Introduction to Bounded Model Checking Armin Biere FATS Seminar

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Using Inductive Invariants BMC 23 • inductive invariants help to speed-up both k-induction (and interpolation) • let P be inductive: I(s) ⇒ P(s) and T (s,s ′ ) ∧ P(s) ⇒ P(s ′ ) • we want to prove that a bad state can not reached • if BMC(k) is unsatisfiable it is enough to prove unsatisfiability of P(s0) ∧ P(s1) ∧ ··· ∧ P(s k) ∧ B(s0) ∧ ··· ∧ B(s k−1) ∧ T (s0,s1) ∧ ··· ∧ T (s k−1,s k) ∧ B(s k) ∧ V 0≤i< j≤k si = s j • this formula can become unsatisfiable much earlier, i.e. for smaller k, than B(s0) ∧ ··· ∧ B(s k−1) ∧ T (s0,s1) ∧ ··· ∧ T (s k−1,s k) ∧ B(s k) ∧ V 0≤i< j≤k si = s j Introduction to Bounded Model Checking – FATS Seminar ETH 2009 Armin Biere – FMV – JKU Linz
Simple Path Constraints Symbolic All-Different Constraints [BiereBrummayer-FMCAD’08] 24 • bounded model checking: [BiereCimattiClarkeZhu’99] I(s1) ∧ T (s1,s2) ∧ ... ∧ T (sk−1,sk) ∧ _ B(si) satisfiable? 0≤i≤k • reoccurrence diameter checking: [BiereCimattiClarkeZhu’99] T (s1,s2) ∧ ... ∧ T (sk−1,sk) ∧ ^ si = s j unsatisfiable? 1≤i< j≤k • k-induction base case: [SheeranSinghSt˚almarck’00] I(s1) ∧ T (s1,s2) ∧ ... ∧ T (sk−1,sk) ∧ B(sk) ∧ ^ ¬B(si) satisfiable? 0≤i
Page 1 and 2: Introduction to Bounded Model Check
Page 3 and 4: What is Model Checking? Model Check
Page 5 and 6: Forward Fixpoint: Initial and Bad S
Page 7 and 8: Forward Fixpoint: Step 2 Model Chec
Page 9 and 10: Forward Fixpoint: Bad State Reached
Page 11 and 12: Forward Least Fixpoint Algorithm fo
Page 13 and 14: Linear Size BDD for Bit-Vector Comp
Page 15 and 16: Unrolling of Forward Least Fixpoint
Page 17 and 18: Bounded Model Checking BMC [BiereCi
Page 19 and 20: Bounded Model Checking State of the
Page 21 and 22: Interpolation in Model Checking BMC
Page 23: Mining Inductive Invariants BMC 22
Page 27 and 28: Symbolic ADCs for Large Domains Sym
Page 29 and 30: Lemmas on Demand for Satisfiability
Page 31 and 32: Lemmas on Demand for Extensional Ar
Page 33 and 34: Combining Over- and Under-Approxima
Page 35 and 36: All Different Objects (ADOs) Symbol
Page 45 and 46: Implementation Details Symbolic All
Page 47 and 48: Mixed Approach versus Refine Only S
Page 49 and 50: SAT Solver Progress (SAT’06 Race

Introduction to Bounded Model Checking Armin Biere FATS Seminar

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