Action Language: A Specification Language for Model Checking Reactive Systems

1. Action Language: A Specification Language for Model Checking Reactive Systems Tevfik Bultan Department of Computer Science University of California, Santa Barbara bultan@cs.ucsb.edu http://www.cs.ucsb.edu/~bultan/

2. Initial Goal • To develop an input language for a model checker that is based on following techniques: • [Bultan, Gerber, Pugh 97, 99] Using Presburger arithmetic constraints for model checking infinite state systems • [Bultan, Gerber, League 98, 00] Composite model checking: Model checking with type-specific symbolic representations (using Presburger arithmetic constraints and BDDs together) • How about a broader perspective?

3. Model Checking Software Specifications • [Atlee, Gannon 93] Translating SCR mode transition tables to input language of explicit state model checker EMC [Clarke, Emerson, Sistla 86] • [Chan et al. 98] Translating RSML specifications to input language of symbolic model checker SMV [McMillan 93] • [Bharadwaj, Heitmeyer 99] Translating SCR specifications to Promela, input language of automata-theoretic explicit state model checker SPIN [Holzmann 97]

4. Issues Addressed in These Studies • Using abstractions and simplifications to avoid the state-space explosion problem • State-space explosion is the main weakness of model checking • Expressing correctness properties in temporal logics • Translation from a high level specification language • SCR, RSML, Statecharts to a lower level specification language • input language of the model checker: Promela, SMV

5. Language Translation Reactive System Specification (Statecharts, RSML, SCR) • Why should we have two languages? • User can make abstractions on the intermediate language • User can interact with various options of the model checker using the intermediate language • Separation of concerns • Analogy: A programming language and instruction set of a microprocessor • Input language of the model checker is like an assembly language Translation requires abstractions or simplifications Input Language of the Model Checker (Promela, SMV) Automated translation by the model checker Transition System Model

6. Revised Goal • Develop a low level specification language for model checking • The language should be able to “handle” different high level specification languages • The language should expose the structure of the transition system model for interactive use of the model checker

7. Outline • Model Checking • Symbolic model checking • Automata theoretic model checking • Action Language • Actions: State Changes • Synchronous vs. Asynchronous Composition • Translating Statecharts to Action Language • Translating SCR to Action Language • Conclusions and Future Work

8. Model Checking View • Every reactive system • safety-critical software specification, • cache coherence protocol, • communication protocol, etc. is represented as a transition system: • S : The set of states • I  S : The set of initial states • R  S  S: The transition relation

9. Model Checking View • Properties of reactive systems are expressed in temporal logics • Invariant(p) : is true in a state if property p is true in every state reachable from that state • Also known as AG • Eventually(p) : is true in a state if property p is true at some state on every execution path from that state • Also known as AF

10. Model Checking Technique Given a program and a temporal propertyp: • Either show that all the initial states satisfy the temporal propertyp • set of initial states  truth set of p • Or find an initial state which does not satisfy the propertyp • a state  set of initial states  truth set of p

11. Symbolic Model Checking • Represent sets of states and the transition relation using Boolean logic formulas (and linear arithmetic formulas). • Represent these formulas using an efficient data structure (such as BDDs) • Using this data structures compute the truth set of temporal logic formulas: backward, or forward fixpoint computations

12. Automata-Theoretic Model Checking • Represent the negation of the input temporal property as a Büchi automata • Represent the transition system as a Büchi automata • Take the synchronous product of these two automata • If the language accepted by the product automata is empty, then the property is true. If not generate a counter-example.

13. Action Language • A state based language, actions correspond to state changes • Unlike CCS • Transition relation is defined using actions • Basic actions: Predicates on current and next state variables • Action composition: synchronous or asynchronous • Modular • Local, imported, exported, shared variables • Modules can be composed using synchronous or asynchronous composition

14. Action Language – TLA Connection • Similarities: • Transition relation is defined using predicates on current and next state variables • Each predicate is defined mathematically using • integer arithmetic, boolean logic, etc. • Differences: In Action Language • Temporal operators are not used in defining the transition relation • Dual language approach: temporal properties are redundant, they are used to check correctness • Synchronous and asynchronous composition operators are not equivalent to logical operators

15. An Action Language Specification module producer_consumer integer produced, consumed, count; parameterized integer size; initial : produced = consumed = count = 0; restrict : size >= 1; producer : count < size & count’ = count + 1 & produced’ = produced + 1; consumer : count > 0 & count’ = count – 1; & consumed’ = consumed + 1; producer_consumer : producer | consumer; spec : invariant(produced – consumed = count & count <= size); endmodule

16. A Closer Look at Action Language S : Cartesian product of variable domains defines the set of states module producer_consumer integer produced, consumed, count; parameterized integer size; initial : produced = consumed = count = 0; restrict : size >= 1; producer : count < size & count’ = count + 1 & produced’ = produced + 1; consumer : count > 0 & count’ = count – 1; & consumed’ = consumed + 1; producer_consumer : producer | consumer; spec : invariant(produced – consumed = count & count <= size); endmodule I : Predicate defining the initial states S : Restricts set of states R : Atomic actions of the system used to define the transition relation R : Defines the transition relation Temporal property

17. Actions in Action Language • Basic actions (no composition) • Predicates on current and next state variables • Current state variable: produced • Next state variable: produced’ • Logical operators • Negation ! • Conjunction & • Disjunction | • An action is a predicate: count < size & count’ = count + 1 & produced’ = produced + 1

18. No Assignments, Guards, Ifs, etc. • Assignment • x’ = y + 1 • Equivalent to x’ – 1 = y, 0 = y – x’ + 1 • Guarded commands • x > 0 & x’=y+1 • If-then-else • (x > 0 & x’=x+1) | (!(x > 0) & x’=x-1) guard assignment

19. Composition in Action Language • There are two basic composition operators in action language • Asynchronous composition: a1 | a2 • Synchronous composition: a1 & a2 • Asynchronous composition is almost equivalent to logical OR • Synchronous composition is almost equivalent to logical AND

20. Asynchronous Composition • Asynchronous composition is equivalent to logical OR if composed actions have the same next state variables a1 : i > 0 & i’ = i + 1; a2 : i <= 0 & i’ = i – 1; a3 : a1 | a2 a3 : (i > 0 & i’ = i + 1) | (i <= 0 & i’ = i – 1);

21. Asynchronous Composition • Asynchronous composition preserves values of variables which are not explicitly updated a1 : i > j & i’ = j; a2 : i <= j & j’ = i; a3 : a1 | a2; a3 : (i > j & i’ = j) & j’ = j | (i <= j & j’ = i) & i’ = i

22. Asynchronous Composition Example module producer_consumer integer produced, consumed, count; parameterized integer size; initial : produced = consumed = count = 0; restrict : size >= 1; producer : count < size & count’ = count + 1 & produced’ = produced + 1; consumer : count > 0 & count’ = count – 1; & consumed’ = consumed + 1; producer_consumer : producer | consumer; spec : invariant(produced – consumed = count & count <= size); endmodule

23. Synchronous Composition • Synchronous composition is equivalent to logical AND if two actions do not disable each other a1 : i’ = i + 1; a2 : j’ = j + 1; a3 : a1 & a2; a3 : i’ = i + 1 & j’ = j + 1;

24. Synchronous Composition • A disabled action does not block synchronous composition a1 : i < max & i’ = i + 1; a2 : j < max & j’ = j + 1; a3 : a1 & a2; a3 : (i < max & i’ = i + 1 | i >= max & i’ = i) & (j < max & j’ = j + 1 | j >= max & j’ = j);

25. Modules in Action Language • A module has • A set of states • A set of initial states • A transition relation • Modules can be composed like actions using asynchronous and synchronous composition

26. Shared Variables • Modules can share variables exported :gives read access to other modules imported :gets read access of an exported variable shared :both read and write accessed by different modules

27. Modular Producer-Consumer Example module producer integer produced; shared integer count; shared parameterized integer size; initial : produced = 0; restrict : size>=1; producer : count<size & count’=count+1 & produced’=produced+1; endmodule module consumer integer consumed; shared integer count; shared parameterized integer size; initial : consumed = 0; restrict : size >= 1; consumer : count>0 & count’=count–1; & consumed’=consumed+1; endmodule module producer_consumer module producer, consumer; shared int count = 0; initial count=0; producer_consumer : producer | consumer; spec : invariant(produced – consumed = count) & count <= size); endmodule

28. Temporal Properties in Action Language • Temporal properties can be declared using high level temporal operators • invariant • eventually • Or CTL temporal operators • AG, AF, etc.

29. Statecharts • Hierarchical state machines • States can be combined to form superstates • OR decomposition of a superstate • The system can be in only one of the OR states at any given time • AND decomposition of a superstate • The system has to be in both AND states at the same time • Transitions • Transitions between states

30. Statecharts to Action Language • Statecharts transitions (arcs) correspond to actions • OR states correspond to enumerated variables and they define the state space • Transitions (actions) of OR states are combined using asynchronous composition • Transitions (actions) of AND states are combined using synchronous composition

31. Statecharts to Action Language Alarm module AlSys enum Alarm {Shut, Op}; enum Mode {On, Off}; enum Vol {1, 2}; initial : Alarm=Shut & Mode=Off & Vol=1; t1 : Alarm=Shut & Alarm’=Op & Mode’=On & Vol’=1; t2 : Alarm=Shut & Alarm’=Op & Mode’=Off & Vol’=1; t3 : Alarm=Op & Alarm’=Shut; t4 : Alarm=Op & Mode=On & Mode’=Off; t5 : Alarm=Op & Mode=Off & Mode’=On; ... AlSys : t1 | t2 | t3 | (t4 | t5) & (t6 | t7); endmodule Shut t1 t2 Op t3 Mode Vol On 1 t4 t5 t6 t7 Off 2

32. SCR • Tabular specifications • Mode transition tables • Condition tables • Event tables • Events • @T(c) = c  c’ • In action language: !c & c’ • @T(c) WHEN d = c  c’  d • In action language: !c & c’ & d

33. SCR to Action Language • Each row in an SCR table corresponds to an action • The transition relation of a table is defined by asynchronous composition of actions that correspond to its rows • The transition relation of the whole system is defined by the synchronous composition of transition relations of tables

34. SCR to Action Language module HeaterACSys enum Heater{On, Off}; enum AC{On, Off}; int temp; parameterized int low, high; initial : low<=temp<=high & Heater=AC=Off; r1 : !(temp<low) & temp’<low & Heater=Off & Heater’=On; r2 : !(temp>=low) & temp’>=low & Heater=On & Heater’=Off; t_heat : r1 | r2; ... HeaterACSys: t_heat & t_AC; endmodule Heater AC

35. Conclusions • It is possible to represent specification languages such as Statecharts and SCR using simple composition operators • Action language can provide an intermediate language for verification • It preserves the structure of high-level specifications • It is closer to the transition system models used by model checkers

36. Related Work • Specification languages for verification • [Milner 80] CCS • [Chandy and Misra 88] Unity • [Lamport 94] Temporal Logic of Actions (TLA) • Specification languages for model checking • [Holzmann 98] Promela • [McMillan 93] SMV • [Alur and Henzinger 96, 99] Reactive Modules

37. Future Work • Developing efficient model checking procedures for Action Language specifications • Exploiting modularity in model checking Action Language specifications • Introducing constructs in Action Language for user directed state-space reductions • Abstractions • Variable hiding