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Linear Completeness Thresholds for Bounded Model Checking

Linear Completeness Thresholds for Bounded Model Checking. Thomas Wahl with: Daniel Kroening, Joel Ouaknine, Ofer Strichman, James Worrell. CAV 2011, Snowbird, Utah. Bounded LTL Model Checking. = search for CEXs along bounded paths:. Toward Verification: Lifting the Bound.

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Linear Completeness Thresholds for Bounded Model Checking

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  1. Linear Completeness Thresholdsfor Bounded Model Checking Thomas Wahl with: Daniel Kroening, Joel Ouaknine, Ofer Strichman, James Worrell CAV 2011, Snowbird, Utah

  2. Bounded LTL Model Checking = search for CEXs along bounded paths: Computer-Aided Verification, Snowbird, Utah

  3. Toward Verification: Lifting the Bound Computer-Aided Verification, Snowbird, Utah

  4. Doesn’t that already exist? Computer-Aided Verification, Snowbird, Utah

  5. Even for all of LTL? • Awedh & Somenzi, • CAV’04 • Clarke et al., • VMCAI’04 Computer-Aided Verification, Snowbird, Utah

  6. Our Goal ⇒ no product; result parametric Computer-Aided Verification, Snowbird, Utah

  7. Def.: Linear Compl. Thresholds Computer-Aided Verification, Snowbird, Utah

  8. A Non-Linear Example and family of Kripke structures: Computer-Aided Verification, Snowbird, Utah

  9. Cliqueyness “Directed graph is cliquey”:every strongly connected component (SCC) is a clique. cliquey! not cliquey Computer-Aided Verification, Snowbird, Utah

  10. Cliqueyness is what we need! Theorem: Cliquey automata have linear completeness thresholds. Computer-Aided Verification, Snowbird, Utah

  11. Tightening the Threshold Algorithm itself also has linear complexity! Computer-Aided Verification, Snowbird, Utah

  12. Cliquey Automata and LTL Computer-Aided Verification, Snowbird, Utah

  13. Is all of LTL\X cliquey? This formula’s BA is semantically non-cliquey. Computer-Aided Verification, Snowbird, Utah

  14. A Cliquey LTL\X Fragment Theorem:Unary LTL\X formulas (LTL\XU) have cliquey automata encodings. Corollary: LTL\XU ⇒ Cliquey ⇒ LCT. Computer-Aided Verification, Snowbird, Utah

  15. Summary:Cliqueyness and LTL Fragments All inclusions are strict! Computer-Aided Verification, Snowbird, Utah

  16. Back toLinear Completeness Thresholds Computer-Aided Verification, Snowbird, Utah

  17. Non-Linear CTs:How complex does it get? Computer-Aided Verification, Snowbird, Utah

  18. Summary Computer-Aided Verification, Snowbird, Utah

  19. Open Issues Computer-Aided Verification, Snowbird, Utah

  20. Open Issues Computer-Aided Verification, Snowbird, Utah

  21. End. Computer-Aided Verification, Snowbird, Utah

  22. Roadmap BAs of class “X” permit LCTs LTL formulas of class “Y” have “X” automata If not LCT, how bad is it? Computer-Aided Verification, Snowbird, Utah

  23. Nomenclature Computer-Aided Verification, Snowbird, Utah

  24. Product Automaton Computer-Aided Verification, Snowbird, Utah

  25. Cliqueyness Expressible in LTL • Cliqueyness is expressible in LTL (*-free ω-regular expression) • Thus, cliquey BAs encode LTL formulas • Cliqueyness not expressible in LTL\X In fact, there are cliquey BAs that do not correspond to any LTL\X formula. (Problem: stuttering!) Computer-Aided Verification, Snowbird, Utah

  26. Cliquey = LCT ? Computer-Aided Verification, Snowbird, Utah

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