1. Verifying Atomicity via Data Independence Ohad Shacham Yahoo Labs, Israel Eran Yahav Technion, Israel Guy Gueta Yahoo Labs, Israel Alex Aiken Stanford University, USA Nathan Bronson Stanford University, USA Mooly Sagiv Tel Aviv University, Israel Martin Vechev ETH, Zurich

2. Concurrent Data Structures Writing highly concurrent data structures is complicated Modern programming languages provide efficient concurrent collections with atomic operations. … … … … … … … …

3. TOMCAT Motivating Example attr = new HashMap(); … Attribute removeAttribute(String name){ Attribute val = null; synchronized(attr) { found = attr.containsKey(name) ; if (found) { val = attr.get(name); attr.remove(name); } return val; } TOMCAT 5.*TOMCAT 6.* Invariant: removeAttribute(name) returns the value it removes from attr or null attr = new ConcurrentHashMap(); … Attribute removeAttribute(String name){ Attribute val = null; /* synchronized(attr) { */ found = attr.containsKey(name) ; if (found) { val = attr.get(name); attr.remove(name); } /* } */ return val; }

4. removeAttribute(“A”) { Attribute val = null; found = attr.containsKey(“A”) ; if (found) { val = attr.get(“A”); attr.remove(“A”); } return val; attr.put(“A”, o); attr.remove(“A”); o

5. Violation Detection Testing Atomicity of Composed Concurrent Operation – OOPSLA’11 Use library influence specification for POR Many violations we found in real applications Many were already fixed

6. Challenge Verifying the atomicity of composed operations … … … … … … … …

7. Challenges in Verification What do we want to check? –Specifying software correctness Scalability of static checking –Large programs Many sources of unboundedness –Inputs –# threads –# operations

8. Challenges in Verification What do we want to check? –Specifying software correctness Scalability of static checking –Large programs Many sources of unboundedness –Inputs –# threads –# operations

9. Linearizability Check that composed operations are Linearizable [Herlihy & Wing, TOPLAS’90] –Returns the same result as some sequential run

10. Linearizability removeAttribute(“A”) { Attribute val = null; found = attr.containsKey(“A”) ; if (found) { val = attr.get(“A”); attr.remove(“A”); } return val; attr.put(“A”, o); attr.remove(“A”); attr.put(“A”, o); attr.remove(“A”); removeAttribute(“A”) { Attribute val = null; found = attr.containsKey(“A”) ; if (found) { return val; removeAttribute(“A”) { Attribute val = null; found = attr.containsKey(“A”) ; if (found) { return val; attr.put(“A”, o); attr.remove(“A”); attr.put(“A”, o); attr.remove(“A”); removeAttribute(“A”) { Attribute val = null; found = attr.containsKey(“A”) ; if (found) { val = attr.get(“A”); attr.remove(“A”); } return val; o o null o o o

11. Challenges in Verification What do we want to check? –Specifying software correctness Scalability of static checking –Large programs Many sources of unboundedness –Inputs –# threads –# operations

12. Modular Checking Modularity Generates simple traces Base linearizabilityRestrict generated traces Enables Env control

13. removeAttribute(“A”) { Attribute val = null; found = attr.containsKey(“A”) ; if (found) { val = attr.get(“A”); attr.remove(“A”); } return val; attr.put(“A”, o); attr.remove(“A”); Modular Checking

14. Challenges in Verification What do we want to check? –Specifying software correctness Scalability of static checking –Large programs Many sources of unboundedness –Inputs –# threads –# operations

15. Modular Checking RA(“A”) RA(“F”) p(“R”) d(“R”) g(“B”) …

16. Modular Checking RA(“A”) p(“R”) d(“R”) g(“B”) …

17. Modular Checking RA(“A”) p(“A”) d(“A”)

18. Data Independence [Wolper, POPL’86] Attribute removeAttribute(String name){ Attribute val = null; found = attr.containsKey(name) ; if (found) { val = attr.get(name); attr.remove(name); } return val; } Attribute removeAttribute(String name){ Attribute val = null; found = attr.containsKey(name) ; if (found) { val = attr.get(name); attr.remove(name); } return val; } Attribute removeAttribute(String name){ Attribute val = null; found = attr.containsKey(name) ; if (found) { val = attr.get(name); attr.remove(name); } return val; } Attribute removeAttribute(String name) { Attribute val = null; found = attr.containsKey(name) ; if (found) { val = attr.get(name); attr.remove(name); } return val; } Program behaves the same for all Inputs

19. Data Independence for CCC Wolper’s definition is too restrictive for real life CCC We defined a data independence of linearizability for CCC A CCC is linearizable for a single input iff it is linearizable for every input

20. Data Independence Syntactic Rules Data Independence detection is in general undecidable Syntactic rules that imply a program as data-independent Attribute removeAttribute(String name){ Attribute val = null; found = attr.containsKey(name) ; if (found) { val = attr.get(name); attr.remove(name); } return val; }

21. Verifying Data Independent Operations Data independentVerified using single input Influence CO adds one value Map elements are bounded Single Mutation

22. Verifying data independent operations Small model reduction Decidable when the local state is bounded Explore all possible executions using: –One input key and finite number of values –Influenced based environment uses single value Employ a model check

25. Summary Writing concurrent data structures is hard Employing atomic library operations is error prone Modular linearizability checking Leverage influence Leverage data independence Prove the linearizability of several composed operations Simple and efficient technique