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Data Structure Repair

Data Structure Repair. Data structure repair problem. Broken Data Structure. Errors Missing elements Inappropriate sharing Dangling references Out of bounds array indices Inconsistent values. F = 20 G = 10 . F = 20 G = 5 . I = 5. J = 2. Solution. Broken Data Structure.

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Data Structure Repair

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  1. Data Structure Repair

  2. Data structure repair problem Broken Data Structure Errors • Missing elements • Inappropriate sharing • Dangling references • Out of bounds array indices • Inconsistent values F = 20 G = 10 F = 20 G = 5 I = 5 J = 2

  3. Solution Broken Data Structure Consistent Data Structure F = 20 G = 10 F = 2 G = 1 F = 10 G = 5 F = 20 G = 10 F = 20 G = 5 Repair Algorithm I = 3 I = 5 J = 2 J = 2

  4. Repair is computed over abstract model Broken Abstract Model Repaired Abstract Model Abstract Repair Model Definition Rules 10111001011 10101011101 10101110110 00011001011 10101011101 10101110110 Concrete Data Structure Updates Broken Bits Repaired Bits

  5. Reasoning at Compile Time • Compile specifications into repair algorithms • Goal-directed reasoning takes place at compile time • Consider possibility that |Bitmap| = 0 • Abstract repair • Choose a block in Free set • Add block to Bitmap set • Concrete repair • Find relevant model definition rule: true  d.block[d.blockbitmap]  Bitmap • Goal-directed reasoning finds following update: d.blockbitmap = index of block in d.block array • Check that block is an element of d.block array: b in [0..numblocks-1], d.block[b] Used d.block[b]Free

  6. Multiple Repairs • Some broken data structures may require multiple repairs • Reconstruct model • Reevaluate consistency constraints • Perform any required additional repairs

  7. Architecture Broken Abstract Model Repaired Abstract Model Abstract Repair . . . . Model Translation 10111001011 10101011101 10101110110 01011001011 10101011101 10101110110 00011001011 10101011101 10101110110 . . . . Automatically Generated Concrete Repair Broken Bits Repaired Bits

  8. Acyclic Repair Dependences • Questions • Isn’t it possible for the repair of one constraint to invalidate another constraint? • What about infinite repair loops? • What about unsatisfiable specifications? • Answer • We require specifications to have no cyclic repair dependences between constraints • So all generated repair sequences terminate • Repair can fail only because of resource limitations • But, some repairs are never attempted

  9. Repair Dependence Graph 4. Satisfy Rule 6 (BlockStatus) 1. |Bitmap|=1 2. Add block to Bitmap 5. f.BlockStatus=false 3. d.blockbitmap=indexof(bfree) 6. Replace <f,true> with <f,false> in BlockStatus 8. Remove <f,true> from BlockStatus by removing Bitmap 7. b.bitmap[j]=false for j=indexof(f)

  10. Repair Dependence Graph 4. Satisfy Rule 6 (BlockStatus) 1. |Bitmap|=1 2. Add block to Bitmap 5. f.BlockStatus=false 3. d.blockbitmap=indexof(bfree) 6. Replace <f,true> with <f,false> in BlockStatus 8. Remove <f,true> from BlockStatus by removing Bitmap 7. b.bitmap[j]=false for j=indexof(f)

  11. Repair Dependence Graph 4. Satisfy Rule 6 (BlockStatus) 1. |Bitmap|=1 2. Add block to Bitmap 5. f.BlockStatus=false 3. d.blockbitmap=indexof(bfree) 6. Replace <f,true> with <f,false> in BlockStatus 7. b.bitmap[j]=false for j=indexof(f)

  12. When to Test for Consistency and Repair • Persistent data structures • Repair can be independent activity, or • Repair when data written out or read in • Volatile data structures in running program • Under programmer control • Transaction-based approach • Identify transaction start and end • Repair at start, end, or both • Failure-based approach • Wait until program fails • Repair and restart from latest safe point

  13. Experience • We acquired five benchmarks (written in C/C++) • AbiWord • x86 emulator • CTAS (air-traffic control tool) • Simplified Linux file system • Freeciv interactive game • We developed specifications for all five • Little development time (days, not weeks) • Most of time spent figuring out Freeciv and CTAS • Each benchmark has • Workload • Bug or fault insertion methodology • Ran benchmarks with and without repair

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