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Evidence-Based Verification

Evidence-Based Verification. Li Tan Computer Science Department Stony Brook Joint work with Rance Cleaveland Nov. 2002. Outline. Part I. Evidence-based Verification. Motivations. The general framework. Applications. Part II. Evidence-based Model Checking.

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Evidence-Based Verification

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  1. Evidence-Based Verification Li Tan Computer Science Department Stony Brook Joint work with Rance Cleaveland Nov. 2002 Evidence-Based Verification

  2. Outline Part I. Evidence-based Verification. • Motivations. • The general framework. • Applications. Part II. Evidence-based Model Checking. • Introducing support set as checker-independent evidence. • Extracting support set from existing checkers. • Post-model-checking analysis based on support sets. • Efficiently certifying model-checking result. • Generating the diagnostic information. • Evaluating the quality of model-checking process. • Prototype work on the Concurrency Workbench (CWB-NC). Evidence-Based Verification

  3. Automatic Verification • Verification algorithm (checker) decides in a fully automatic fashion whether or not a transition system satisfies a property. • A simple "Yes/No" may not satisfy users. • Why does my design go wrong [CGMZ95]? • Could my design satisfy the property trivially [KV99]? • Can I trust the verification result [Nam01]? Evidence-Based Verification

  4. Understanding the verification result To answer these questions, users may demand, • Diagnostic information. A diag. routine usually reuse the proof already computed by a checker, • Implementation requires the understanding of checkers. • Migrating a diag. routine onto a different checker requires changes on both diag. routine and checker. • Proof used for one diagnostic schema may not be suitable for a different schema. • Measurement on how well a system has been checked. • Evidence to support verification result. Currently we lack of the proof of correctness which is, • Independent of the checker, and • Able to be verified efficiently. Evidence-Based Verification

  5. Invalid Proof Evidence-Based Verification Let the result carry its own certifiable and check-independent proof Diagnostic schema 1..k Certification of result Evaluating verification process … Verifier Portable Proof of Correctness … Checker 1 Checker 2 Checker n Evidence-Based Verification

  6. The general framework • Defining abstract proof structures (APS). • APS encodes the proof structures of different checkers in a standard form. • APS may be used as the certification for correctness of result. • APS is rich enough to support a variety of analyses, while still abstract enough to save the space. • APS can be verified independently and efficiently. • Extracting APS from existing checkers. • Extraction should NOT compromise the complexities of checkers. • Utilizing support set to perform diagnoses. • Certifying verification result. • Generating diagnostic information. • Measuring the quality of verification process Evidence-Based Verification

  7. b s2 a,b s1 T Part II. Evidence-based Model Checking:An introduction by case study s0 Evidence-Based Verification

  8. Boolean Equation System=Temporal Property+Transition System Evidence-Based Verification

  9. Support Set Evidence-Based Verification

  10. Support Set Evidence-Based Verification

  11. Boolean Equation System=Temporal Property+Transition System Evidence-Based Verification

  12. Support Sets (Continue) Support set reflects how a checker “reasons” model-checking problem. • By properties 1 and 2, support set implies a fixpoint solution for BES. • By property 3, support set respects the semantics of fixpoint operators in BES. Theorem 1 [TanCle02] There exists a support set G=<r, X,x> , [E](X)=r. Evidence-Based Verification

  13. Support sets for other temporal logics • Boolean equation system (BES)=transition system + temporal property. • Model checkers explicitly or implicitly construct BES . • Variables in support set stands for pairs of subformula and state in transition system. • Decorated support set <G, pT, pF>, where G=<r, X, x>, resolves subformulas and states associated with the variables in G. In our example, • pT(h s0, X0 i)= s0 …… • pF(h s0, X0i)= AF(: a Æ AG : b) …… Evidence-Based Verification

  14. Extracting Support Set The extraction is, • practical. Support sets can be extracted from a wide range of existing checkers, • Boolean-Graph algorithm [And92], Linear Alternation-Free algorithms[CleSte91], On-the-fly algorithms for full m-calculus LAFP [LRS98] and SLP [TanCle02b], Automaton-based model checkers([BhaCle96a] and [KVW00]). • efficient. The overhead doesn't affect the original complexities of these checkers. • simply. We only need to record the immediate dependency of variables. Evidence-Based Verification

  15. Application I: Certifying model-checking results • Checking (a) and (b) can be done in linear time. • Checking (c) can be reduced to even-loop problem (a O(n log ad) problem[KKV01]). • Model checking is a NP Å co-NP problem [EmeJutSis93]. • The cost of certifying results < The cost of model checking. Evidence-Based Verification

  16. hs0, X0i hs0, X2i hs0, X1i hs0, X3i hs1, X0i hs0, : bi hs1, X2i hs2, X1i hs2, X0i hs1, X1i hs1, : ai hs2, X2i hs2, X3i hs2, X4i hs1, X3i hs1, : bi Application II: Generating Tree-like Counterexample [CJLV02] Step 1: Presenting support set as a graph  X1=[-] X0  X1=[-] X0  X1=[-] X0  X4=[-] X3 Evidence-Based Verification

  17. Step 2: Labelling the graph • hsi, : ai has the label a (h si, : ai means si²:: a) • The label of hsi,Xji will be added to its parent h si, Xii ‘s label if Xi , Xj is not connected by a modal operator ([-] or <->). b hs0, X0i hs0, X2i b hs0, X1i hs0, X3i b a hs1, X0i b hs0, : bi hs1, X2i a hs2, X1i hs2, X0i hs1, X1i hs1, : ai a hs2, X2i hs2, X3i hs2, X4i hs1, X3i hs1, : bi b b Evidence-Based Verification

  18. Step 3: Obtaining a skeletion. Remove those edges which make “no progress” on transition system. • Remove h si, Xii!h si, Xji such that Xi and Xj is not connected by a modal operator. • Let h si, Xii have all the transitions of h si, Xii. b hs0, X0i a hs1, X0i hs2, X0i hs1, X3i b Evidence-Based Verification

  19. Generating Tree-like counterexample 4/4 • T’ is tree-like [CJLV02] • The component graph of T’ is a tree • Strongly connected components are cycles • T’ ²: AF(: a Æ AG : b) = EG(a Ç EF b) • T’ Á T s0 b b a s2 Á a,b s1 T T’ b Evidence-Based Verification

  20. Application III:Evaluate the quality of MC • A positive result may hide the problem • T may pass AG(c ) AF b) trivially because c never occurs in T. • Is there the status of a state (Minicoverage [CKV01]) or a subformula (Vacuity [KV99]) irrelevant to the result? • Coverage problem of support set. • Has support set covered all the states and properties? Evidence-Based Verification

  21. Furture Work I:A Client-Server Model for model checking • Server: checkers • Inputting system and properties encoded in some temporal logic. • Outputting support set. • Client: user interface, diagnostic generation, and evidence-verifier. Abstract Proof Structures Design Systems and Properties Evidence-Based Verification

  22. Future Work II:Proof-Carrying Code • Mobile code [Nec97] carries its own proof attesting to its safeness. • Currently compilers are modified to produce the proof for a predefined set of safety rules. • Integrate support-set-ready model checkers with compilers. • Certifying compiler enjoys the richness of temporal logics. Evidence-Based Verification

  23. A Prototype on CWB-NC Evidence-Based Verification

  24. Conclusion Checkers produce abstract proof structures as evidence. • Support set provides the portable evidence for justifying model-checking result. • Extracting support set won't affect the complexities of checkers. • Applications of support set. • Efficiently certifying the model-checking result. • Evaluating the quality of model-checking process. • Generating a wide range of diagnostic information. • APSs are defined for Model checking, Equiv. checking, and Preordering Checking. Evidence-Based Verification

  25. Related Work • Mateescu [Mat00] proposed Extended Boolean Graphies(EBG) as the evidence for boolean equation system. • The framework works only in alternation-free fragment of m-calculus. • Namjoshi [Nam01] proposed a deductive proof as the evidence for m-calculus model checking. • The proof need recode the ranking information. • Ranking information is not generally available for on-the-fly algorithm, and it costs more space to store this information. Evidence-Based Verification

  26. Future Work • Applying the framework to symbolic model checking. • Essentially support set associates with X a set of variable x(X) as its evidence. Sets can be efficiently encoded in OBDD. • Applying the framework to first-order logic model checking. • A client-server model for model-checking. • Model-checking server takes trans. System and property as input from client, and produces support sets as output. • Client generates a variety of diag. Info. from support set. • Generating proof-carrying code. • Support-set ready model checker can be integrated with the compiler. • The support set generated during support-set ready compiler will be translated to the proof for proof-carrying code. Evidence-Based Verification

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