The STATEMATE Semantics of Statecharts

The STATEMATE The STATEMATE Semantics of StatechartsSemantics of Statecharts

David Harel and Amnon Naamad

1996.

Jolan FarkasJolan Farkas

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OverviewOverview

Introduction Basic concepts of semantics

– Hierarchy of states– Orthogonality of states– Transitions– History

Other issues

Statecharts

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STATEMATESTATEMATE

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

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Commercial ToolCommercial Tool

Real-life complex systems Support of different styles of modeling Simple and intuitive VHDL adopted the same approach

Statecharts - STATEMATE

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TopicsTopics

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

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The BasicsThe Basics

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The BasicsThe 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

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Structure of Activity HierarchyStructure of Activity Hierarchy

A1S1

A11S11

A112 S112

A1123A111

A12A13

A131S13

Activity

Control activity


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The Basics …The Basics …cont’dcont’d

State hierarchy– OR: substances in exclusive OR relation– AND: orthogonal components related by AND– BASIC: at the hierarchy bottom


A

B

C

D

E F

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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


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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


A

B C

SR: ev/act

t1

A

B

C

Dt1

ev/act

=

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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


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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


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PrinciplesPrinciples

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

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Principles …Principles …cont’dcont’d

Less trivial situations– Enabled conflicting transitions in the same step– Transition crosses boundary of nested states

(exited/entered states ?)

Statecharts - Principles

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Basic System ReactionsBasic System Reactions

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Basic system reactionsBasic 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

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Basic configuration– maxl set of basic states that the system can be in simultaneously


S

EB1

B2

C1

C2

D1

D2

B C DA

Full: {S, A, B, C, D}Basic: {B1, C1, D1}

Full: {S, E}Basic: {E}

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4 operation types– Transitions– Static reactions– Entering actions– Exiting actions


BA

S

t1:ev/act

1. ev occurs2. t1 enabled3. Execute act4. exited(A), entered(B)

generated, sensed in next step (SR’s)

5. in(A)=false, in(B)=true6. Actions on exit(A),

enter(B) executed7. All enabled SR’s of S8. Within/throughout:

deactivated in A, activated in B

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Compound TransitionsCompound Transitions

Statecharts – 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

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Dealing with HistoryDealing with History

Statecharts – Dealing with History

Two kinds of History connectors– H: target is one substate of S– H*: target is basic configuration relative to S

H

B2 B1

B S

At1:eC

t2:[C1][C2]

t3 ![C2]!

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Scope of TransitionsScope 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

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Scope of TransitionsScope of Transitions


Scope of tr– The lowest OR state in the state hierarchy– Common ancestor of all sources and targets of tr

H

V R

UW

Zt2

SAB

B1

B2

C1

C2

C

t1

SW

t1

t2

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Conflicting TransitionsConflicting Transitions


Two CTs are in conflict if their scopes cannot be orthogonal or exclusive– Nondeterminism vs. priority

B C

U S

D

At1t2

t3

t4 t1 vs. t2t4 vs. {t1, t2, t3}

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Racing ConditionsRacing 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

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Racing ConditionsRacing Conditions


Race situation

E F

S

G

At1: e / f

t2: f / X:=5

t3: f t4: / Y:=X+1

B

C D

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Two Models of TimeTwo 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

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New IssuesNew Issues

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Combinational AssignmentsCombinational Assignments


Associated with the entire chart Continuous function

– Recomputed immediately after any parameter change– Possible loops

A := 5 when B = 3 else 10B := 3 when A > 5 else 4

– The event changed(var) generated only when it has a new value at the end of CA execution

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Priority of TransitionsPriority 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 C

D

BS

Et1

Ft3

t2

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Priority of TransitionsPriority of Transitions


Priority number– The first different segment is definitive

S T1

T2

T3

T4

T5

T6

(5)

(5) (5)

(6)

(6)

(7)

(8)

(8)

(8)(40)

The STATEMATE Semantics of Statecharts

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