1. Automated Refinement Checking of Concurrent Systems Sudipta Kundu, Sorin Lerner, Rajesh Gupta Department of Computer Science and Engineering, University of California, San Diego

2. 2 Power Perfor mance Area Hardware Design Methodology Algorithmic Description RTL Description Functionally Equivalent Behavior Description Functionally Equivalent Functionally Equivalent Controller S0 S1 S2S3 S4 f !f Data path …. x = a * b; c = a < b; if (c) then a = b – x; else a = b + x; a = a + x; b = b * x; ….  C/C++, SystemC  Verilog, VHDL High Level Synthesis

3. 3 The Model Properties of interest: Concurrency Visible events Model both the specification and implementation Formal semantics Various modeling languages Process Algebra [CSP, CCS] Petri Nets SpecC/SystemC

4. 4 The Problem CSP Program (Specification) Transformed CSP Program (Implementation) Refinements (Trace) Refinement Checker

5. 5 Previous Work Manual Semi Automatic Fully Automatic Infinite Finite Level of Automation State Space Relational Approach [Josephs 88] FDR Model Checker [FDR 05, Roscoe 95] Interactive Theorem Provers [Dutertre 97] [Tej 97] [Isobe 05] Our Approach Inspired by translation validation [Necula 00] [Pnueli 98] Previous work in Refinement Checking of CSP programs

6. 6 Outline 1.Motivation and Problem definition 2.Algorithms Checking Algorithm Inference Algorithm 3.Experiments and Results 4.Conclusion

7. 7 An Example of Refinement left Link right Specification: v14*v1 v14*v1 2*v1 Implementation: sendrecv mid ack right left v1 2*v1

8. 8 A relation R that matches a given program state in the implementation with the corresponding state in the specification. The simulation relation is a set of entries of the form (p 1, p 2, Ф). p 1 – program point in Specification p 2 – program point in Implementation Ф – formula that relates the data CFGs for the Example Specification left?a w:=a*4 right!w Link Implementation | left?x y:=x*2 ack?_ SendRecv mid!y mid?u z:=u*2 ack!1 right!z Split state space in two parts: control flow state, which is finite. => explored by traversing the CFG dataflow state, which may be infinite. => explored using Automated Theorem Prover (ATP) a == x True w == z Simulation Relation

9. 9 Checking Algorithm Specification Implementation left?a w:=a*4 right!w Link | left?x y:=x*2 ack?_ SendRecv mid!y mid?u z:=u*2 ack!1 right!z C2: a == x C3: w == z C1: True SpecImpl C1: True left ? aleft ? x C2: a == x SpecImpl C2: a == x w = a*4 y = x*2 u = y (mid?u :: mid!y) z = u*2 C3: w == z SpecImpl C3: w == z right!wright!z left?a _ = 1 left?x C2: a == x ATP[C1 => WP(C2)] ATP[(C2) => WP(C3)] ATP[(C3) => WP(C2)]

10. 10 Outline 1.Motivation and Problem definition 2.Algorithms Checking Algorithm Inference Algorithm 3.Experiments and Results 4.Conclusion

11. 11 Inference Algorithm It works in two steps. Forward pass: collect local condition for externally visible events to be matched. Backward pass: propagate local conditions backward, using weakest preconditions. May not terminate Loops - iterate to a fixed point In practice it can find the required simulation relation.

12. 12 Inference Algorithm: Forward Pass SpecImpl C1 -> C2 Specification left?a w:=a*4 right!w Link Implementation | left?x y:=x*2 ack?_ SendRecv mid!y mid?u z:=u*2 ack!1 right!z w = a*4 y = x*2 u = y z = u*2 right!wright!z left?a _ = 1 left?x left ? aleft ? x C1 C2 C3: w == z C2 -> C3 C3 -> C2

13. 13 Inference Algorithm: Backward Pass SpecImpl Specification left?a w:=a*4 right!w Link Implementation | left?x y:=x*2 ack?_ SendRecv mid!y mid?u z:=u*2 ack!1 right!z w = a*4 y = x*2 u = y z = u*2 right!wright!z left?a _ = 1 left?x left ? aleft ? x C1: True C2: True C3: w == z C2: True C2: a == x C1: True C3: w == z ATP[C2 -> WP(C3)] C2: C2 & WP(C3) ATP[C3 -> WP(C2)] ATP[C1 -> WP(C2)]

14. 14 Outline 1.Motivation and Problem definition 2.Algorithms Checking Algorithm Inference Algorithm 3.Experiments and Results 4.Conclusion

15. 15 Prototype Implementation - ARCCoS CSP Specification CSP Specification Front End Parser Specification (CFG) CSP Implementation CSP Implementation Implementation (CFG) Automated Theorem Prover (Simplify) ARCCoSARCCoS Simulation Relation Simulation Relation Inference Engine Partial Order Reduction Engine Checking Engine

16. 16 Results from ARCCoS Descriptions#ProcessTime (no PO) (min:sec) Time (PO) (min:sec) SpecImplTotal Simple buffer34700:00 Simple vending machine11200:00 Cyclic scheduler33601:0100:49 College student tracking system12300:01 Single communication link381100:01 2 parallel communication links6121801:2800:04 3 parallel communication links91625514:5200:21 4 parallel communication links122032DNT01:11 5 parallel communication links152439DNT02:32 6 parallel communication links182846DNT08:29 7 parallel communication links213253DNT37:28 Hardware refinement35800:00 EP2 System12301:5101:47

17. 17 Outline 1.Motivation and Problem definition 2.Algorithms Checking Algorithm Inference Algorithm 3.Experiments and Results 4.Conclusion

18. 18 Conclusion and Future Directions We have presented an automated algorithm for checking trace refinement of CSP programs that has infinite state spaces. Checking Algorithm Inference Algorithm The work presented here is only the first step in a broader research plan whose goal is to check the refinement of SystemC.

19. 19 Thank You