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Scalable Error Detection using Boolean Satisfiability

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  1. Scalable Error Detection using Boolean Satisfiability Yichen Xie and Alex Aiken Stanford University Scalable Error Detection using Boolean Satisfiability

  2. Motivation Scalable Error Detection using Boolean Satisfiability

  3. Requirements Motivation • Scalability • Millions of lines of code • Precision • Maximize bugs found • Minimize false positives Scalable Error Detection using Boolean Satisfiability

  4. unlock lock unlock Error Unlocked Locked lock Code Example Flow Sensitivity void f(state *x, state *y) { result = spin_trylock(&x->lock); spin_lock(&y->lock); … if (!result) spin_unlock(&x->lock); spin_unlock(&y->lock); } result (&x->lock); spin_trylock (&y->lock); spin_lock Path Sensitivity (!result) Pointers & Heap (&x->lock); (&y->lock); spin_unlock Inter-procedural Scalable Error Detection using Boolean Satisfiability

  5. Saturn • What? • SAT-based approach to static bug detection • How? • SAT-based approach • Program constructs  Boolean constraints • Inference  SAT solving • Why SAT? • Program states naturally expressed as bits • The theory for bits is SAT • Efficient solvers widely available Scalable Error Detection using Boolean Satisfiability

  6. Outline • Motivation and goals • Next: Technical discussion • Straight-line code • Control flow • Pointers • Checking with Saturn • Experimental results • Related work and conclusion Scalable Error Detection using Boolean Satisfiability

  7. x31 … x0 y31 … y0 Bitwise-AND x31y31 … x0y0 == Straight-line Code void f(int x, int y) { int z = x & y ; assert(z == x); } ; z y x & == R Scalable Error Detection using Boolean Satisfiability

  8. Straight-line Code void f(int x, int y) { int z = x & y; assert(z == x); } Query: Is-Satisfiable( ) Answer: Yes x = [00…1] y = [00…0] Negated assertion is satisfiable. Therefore, the assertion may fail. R Scalable Error Detection using Boolean Satisfiability

  9. Control Flow – Preparation • Our Approach • Assumes loop free program • Unroll loops, drop backedges • May miss errors that are deeply buried • Bug finding, not verification • Many errors surface in a few iterations • Advantages • Simplicity, reduces false positives Scalable Error Detection using Boolean Satisfiability

  10. Control Flow – Example • if (c) • x = a; • else • x = b; • res = x; • Merges • preserve path sensitivity • select bits based on the values of incoming guards G = c, x: [a31…a0] G = c, x: [b31…b0] G = cc, x: [v31…v0] where vi = (cai)(cbi) if (c) c c x = a; x = b; true res = x; Scalable Error Detection using Boolean Satisfiability

  11. Pointers – Overview • May point to different locations… • Thus, use points-to sets p: { l1,…,ln } • … but only one at a time • Use guards on points-to relationships p: { (g1, l1), …, (gn, ln) } Scalable Error Detection using Boolean Satisfiability

  12. Pointers – Example G = true, p: { (true, x) } • p = &x; • if (c) • p = &y; • res = *p; if (c) res = y; else if (c) res = x; G = c, p: { (true, y) } G = true, p: { (c, y); (c, x)} Scalable Error Detection using Boolean Satisfiability

  13. Pointers – Recap • Guarded Location Sets { (g1, l1), …, (gn, ln) } • Guards • Condition under which points-to relationship holds • Mutually exclusive • Collected from statement guards • Pointer Dereference • Conditional Assignments Scalable Error Detection using Boolean Satisfiability

  14. Not Covered in the Talk • Other Constructs • Structs, … • Modeling of the environment • Optimizations • several to reduce size of formulas • some form of program slicing important • See paper . . . Scalable Error Detection using Boolean Satisfiability

  15. if (l->state == Unlocked) l->state = Locked; else l->state = Error; unlock if (l->state == Locked) l->state = Unlocked; else l->state = Error; lock unlock Error Locked Unlocked lock What can we do with Saturn? int f(lock_t *l) { lock(l); … unlock(l); } Scalable Error Detection using Boolean Satisfiability

  16. General FSM Checking • Encode FSM in the program • State  Integer • Transition  Conditional Assignments • Check code behavior • SAT queries Scalable Error Detection using Boolean Satisfiability

  17. How are we doing so far? • Precision:  • Scalability:  • SAT limit is 1M clauses • About 10 functions • Solution: • Divide and conquer • Function Summaries Scalable Error Detection using Boolean Satisfiability

  18. Function behavior can be summarized with a set of state transitions Summary: *l: Unlocked  Unlocked Locked  Error int f(lock_t *l) { lock(l); … … unlock(l); return 0; } Function Summaries (1st try) Scalable Error Detection using Boolean Satisfiability

  19. int f(lock_t *l) { lock(l); … if (err) return -1; … unlock(l); return 0; } Problem two possible output states distinguished by return value (retval == 0)… Summary 1. (retval == 0) *l: Unlocked  Unlocked Locked  Error 2. (retval == 0) *l: Unlocked  Locked Locked  Error A Difficulty Scalable Error Detection using Boolean Satisfiability

  20. FSM Function Summaries • Summary representation (simplified): { Pin, Pout, R } • User gives: • Pin: predicates on initial state • Pout: predicates on final state • Express interprocedural path sensitivity • Saturn computes: • R: guarded state transitions • Used to simulate function behavior at call site Scalable Error Detection using Boolean Satisfiability

  21. int f(lock_t *l) { lock(l); … if (err) return -1; … unlock(l); return 0; } Output predicate: Pout = { (retval == 0) } Summary (R): 1. (retval == 0) *l: Unlocked  Unlocked Locked  Error 2. (retval == 0) *l: Unlocked  Locked Locked  Error Lock Summary (2nd try) Scalable Error Detection using Boolean Satisfiability

  22. Lock checker for Linux • Parameters: • States: { Locked, Unlocked, Error } • Pin = {} • Pout = { (retval == 0) } • Experiment: • Linux Kernel 2.6.5: 4.8MLOC • ~40 lock/unlock/trylock primitives • 20 hours to analyze • 3.0GHz Pentium IV, 1GB memory Scalable Error Detection using Boolean Satisfiability

  23. Double Locking/Unlocking static void sscape_coproc_close(…) { spin_lock_irqsave(&devc->lock, flags); if (…) sscape_write(devc, DMAA_REG, 0x20); … } static void sscape_write(struct … *devc, …) { spin_lock_irqsave(&devc->lock, flags); … } Scalable Error Detection using Boolean Satisfiability

  24. Ambiguous Return State int i2o_claim_device(…) { down(&i2o_configuration_lock); if (d->owner) { up(&i2o_configuration_lock); return –EBUSY; } if (…) { return –EBUSY; } … } Scalable Error Detection using Boolean Satisfiability

  25. Bugs Previous Work: MC (31), CQual (18), <20% Bugs Scalable Error Detection using Boolean Satisfiability

  26. Function Summary Database • 63,000 functions in Linux • More than 23,000 are lock related • 17,000 with locking constraints on entry • Around 9,000 affects more than one lock • 193 lock wrappers • 375 unlock wrappers • 36 with return value/lock state correlation Scalable Error Detection using Boolean Satisfiability

  27. Why SAT? (Retrospect) • Moore’s Law • Uniform modeling of constructs as bits • Constraints • Local specification • Global solution • Incremental SAT solving • makes multiple queries efficient Scalable Error Detection using Boolean Satisfiability

  28. Related Work • Bug Detection Tools • SLAM (Ball & Rajamani, MSR) • BLAST (Henzinger et. al., UCB) • MC (Engler et. al., Stanford) • ESP (Das et. al., MSR) • PREfix (Bush & Pincus, MSR) • CQual (Foster & Aiken, UCB) • SAT-based tools • CBMC (Clarke et. al., CMU) • Magic (Chaki et. al., CMU) Scalable Error Detection using Boolean Satisfiability

  29. Thank you! Project Web-page: http://glide.stanford.edu/saturn/ Or, Google: “Saturn, Boolean” Email: saturn@glide.stanford.edu Scalable Error Detection using Boolean Satisfiability