2. Formal Design and Verification Methods for Shared Memory Systems Ratan Nalumasu Dissertation Defense September 10, 1998

3. 9/10/1998Design Complexity2 Problems Facing Digital Design Complexity Longer design time Shorter time to market

4. 9/10/1998Design Complexity3 Current Debugging Technology +Full model –Partial examination  No assurance –Weaker properties –Difficult correctness metrics –Full model

5. 9/10/1998Introduction to FM4 Formal Methods Formal methods = Math based techniques Continuous math : Engineering = Discrete math : Digital system design “It is what the designers want. It’s just challenging to prove.”

6. 9/10/1998Introduction to FM5 Formal Methods based Design –Reduced model +Complete examination +Better assurances (on the reduced model) +Stronger property language +Better correctness metrics +Reduced model

7. 9/10/1998Introduction to FM6 FM Taxonomy Manual verification techniques: Interactive theorem provers Automatic verification techniques: Model checkers Compilation techniques: Refinement rules

8. 9/10/1998Theorem Provers7 Interactive Theorem Provers +Can deal with infinite state systems –Extensive manual reasoning Proof of a compilation scheme +Good for algorithm verification

9. 9/10/1998Model Checking8 process p(x) { global G; local L; while (...) { recv...; send...; } process q(x,y)... 2 0 1 3 (G=0, p.L=0,...)

10. 9/10/1998Model Checking9 Model Checking Strengths Automatic If property fails, model checker shows the error trace –Deadlock: How initial state reached it –Assertion: How initial state reached it –Starvation: A loop where no progress is made

11. 9/10/1998Model Checking10 Model Checking: Example Construct graph of the system, and check the property: Deadlock at (22) 0 1 2 0 1 20 1010 2020 2121 2 0101 10202 1212 State Explosion Partial Order Reductions

12. 9/10/1998Refinement Algorithms11 Refinement Algorithms Need to verify only high-level protocols Domain-specific compilers can generate efficient implementations Refinement rules for DSM protocols

13. 9/10/1998Applied FM12 State of the art of Applied FM +General purpose +Widely applicable techniques –Inefficient algorithms –Inefficient “compilers” –Do not help with domain specific concerns

14. 9/10/199813 Thesis Statement Domain specific formal methods Efficient verification techniques Address domain specific concerns Domain: Memory CPU Memory

15. 9/10/199814 Overview Introduction to formal verification K Shared memory systems Contributions Conclusions

16. 9/10/1998Memory Bottleneck15 Memory Bottleneck Processor speed increases at 55% a year, while memory speed increases at 7% –Caches Tendency toward multiprocessors –Further imbalance  complex protocols –SMP systems –DSM systems

17. 9/10/1998SMP Architecture16 Symmetric Multiprocessors Can scale upto 10s of processors Modern caches have support for such SMP protocols CPU $ Memory CPU $ CPU $

18. 9/10/1998SMP Protocols17 SMP Protocol Design Bus protocols –Bus arbitration algorithm –Cache invalidation scheme –Lack of atomicity on the bus Bus and CPU interaction –Does CPU have out-of-order execution? –Does bus allow out-of-order completion? Are these decisions visible to software?

19. 9/10/1998DSM Architecture18 Distributed Shared Memory NODE MEM Network Each node may be a SMP or a single CPU

20. 9/10/1998DSM Protocols19 DSM Protocol Design Network port arbitration Coherency maintenance across the network –Maintaining distributed state –Little atomicity –“Ghost” messages –Transient states Are these decisions visible to software?

21. 9/10/1998Shared Memory Systems20 Shared Memory Correctness Low level: –deadlock –forward progress –bus arbitration Intermediate level: –at most one owner of a cache line at a time High-level: –abstraction provided to the software

22. 9/10/1998Software Interface21 Abstraction Provided to Software Multiprocessor: P1 write(a,new) read(b) P2 write(b,new) read(a) P1 read(b) write(a,new) P2 read(a) write(b, new) Not ok under S.C. Uniprocessor: P1 write(a,new) read(b) P1 read(b) write(a,new) ok cache/compiler/ out-of-order execution Test model checking

23. 9/10/199822 Overview Introduction to formal verification Shared Memory systems K Contributions –mitigating state explosion Partial order reduction algorithm –facilitating high-level design Protocol synthesis algorithm –enhancing applicability High-level correctness such as SC Conclusions

24. 9/10/1998Contributions23 Contributions Protocol PO algorithm 1 Test Model checking 2 2 Refinement rules 3 Efficient implementation 3

25. Contribution #1 Mitigating State Explosion Problem Partial Order Reductions

26. 9/10/1998PO Reductions25 Partial Order Reductions0 1010 2020 2121 2 0 1 2 0 1 20 1010 2020 2121 2 0101 10202 1212 If two transitions are independent, then explore one of them postponing the other

27. 9/10/1998PO Reductions26 Ignoring Problem Select some transitions, and postpone others  but do not postpone forever S0 S1 Postponed

28. 9/10/1998PO Reductions27 Proviso based Solution Godefroid, Valmari, Holzmann, Peled’s solutions are very similar: Proviso –Expands the “last” state of the loop completely S0 S1 Postponed Expand

29. 9/10/1998PO Reductions28 Problem with Proviso 12 11012100 Q postponed 10 20 2202 ALL 9 states 0 12P 0 12Q

30. 9/10/1998PO Reductions29 Our Algorithm: 2-phase 00 011020 02 0 12P 0 12Q Only 5 states

31. 9/10/1998PO Reductions30 Performance Comparison (20x)

32. Contribution #2 Facilitating High-level Design Protocol Refinement

33. 9/10/1998Refinement Algorithms32 Protocol Refinement PO reductions not sufficient, theorem provers ruled out Compile from high-level protocol specification –easier to design –easier to verify –can generate efficient implementation using domain knowledge

34. 9/10/1998Refinement Algorithms33 Unexpected Messages P recv ack from Q Send a req to Q Some request ??? Always nack  no forward progress Always Silence  Deadlock

35. 9/10/1998Refinement Algorithms34 Refinement Procedures Debug the high-level specification: Synchronous communication with no transient states Automatic refinement procedures transforms it into detailed implementation –No need to verify the implementation –Needs domain specific knowledge for efficiency

36. 9/10/1998Refinement Algorithms35 Related Work Buckley & Silberschatz, 83 –For OS environments, not fit for hardware Gribomont,90 –Protocols where synchronous messages can be simply replaced by asynchronous messages

37. 9/10/1998Refinement Algorithms36 Related Work (contd) Teapot, 96 for DSM systems (Chandra) –Protocol programming language –“Suspend” construct for transient states –Not high-level: Suspend states still specify what to do in a transient state

38. 9/10/1998Refinement Algorithms37 Context: DSM Protocols Network Protocol per each cache line 1 home, n “remote” nodes per each line Home is responsible for maintaining consistency (Hub) NODE MEM NODE MEM NODE MEM

39. 9/10/1998Refinement Algorithms38 Refinement Rules Req Ack or Nack Home Remote Req Ack or Nack HomeRemote

40. 9/10/1998Refinement Algorithms39 Refinement Rules (2) Req1 is ignored by both processes HomeRemote Req1 Req2 Ack or Nack

41. 9/10/1998Refinement Algorithms40 Debugging Effort Protocol compilation scheme has been proved using a theorem prover

42. Contribution #3 Enhancing Applicability Shared Memory Model Verification

43. 9/10/1998Test Model Checking42 Relaxing Instruction Orders P1 write(a,new) read(b) P2 write(b,new) read(a) P1 read(b) write(a,new) P2 read(a) write(b,new) Under SC

44. 9/10/1998Test Model Checking43 Verification of HW/SW Interface SC: The result can be explained by some interleaving of the instructions. Test model checking CPU $ Memory CPU $ CPU $

45. 9/10/1998Test Model Checking44 Current Verification Techniques Simulation –Must study lengthy executions –Must choose non-trivial programs Formal techniques (next slide)

46. 9/10/1998Test Model Checking45 Related Work Graf’s Lazy caching in ACTL* Gibbons approach  run programs and check if the results are SC McMillan’s thesis  data abstraction for a test Hojati  data abstraction in a different context Undecidability result by Alur et al

47. 9/10/1998Test Model Checking46 ACTL* for (stronger than) SC AG(enabled( read(a,d) ))  avail(a,d) AG(avail(a,d) AND EF(enable(read(a,d))))  A[NOT avail(a,d) W AG NOT avail(a,d)]... init  AG[after(write(a,d))  A(NOT enabled(read(a,d) W avail(a,d))] Such MODEL DEPENDENT SPECS do not fit in an iterative industrial frame

48. 9/10/1998Test Model Checking47 Test Model Checking Adaptation of simulation to model checking –model checking (full coverage) + testing (“black box approach’’) Tests are independent of the model being verified  manual effort is considerably reduced –Test model-checking can be used early in the design cycle

49. 9/10/1998Test Model Checking48 Results Defined a shared memory description language –“data is not used for control decisions” –“addresses are symmetric” –Can specify HP’s Runway/PA,... Model checking technique –“Small number of addresses is sufficient” Application to runway/PA using PV

50. 9/10/1998Test Model Checking49 If P1 executes two write instructions, then P2 sees them in the program order of P1 P1 A := 1 A := 2 A := 3.... A := k P2 X1 := A X2 := A X3 := A.... Xk := A Many deficiencies Read Order, Write Order X(i+1)  X(i)

51. 9/10/1998Test Model Checking50 Deficiencies of the Test Finite k –What if an error occurs for a really large k? Location “A” is never written by P2 –What if an error occurs when the ownership changes? Only 1-address –The definitions of RO and WO are not restricted to a single address at a time –How many addresses to consider?

52. 9/10/1998Test Model Checking51 Data abstraction + non-determinism Unbounded k rd(1) rd(0) rd(1) wr(0) wr(1) Non-deterministic change

53. 9/10/1998Test Model Checking52 Ownership Changes rd(1) rd(0) rd(1) wr(0) wr(1) or rd(-) or wr(2) Complete 1-address test

54. 9/10/1998Test Model Checking53 2-address (RO, WO) test wr(1) rd(0) rd(-) OR wr(0) rd(-) OR wr(2) rd(-) OR wr(1) rd(1) rd(A,-) OR rd(B,-) OR wr(A,0) OR wr(B,0) rd(A,-) OR wr(A,1) OR rd(B,-) OR wr(B,1) rd(A,-) OR or rd(B-) OR wr(A,2) OR wr(B,2) rd(B,1)wr(A,1) rd(A,0)

55. 9/10/1998Test Model Checking54 2-address (RO, WO) test rd(A,-) OR rd(B,-) OR wr(A,0) OR wr(B,0) rd(A,-) OR wr(A,1) OR rd(B,-) OR wr(B,1) rd(A,-) OR or rd(B-) OR wr(A,2) OR wr(B,2) rd(B,1)wr(A,1) rd(A,0)

56. 9/10/1998Test Model Checking55 Complete Test for (RO, WO) Theorem: A system implements (RO, WO) if and only if it has no errors on all 1- and 2-address programs Complete 1-address and 2-address tests

57. 9/10/1998Test Model Checking56 Program Order PO generalizes RO and WO to include orderings between a read followed by write, and write followed by read rd(A) rd(B) wr(A) rd(B) RO RW WR PO

58. 9/10/1998Test Model Checking57 All processors agree on the order of writes –WO imposes the order only if the writes are from same program Write Atomicity wr(A,0) wr(B,1) SC is (PO, WA)

59. 9/10/1998Test Model Checking58 1-address SC test ORDER: 1, 4 OR 4, 1P0 A := 0 rd(A) A := 1 A := 2 rd(A)P1 A := 3 rd(A) A := 4 A := 5 rd(A) Barrier

60. 9/10/1998Test Model Checking59 Complete Tests for SC Theorem: A system with N processors implements SC if and only if it has no errors on programs n<N address programs Scheme for N processors –N barriers –Data written before, at, and after barrier are different data 0, 1, 2 for P0, and data 3, 4, 5 for P1

61. 9/10/1998Test Model Checking60 Case Studies Serial memory (operational semantics of SC) Lazy caching Runway/PA system model –Bus based design –An aggressive split transaction protocol –Out-of-order completion of transactions on Runway for high-performance –In-order completion of instructions in PA for sequential consistency

62. 9/10/1998Test Model Checking61 Test Model checking of HP/Runway

63. 9/10/199862 Conclusion Showed that specializing formal methods for a particular domain (shared memory) leads to efficient verification techniques for the domain, and increases the applicability of the formal methods –Two phase algorithm –Refinement procedure –Memory model verification

64. 9/10/199863 Future Work Model checking algorithms –better partial order algorithms –tune for test model checking Protocol synthesis –More optimizations Test model checking –Weaker memory models, other objects –Application to other fields

65. 9/10/1998Model Checking64 h!msg (Remote) T h?m h?m2 (Home) T r(i)?m r(j)!m’ Communication States

66. 9/10/1998Model Checking65 Debugging Effort Protocol compilation scheme has been proved using a theorem prover