The STATEMATE Semantics of Statecharts

1. The STATEMATE Semantics of Statecharts David Harel and Amnon Naamad 1996. Jolan Farkas

2. Overview • Introduction • Basic concepts of semantics • Hierarchy of states • Orthogonality of states • Transitions • History • Other issues Statecharts

3. STATEMATE • No consensus about semantics • Clarity, simplicity, intuitive • Unofficial language => no official semantics • Main difference between Harel’s (87) and P&S (91) • Changes occurring in a given step take effect in the current step or in the next one • STATEMATE implements the latter approach Statecharts - STATEMATE

4. Commercial Tool • Real-life complex systems • Support of different styles of modeling • Simple and intuitive • VHDL adopted the same approach Statecharts - STATEMATE

5. Topics • Statechart notions • Hierarchy of states • Orthogonality • History connector • Not unique to statecharts • Combinational assignments • Priority of transitions • Generic charts • Multi-value logic • Queues i-Logic documents Statecharts - Topics

6. The Basics

7. The Basics • Model of reactive systems • Backbone: activity-chart • Hierarchical dataflow diagram • Functional capabilities of the system • Dynamically noncommitting • Behavioral aspect: control activities • One for each activity • Controls the dynamics of subactivities and their dataflow Statecharts - Basics

8. A1 S1 A11 S11 S112 A112 A111 A1123 A13 A12 A131 S13 Structure of Activity Hierarchy Activity Control activity Statecharts - Basics

9. A F E B D C The Basics …cont’d • State hierarchy • OR: substances in exclusive OR relation • AND: orthogonal components related by AND • BASIC: at the hierarchy bottom Statecharts - Basics

10. The Basics …cont’d • Transition labeling: e[c]/a • e: event, triggers the transition • c: condition, guards transition from being taken • a: action carried out if and when transition is taken • Actions associated with the entrance to or exit from a state S • Entrance to: on transition leading to S • Exit from: on transition exiting from S Statecharts - Basics

11. A A B t1 B C D t1 C ev/act SR: ev/act The Basics …cont’d • Static reactions • Same format: e[c]/a • Carried out as long as the system is in the given state • Transition in virtual susbtate VS • VS is orthogonal to all substates and SR’s = Statecharts - Basics

12. The Basics …cont’d • Throughout vs. within • Throughout: active upon entering, stops upon leaving • Within: active when system is in S, stops when exiting • Schedule • sc!(a, d): d time units later • Timeout • tm(e, d): d time units after e Statecharts - Basics

13. The Basics …cont’d • Behavior • Described by possible runs: series of statuses • Initial status: first snapshot • Each subsequent: by executing a step • Status: detailed internal information • Step: status change on external stimuli and internal changes Statecharts - Basics

14. Principles • Reactions and changes sensed after step-completion • Events: live for step-duration, not remembered • Decisions based on situation at the beginning of the step • A maximal subset of non-conflicting transitions and SR’s is always executed • Execution of a step takes zero time Statecharts - Principles

15. Principles …cont’d • Less trivial situations • Enabled conflicting transitions in the same step • Transition crosses boundary of nested states (exited/entered states ?) Statecharts - Principles

16. Basic System Reactions

17. Basic system reactions • Configuration: C is the maxl set of states that the system can be in simultaneously • C contains R • If C contains an OR state O, it contains exactly 1 substate of O • If C contains an AND state A, it contains all substates of A • The only states in C are those required above. • Closed upwards, sufficient to know its basic states Statecharts – Basic system reactions

18. S A B C D B1 C1 D1 E B2 C2 D2 Basic system reactions • Basic configuration • maxl set of basic states that the system can be in simultaneously Full: {S, A, B, C, D} Basic: {B1, C1, D1} Full: {S, E} Basic: {E} Statecharts – Basic system reactions

19. S t1:ev/act A B Basic system reactions • 4 operation types • Transitions • Static reactions • Entering actions • Exiting actions • ev occurs • t1 enabled • Execute act • exited(A), entered(B) generated, sensed in next step (SR’s) • in(A)=false, in(B)=true • Actions on exit(A), enter(B) executed • All enabled SR’s of S • Within/throughout: deactivated in A, activated in B Statecharts – Basic system reactions

20. Compound Transitions • Execution of a step must always lead to a legal configuration • Actual transition: a set of separate transitions • Basic compound transition (CT) • Maxm chain of transition segments executable as single transition • Joint and fork are AND connectors • Condition, selection, and junction are OR connectors • Initial, continuation and full CT Statecharts – Compound transitions

21. S B t3 ![C2] C H t1:e A [C2] t2:[C1] B1 B2 Dealing with History • Two kinds of History connectors • H: target is one substate of S • H*: target is basic configuration relative to S ! Statecharts – Dealing with History

22. Scope of Transitions • Full CT • Source contains states only (no connectors) • Target contains basic states and termination connectors only • Every two source and every two target states are mutually orthogonal • Target set is maximal • Enabled, if at beginning of the step system is in all of its source states and its trigger is true Statecharts – Dealing with History

23. S A W C B U H t2 B1 C1 Z V R C2 B2 t1 Scope of Transitions • Scope of tr • The lowest OR state in the state hierarchy • Common ancestor of all sources and targets of tr S W t2 t1 Statecharts – Dealing with History

24. S U t1 t2 t4 A D t3 C B Conflicting Transitions • Two CTs are in conflict if their scopes cannot be orthogonal or exclusive • Nondeterminism vs. priority t1 vs. t2 t4 vs. {t1, t2, t3} Statecharts – Dealing with History

25. Racing Conditions • Racing condition: one action changes, others use the value of some variable in the same step • Ex.: X := X+1, Y := X*5 • Working with supersteps => between transitions or actions • Race situation: Different (but still legal) execution orders of enabled transitions provide different results Statecharts – Dealing with History

26. S t1: e / f t2: f / X:=5 A C G t3: f t4: / Y:=X+1 F B D E Racing Conditions • Race situation Statecharts – Dealing with History

27. Two Models of Time • Synchronous time model • A single step every time unit • Highly synchronous systems • Asynchronous time model • The system reacts whenever an external change occurs • Several external changes simultaneously • Superstep: Several steps in a single point in time • Steps take zero time Statecharts – Dealing with History

28. New Issues

29. Combinational Assignments • Associated with the entire chart • Continuous function • Recomputed immediately after any parameter change • Possible loops A := 5 when B = 3 else 10 B := 3 when A > 5 else 4 • The event changed(var) generated only when it has a new value at the end of CA execution Statecharts – Dealing with History

30. S B t1 C E F t2 D t3 Priority of Transitions • Two aspects • Structural priority of a compound transition • Priority number of a transition segment • Structural priority determinant • Based on the source(s) and target(s) of CT Statecharts – Dealing with History

31. Priority of Transitions • Priority number • The first different segment is definitive (5) (8) (6) S T1 (5) (5) T2 (7) T5 (6) (8) T3 (40) (8) T4 T6 Statecharts – Dealing with History