Simulation-Based Invariant Verification Technique for the OTS/CafeOBJ Method

We demonstrate the power of the simulation-based invariant verification technique through two case studies in which it is formally verified that two mutual exclusion protocols, MCS protocol and Anderson protocol, enjoy the mutual exclusion property by the simulation-based invariant verification technique. We initially attempted formally verifying that the two protocols enjoy the property by the induction-based invariant verification technique. We successfully completed the formal proof for MCS protocol by the simulation-based invariant verification technique earlier than the one by the induction-based invariant verification technique even though we started the latter earlier than the former. We did not successfully complete the formal proof for Anderson protocol by the induction-based invariant verification technique as of the time of this paper submission. We define a variant of simulation, “observably equivalent simulations,” and prove some theorems on them to conduct the MCS case study. Given a state machine
$M$
, another state machine
$M'$
constructed by introducing auxiliary variables into
$M$
observably equivalently simulates
$M$
. In this sense,
$M'$
can be regarded as an abstract version of
$M$
.