Linear Completeness Thresholds for Bounded Model Checking Thomas Wahl with: Daniel Kroening, Joel...
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Linear Completeness Thresholds for Bounded Model Checking Thomas Wahl with: Daniel Kroening, Joel Ouaknine, Ofer Strichman, James Worrell CAV 2011, Snowbird, Utah
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Transcript of Linear Completeness Thresholds for Bounded Model Checking Thomas Wahl with: Daniel Kroening, Joel...
Linear Completeness Thresholdsfor Bounded Model Checking
Thomas Wahlwith: Daniel Kroening, Joel Ouaknine,
Ofer Strichman, James Worrell
CAV 2011, Snowbird, Utah
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Bounded LTL Model Checking
= search for CEXs along bounded paths:
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Toward Verification: Lifting the Bound
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Doesn’t that already exist?
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Even for all of LTL?
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• Awedh & Somenzi, CAV’04• Clarke et al., VMCAI’04
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Our Goal•
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⇒ no product; result parametric
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Def.: Linear Compl. Thresholds
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A Non-Linear Example
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and familyof Kripkestructures:
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Cliqueyness
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“Directed graph is cliquey”: every strongly connected component (SCC) is a clique.
cliquey! not cliquey
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Cliqueyness is what we need!
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Theorem: Cliquey automatahave linear completeness thresholds.
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Tightening the Threshold
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Algorithm itself also has linear complexity!
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Cliquey Automata and LTL
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Is all of LTL\X cliquey?
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This formula’s BA is semantically non-cliquey.
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A Cliquey LTL\X Fragment
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Theorem: Unary LTL\X formulas (LTL\XU)have cliquey automata encodings.
Corollary: LTL\XU ⇒ Cliquey ⇒ LCT.
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Summary:Cliqueyness and LTL Fragments
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All inclusions are strict!
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Back toLinear Completeness Thresholds
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Non-Linear CTs:How complex does it get?
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Summary
•
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Open Issues
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Open Issues
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End.
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Roadmap
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BAs of class “X”permit LCTs
LTL formulas of class “Y”have “X” automata
If not LCT,how bad is it?
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Nomenclature
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Product Automaton
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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!)
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Cliquey = LCT ?
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