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BLACK BOX INVARIANT SYNTHESIS

BLACK BOX INVARIANT SYNTHESIS. Joint work with: P. madhusudan ( uiuc ), christof loding (RWTH AAchen ) daniel neider (RWTH Aachen) In consultation with: dan roth (UIUC). Pranav Garg University of illinois at urbana-champaign. Automated Program verification.

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BLACK BOX INVARIANT SYNTHESIS

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  1. BLACK BOX INVARIANT SYNTHESIS Joint work with: P. madhusudan (uiuc), christofloding (RWTH AAchen) danielneider (RWTH Aachen) In consultation with: danroth (UIUC) PranavGarg University of illinois at urbana-champaign

  2. Automated Program verification • Does a program P meet its safety specification ? • Floyd-Hoare style Deductive Verification • To alleviate this burden of annotation  Invariant synthesis pre: true foo(int x) { y := x; while (x != 0) { x := x - 1; y := y - 1; } return y; } Invariant: x = y post: y = 0

  3. Invariant synthesis I1 I2 • Reach – post-closed, contains Init avoids Bad • Adequate Invariant: any post-closed set, contains Init, avoids Bad • --- Many choices; which one to pick? • Learn the “simplest” invariant! Bad Reach Init

  4. Syntax guided synthesis Synthesize Inv such that Can be reduced to Syntax-guided synthesis (SyGus)

  5. Black-box learning of invariants concrete data-points H (hypothesis) Program Learner Constraint Solver check hypothesis? Teacher

  6. active learning of invariants concrete data-points Bad H H (hypothesis) Reachk Init Program Learner Constraint Solver check hypothesis? Teacher

  7. active learning of invariants concrete data-points Bad H H (hypothesis) Reachk Init Program Learner Constraint Solver check hypothesis? Teacher

  8. active learning of invariants concrete data-points Bad H H (hypothesis) Reachk Init p’ p Program Learner Constraint Solver check hypothesis? Teacher

  9. ICE: Learning using examples, counter-examples and implications • To refute non-inductiveness of H, the teacher communicates (p, p’) • - if then -- learner’s choice depends on simplicity, etc. • Robust framework • Ensures progress and honest teacher • Strong convergence • - Can the learner eventually learn an invariant irrespective of the teacher’s answers ? concrete data-points H (hypothesis) Program Learner (Passive) Constraint Solver check hypothesis? Teacher

  10. ) ( ice-learning numerical invariants Learning algorithm is strongly convergent Implemented as a tool over Boogie (from Microsoft Research) - - j i

  11. ice-learning numerical invariants

  12. learning data structure invariants • Learn invariants over linear data structures (arrays and lists) • Unbounded size of the heap • - properties are universally quantified • General form: • Strongly convergent algorithms for learning quantified invariants. • Quantified Data Automata (QDA) normal form for such invariants • - adapt passive Regular Positive Negative Inference (RPNI) for learning QDAs head list pointed to by headis sorted 5 7 8 9

  13. Ongoing Work • Applying machine learning algorithms for synthesizing invariants • Applying machine learning algorithms to program synthesis • Synthesizing invariants for separation logic.

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