Interpolation-sequence based model checking

Q: What is the main drawback of the proposed algorithm?

The proposed algorithm explores the state space of the model by means of an overapproximation using BMC and interpolation-sequence.

Q: What is the runtime of falsified properties?

7: Runtime of falsified properties.cone of influence for the properties contains thousands of state variables and tens of thousands of gates and signals.

Q: What is the interpolant for the pair?

Ii is the interpolant for the pair (A(i), B(i)) extracted using Π then the set {>, I1, I2, . . . , In−1,⊥} is an interpolant sequence for Γ.Model checking [6] is an automatic approach to formally verifying that a given system satisfies a given specification.

Question

1. What are the contributions mentioned in the paper "Interpolation-sequence based model checking" ?

2. What is the definition of a Kripke structure?

3. how many times can the authors simplify the BMC run for bound N?

4. What is the labeling function for a Kripke structure?

Accepted Answer

In this work the authors present a novel SAT-based approach to full verification.. The authors demonstrate the usefulness of their method by applying it to industrial-size hardware designs from Intel.

Accepted Answer

Given a set of atomic propositions AP , a Kripke structure M is the quadruple M = (S, INIT,TR, L) where S is a finite set of states, INIT ⊆ S is a set of initial states and TR ⊆ S×S is a total transition relation.

Accepted Answer

In addition, the authors believe that the over-approximated sets of reachable states computed using their method at the N -th iteration can be used to simplify the BMC run for bound N + 1.

Accepted Answer

L : S −→ P(AP ) is the labeling function which associates with every state s ∈ S the set L(s) of atomic propositions that hold in s.A path in a Kripke structure M is a sequence of states π = (s0, s1, . . .) such that for all i > 0, si ∈ S and (si, si+1) ∈ TR.

Accepted Answer

An interpolation-sequence for Γ is a set {I0, I1, . . . , In} such that:1) I0 ≡ > and In ≡ ⊥ 2) For every 0 ≤ j < n it holds that Ij ∧Aj+1 ⇒ Ij+1 3) For every 0 < j < n it holds that L(Ij) ⊆ L(A1, . . . , Aj) ∩ L(Aj+1, . . . , An)Computing an interpolation-sequence for a sequence of formulas is done in the following way: for each Ii, 0 < i < n, the sequence of formulas is partitioned in a different way suchthat Ii is the interpolant for the formulas A(i) = i∧j=1Aj andB(i) = n∧j=i+1Aj .

Accepted Answer

The proposed algorithm explores the state space of the model by means of an overapproximation using BMC and interpolation-sequence.

Accepted Answer

7: Runtime of falsified properties.cone of influence for the properties contains thousands of state variables and tens of thousands of gates and signals.

Accepted Answer

Ii is the interpolant for the pair (A(i), B(i)) extracted using Π then the set {>, I1, I2, . . . , In−1,⊥} is an interpolant sequence for Γ.Model checking [6] is an automatic approach to formally verifying that a given system satisfies a given specification.

Accepted Answer

The authors consider a subset of LTL properties called safety properties since Liveness checking can be achieved by the method presented in [2].

Accepted Answer

Given V where |V | = n, a state s ∈ S is represented by a vector in the set {0, 1}n and by that s is a valuation of the state variables in V .

Accepted Answer

B. Interpolation-Sequence Based Model CheckingDefinition 3.1. A BMC-partitioning for ϕN is the set Γ = {A1, A2, . . . , AN+1} of formulas such that A1 = INIT(V 0)∧ TR(V 0, V 1), for every 2 ≤ i ≤ N Ai = TR(V i−1, V i) andAN+1 = ¬q(V N ).

Accepted Answer

Through all their experiments, when convergence for IB could be achieved only at high bounds, ISB always performed better while for convergence at lower bounds, IB is the better performer.

Accepted Answer

these sets can be used to imitate the forward reachability analysis of the model’s state-space by means of an over-approximation.

Accepted Answer

If M does not have a counterexample of length N , then Sj ⊆ INj for every 1 ≤ j ≤ N and INN |= q.Proof: M does not have a counterexample of length N .

Accepted Answer

In order to search for a counterexample of length k the following propositional formula is built:Formula 1. ϕkM (f) = INIT(V 0)∧TR(V 0, V 1)∧TR(V 1, V 2)∧ . . . ∧ TR(V k−1, V k) ∧ (¬q(V k))ϕkM (f) is then passed to a SAT solver which searches for a satisfying assignment.

Interpolation-sequence based model checking

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Most frequently asked questions

1. What are the contributions mentioned in the paper "Interpolation-sequence based model checking" ?

2. What is the definition of a Kripke structure?

3. how many times can the authors simplify the BMC run for bound N?

4. What is the labeling function for a Kripke structure?

5. what is the interpolation-sequence for a set of formulas?

6. What is the main drawback of the proposed algorithm?

7. What is the runtime of falsified properties?

8. What is the interpolant for the pair?

9. What is the definition of safety properties?

10. What is the value of the state variables in V?

11. What is the definition of a BMC-partitioning for N?

12. What is the way to verify the properties of IB?

13. What is the purpose of the set Ij?

14. What is the implication of IN N?

15. What is the formula for a counterexample of length k?

Figures

Citations

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Boolean Satisfiability Solvers and Their Applications in Model Checking

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References

The temporal logic of programs

Symbolic model checking: 10/sup 20/ states and beyond

Symbolic Model Checking without BDDs

Interpolation and SAT-Based Model Checking

Bounded Model Checking

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