7. Model Checking and Automated Verification

Model Checking and Automated Verification

Introduction to model checking techniques

Model checking is a formal verification technique used to check whether a system satisfies a given property by exhaustively exploring all possible states of the system. It involves constructing a finite-state model of the system and verifying properties of interest by systematically exploring the state space and checking whether the properties hold in each state.

Automated verification using model checkers

Model checkers are tools that automate the process of model checking by providing algorithms and heuristics for efficiently exploring the state space of a system and checking properties of interest. They allow users to specify properties using temporal logic or other formal languages and automatically verify these properties against the system model.

Coq lab activities: Writing specifications and properties for model checking in Coq

In this lab activity, we will use Coq to write specifications and properties for model checking. Coq's support for formal reasoning and proof allows us to define system models and properties of interest, and verify that these properties hold using automated verification techniques.

Lab Activities

Specification of System Models in Coq

We will define system models in Coq using inductive data types to represent states and transitions between states. For example, we can define a simple model of a finite-state machine:

Inductive state : Type :=
  | State1
  | State2
  | State3.

Inductive transition : state -> state -> Prop :=
  | T_State1_State2 : transition State1 State2
  | T_State2_State3 : transition State2 State3
  | T_State3_State1 : transition State3 State1.

Verification of Properties using Model Checking

We will then verify properties of these system models using Coq's proof assistant. For example, we can prove a safety property of the finite-state machine:

Lemma no_deadlock : forall s,
  reachable s ->
  exists s', transition s s'.
Proof.
  intros s Hreach.
  induction Hreach.
  - destruct x.
    + exists State2. apply T_State1_State2.
    + exists State3. apply T_State2_State3.
    + exists State1. apply T_State3_State1.
  - destruct IHHreach as [s' Htrans].
    exists s'. apply Htrans.
Qed.

The above Coq code proves a safety property of the finite-state machine model, stating that from any reachable state, there exists a transition to another state. This property ensures that the system does not deadlock and can always make progress.