A Translation of Statecharts and Activitycharts into Signal Equations

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https://hal.inria.fr/inria-00073292

Submitted on 24 May 2006

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A Translation of Statecharts and Activitycharts into Signal Equations

Jean-René Beauvais, Roland Houdebine, Paul Le Guernic, Eric Rutten, Thierry Gautier

To cite this version:

Jean-René Beauvais, Roland Houdebine, Paul Le Guernic, Eric Rutten, Thierry Gautier. A Trans- lation of Statecharts and Activitycharts into Signal Equations. [Research Report] RR-3397, INRIA.

1998. �inria-00073292�

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a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

A translation of Statecharts and Activitycharts into Signal equations

J-R Beauvais, R. Houdebine, P. Le Guernic, E. Rutten, T. Gautier

N ˚ 3397

Avril 1998

TH `EME 1

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dZdc2qkm¨_adcacdCadZ² a q_adZ t®kcv~zd~§q_adckd©l9t!dC¸%avm¦ ak! adQq_adCT_l9t#qm Hq_adct®lxq(lA{

qdcbek l9axv~tWdZdcqk ml9ù¢dRdYoa(_l9a~dc¦q_ q_adCdc% t!v~abedcqm\^_ad\T_l9t#qW k)?nat#q_adct

adZ²adcù¢2r´dZq_adct"l9 |Zq!%q}r(_l9t#qWv~t"l¤°<q(lxqdc(_l9t#qm¨¦_ (_ùml9 ¢dqkdZ±adccv~bezv~k(dc

_ dctl9t!T_ mlxrR qv"kna¢%{}T_l9t#qkm^_ad.dcqt#rRzv9 2qKv~tl7bev<adZ kOl9R|7Zq!<q¼r%T_l9t#qm¨¦_ (_

adck(ct# ¢dckOl)k!qt!naZqnatlxadccv~bezv~k!q! v~\¢2r®¢dZ a)< adcR 2qvWkna¢%{¼l9Zq!%q! dckm¨t!dccnat!k!dZr

°%v~bedkna¢%{¼l9Zq!<q! dckI¨mlx dccv~qt!v9»l9Zq!<q! dckI¨ml9¢d"adZ²adc¢rl\°<q(lxqdc(_l9t#qm

)Æ Aax)K LU¯ax Æ + Ê m | °<q(lxqdc(_l9t#qk adck! ~dckkdcq!lxr¬cv~ak k!qk+v9

kq(lxqdckpl9a qtl9ak!q! v~akp ¸~d l¡²qd l9nqv~b\lxqv~½å v~t!adctQqv bev<adZ)adczq_¨lk!q(lxqd

ml9 ¢d+t!dZ²adc l9a cv~2q(lx k(na¢%{}k!q(lxqdck¤l9a 2qdct!lx7qtl9akq! v~akm ^.¦±v k(na(_ t!dZ²adY{

bedc2qk"l9t!d lc~lxl9¢ d~§ (¯Ë l9a+Ê k!q(lxqdckm¨q_lxq)9d lQk!q(lxqd _ dctl9t!(_r7|.q7q_ad¢v9q!qv~b

v9±q_ad\_ dctl9t!T_r¨ a)K {}k!q(lxqdckl9t!dCav9qWKnat#q_adct t!dZ²adcC½¼Mq_adCk!r%kqdcb kzdcZ²dc¡¢rl

°<q(lxqdcT_l9t#qpt!dck adck\ l9 Ê

k!q(lxqd~¨.q_adc qplx k(vt!dck! adck\ dYoal9Zq!r£v~adv9)qkQ t!dcZq

k(na¢%{}k!q(lxqdckm£°<q(lcr% a £l9 (¯Ë kq(lxqd© bez dck\k!q(lcr% aù £lxv97qk\ t!dcZqCkna¢%{}kq(lxqdck

l9a bev%adZ k®cv~acnat!t!dcaZrZ _adc¥l+k!q(lxqdQ k dZ·qm¨dml9T_ k(na¢%{}k!q(lxqdC kelx kv´ dZKqm¨»q_adct!dc¢r

bev%adZ a¡zat!dcdcbezq! v~ °%na¢%{}kq(lxqdckCv9Wl9

(¯Ë

k!q(lxqdb\lcr£cv~2q(lx £qtl9ak!q! v~akQ¦_ (_

ml9¤¢d"dYoadccnqdck! bnq(l9adcv~nakrM^_ad"cv~²~natlxq! v~ v9lC°<q(lxqdcT_l9t#q kadZ²adc+¢rpq_ad

_ dctl9t!T_r v9k!q(lxqdckRl9a k(na¢%{}k!q(lxqdck ¦_ (_ qRk!q(lcrkm ^_adQNM&dct!dcq (¯Ë zl9t#qkRv9l

(13)

f

v9»q_ad®dZdcqkm Qv~t akq(l9acd~¨q_ad dcbR kk! v~ v9Ol9´dZdc2q7v~ leqtl9ak!q! v~ b\lcr+¢dk(dcakdc

½å"q_adM°<q(lxqdcT_l9t#qdYoal9bez dMv9%²~nat!dIa¨Iq_adu¢l9k! ucv~bezv~adcqk»l9t!duk!q(lxqdckl9aWqtl9ak!q! v~akI¨

k(v~bedWk!q(lxqdckZ nakqdct!dc+ Ê

kq(lxqdcv~q(lx a

/\l9a3<µ¦_ dek(v~bed®v9q_adct"~t!v~nazakW (¯Ë cv~bezv~k!q! v~ ³

SA¤ k"l9 (Ë k!q(lxqd

cv~2q(lx a S S#X

¤l9a"S S#X

JaµY

dc2qdct# a l¡k!q(lxqd ¢r lùqtl9akq! v~ zv9 q! aqvq_ad ¢v~naal9t#r£v9"q_ad´k!q(lxqd~¨.q_ad k!q(lxqd

q(l9t!~dZqdcRlxq¯¢2r"q_ad Ë Æ · cv~aadcZqv~t±³«lqtl9akq! v~¦q_av~nq»v~t# 9 µ& k»l9Zq!9lxqdc;Z _adc

v~adq_lxq.¦±l9kl9Zq!d7¦_adcpq_adk!q(lxqd¦±l9k. dZKqmHZ _adcQdc2qdct# aRKv~tuq_ad²t!kqMq! bed)l®k!q(lxqd

cv~2q(lx a¤l\_ k!qv~t#r¤cv~aadcZqv~tc¨q_adWqtl9ak!q! v~´ dmlc% aQq_ k_ k!qv~t#rcv~aadcZqv~t k7nakdc

qv®²apq_ad"kna¢%{}k!q(lxqd7qvel9Zq!~lxqd~ Q lxr¨aadcdcz%{}_ k!qv~t#r ³ aµu kl®cv~aadcZqv~t.q_lxql9Zqk

kdcqdct!dc

¢2r t!dml9Zq! v~akQv9)q_ad?v~t!b¤§ ¨±¦_adct!d kCl9 dZdc2qCq_lxqQzv~kk! ¢r qt# ~~dct!kQq_ad

^_ad®zat!dZ% v~nak7dZdc2q)l9a´q_ad®¢v%v9 dml9+qv~~dZq_adct)9d q_adqt# ~~dct7zl9t#q"v9q_adqtl9akq! v~

S1 S2

a a / b

S3 S4

Idle

Running

b

e

f

Sub_Running_Down Sub_Running_Up

b / d H

Q ~nat!da§ %=& %

(14)

f~f

A

A1 A2

A3 A12

A11

Q ~nat!d %§ !" $

zv~kk! ¢q¼r¥qv¡l9kkv%Zlxqd¤kna(_ l9¢dZ kCqv¡l k!q(lxqd~ Z _adcadZdctCq_ k\k!q(lxqd¤ kpl9Zq!d~¨±q_ad

°%naT_¤qtl9ak!q! v~ak7l9t!dWmlx dck!q(lxq! Wt!dml9Zq! v~akI

^_adu¢l9k! OdZv9 nq! v~®v9l7°<q(lxqdc(_l9t#q»cv~ak! k!qk lk!qdcz¨I¦_adct!dM9dcWq_adOdZdc2qk¯cnat!t!dc2q!r

l9a l9Zq! v~akpl9t!d ml9t!t# dc v~nqm ½¼ °<q(lxqdcb\lxqd´q_ad d MdcZqk´³ØdZdcq¤~dcadctlxq! v~¨~l9t#l9¢ d

kqdcz^_ kb\l9¸~dcklRNM&dct!dcacd"¦q_v9q_adctkdcb\l92q! ck

O

B-"

O

fAIP«

^_adCk!qdczùkdcb\l9q! ck k"q_ade 2qdct!zat!dZq(lxq! v~v9l+°<q(lxqd lxqd\kzdcZ²mlxq! v~¦_adct!de azanqk

l9a9l9t#l9¢ dckmC|av9q_adctWk(dcb\l9q! ckW kWq_ad\knazdct!k!qdcz qdczat!dZq(lxq! v~§®_adct!d~¨E azanqkq(l9¸~d

zl9t#qRv~rù q_adC²t!k!q®v9l+k(dct# dck v9k!qdczakI¨mlx dc¥l´knazdct!kqdcz^_adct!d~¨»q_adC?v9 vm¦ a

kqdczakq(l9¸~d ´cv~ak adctlxq! v~ v~r+q_ad d M&dcZqk)v9q_ad zat!dZ% v~nak)v~adQ³?«Âd~ v<mlxr´dcbRq!qdc

qv+b\l9¸~d~Q^_ k k!qnlxq! v~¨¯mlx dck!q(l9¢ d~¨¯ kWq_ad\dcav9.q_ad\k(nazdct!k!qdcz¨»l9aù azanqk®l9t!d

l9c¶%n t!dc¤?t!v~b5q_adWdc% t!v~abedcq"l9adZ¦W

cv~2qt# ¢anqdc 9lx nad~¨El9a´q_ad®9l9t#l9¢ d®q(l9¸~dck7qk79lx nadck)?t!v~b q_adRl9Zq! v~ cv~2qt# ¢anq! a¤

q_ad"cnat!t!dc2qk!qdcz

(15)

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Q~) )·) Æ ,.dck! adckq_adp°<q(lxqdc(_l9t#qkI¨»l9av9q_adctl9a~nl9~dQv9.q_adQ°<q(lxqd lxqdCdc2< t!v~%{

bedc2qQ kp|7Zq!<q¼r%T_l9t#qk Of

P«§ qQzat!vm% adckpq_ad´adck ~adctC¦q_ lav9q! v~ v9"bnq!¹{« dZdZ

lxq(lA{«ªvI¦ l9~tl9bekm¨l9k nak!qtlxqdcC Q ~nat!d7%»yul9(_Qv9q_ad¢ v<T¸<k \q_ad_ dctl9t!(_2r\t!dY{

zat!dck(dcqkl9Ql9Zq!%q}rO^_ad7l9Zq!<q! dck.ml9Q¢dnakdc\qv®cv~ak!qt!naZqlWk!qt!naZqnat!d7adccv~bezv~k(dc

_ dctl9t!T_ mlxr

|.q.dml9(_p dZdZ«¨v~ad7v9q_ad)l9Zq!%q! dckm¨%adck! ~lxqdcp Cq_ad7~tl9za_ mlxEk!rq(lAoC¢2rplWt!v~naaadc%{

¦q_ l°<q(lxqdcT_l9t#qpadZ² aqkC¢dc_lc% v~tc ^_adlxq!qdctpml9 k!q(l9t#qm¨.k!qv~z¨k(nakzdca l9a

t!dck(nabed"q_adWl9Zq!<q¼r¨l9k¦±dZ¯l9kkdcak(d)qkcnat!t!dcq7k!q(lxqnakm

l9ap_lcd)q_ad7k(l9bed7?v~t!bl9k±l9¢dZ k±k(dcdcpl9kk(v<ZlxqdcQ¦q_pqtl9ak!q! v~akv~tMkq(lxq! 7t!dml9Zq! v~ak

¦q_+k!q(lxqdck +°<q(lxqdc(_l9t#qkI

a¸<k¢dZq¼¦Mdcdc l9Zq!<q! dck7t!dczat!dckdcq7q_adlxq(lCv~tcv~2qt!v9dYoa(_l9a~dck7¢dZq¼¦Mdcdc l9Zq!<q! dckI

^_adZr¤ml9¢dl9na~bedc2qdc+¦q_dZ dcbedc2qkmlx dc´lxq(lA{}k!qv~t!dckt!dczat!dck(dcq! aQq_ad"¦±lmrlxq(l

k"¸~dczq®lx v~a¤k!qdczakmR^_ kl9kzdcZqWv9uq_adRl9a~nl9~de k_avm¦MdZdct ¢l9kdcùv~ q_adRØl9Zq"q_lxq

~l9t#l9¢ dckul9a\dZdc2qkMl9t!d¸%avm¦Clxvmdctul)T_l9t#q³?q_adkcv~zdv9q_adZ tadZ²q! v~µYu^_adct!dY{

ªvI¦¬ a¸%k k¢anql9¤dYoaz Zq(lxq! v~+v9»cv~bebna mlxq! v~ak)dYo k!q! aCl9r%¦±lmr

Q lxr¨lcv~acdczqv9 +v%an dIÀ±_l9t#qkOlx kv7dYo% k!qk¯ e°<q(lxqd´lxqd~¨~_l9a a7q_ad.l9kkv%Zlxq! v~

zat!dck(dcq¦±v~t!¸

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q_adqtl9ak!lxq! v~ Kt!v~b °<q(lxqdc(_l9t#qk)qv¤°< ~lx«¨k(v~bed zat!dcadZ²adc zat!v%cdckkdcknak(dZKn¯Kv~tq_ad

qtl9aklxq! v~+l9t!dW9dcO^_adZr¤cv~t!t!dckzv~a¤qvRq_adW¢l9k! )?dmlxqnat!dckv9q_ad °<q(lxqdcT_l9t#qkm

X54 < %<(?AJ:%KL-< E 7=

|7kClùcv~bebev~ Ktl9bedZ¦±v~t!¸¥Kv~tCt!dml9Zq!d+kzdcZ²mlxq! v~¨±¦Md+adZ²ad lùbev%adZv97t!dml9Zq!d

¢vco¤¦q_ l\av~t!b\lx Ãcdc´ qdct#Øl9cd~yul9(_ zl9t#qv9»q_ad adck! ~qvCqtl9ak!lxqdW¦_lcd q_ k

v~tå{}av%adck ¦±dml9T_¢deqtl9ak!lxqdc qv lzat!v%cdckk ¦q_¡q_ k k!qt!naZqnat!d~¨_adcacdC ak(nat# a

q_ad"_ dctl9t!T_ mlxzat!v~zl9lxq! v~´v9cv~2qt!v9¯k! ~lx kkna(_l9kZ v<T¸<k7l9a¤t!dckdZqkm

½å)q_ad±°< ~lx<l9a~nl9~d~¨~l9" qdct!dck!q! a7zat!v~zdct#q}r" kq_lxq¯q_adO¢dc_lm< v~t¯v9<q_adMcv~bezv~kq! v~

v9q}¦Mv"zat!v%cdckkdck kq_ad± qdct!kdcZq! v~ev9q_adM¢dc_lc% v~t!kOv9q_ad.cv~ak!q!qnadc2qOzat!v<cdck(kdckm^_ k

(16)

fI

Inputs

Tick LocalClock Control

Outputs

Q ~nat!d§

-& %!",Q & # !

k±k! bRl9tMqvq_ad7kv9 nq! v~ak±v9¯l9Cdc¶%nlxq! v~lxk!rk!qdcb¤ dcacd~¨%q_ k±t!dml9Zq!d7¢vcoCbev%adZ k

cv~bezv~k!q! v~lx& \q_ad7k(l9bed7kdcakd)l9aQ9dck.l cv~bezv~k!q! v~lxkdcb\l92q! ck±Kv~t°<q(lxqdc(_l9t#qk

| t!dml9Zq!d)¢vcoC kl ¢vmoCcv~q(lx aR azanql9apv~nqzanq.k ~lx kmu°%v~bed)v9q_adckd 2qdct#?l9cd

Y )K kOq_adZ v%(¸Rv9&q_ad¦_av9 dadck! ~½}qM_l9ku¢dcdcCl9aadcC¢dcml9nakd Q°<q(lxqdcb\lxqd~¨

q_addZdcqkM~dcadctlxqdc\¢r\l7k!qdcz\l9t!dkdcak(dc®v~relxqq_ad¢dc9 a aWv9q_ad.?v9 vm¦ a

k!qdcz¡³Ø~dcadctlxqdc dZdcqk"l9t!d k_·qdcµY^_ k7k! ~lx¯ kq_adt!dZ?dct!dcacd®Z v<T¸¤nakdc?v~t

q_adCzanat!zv~kdCv9k_Kq! aq_adck(dCdZdcqkel9a¡9lx nadQ(_l9a~dckR¢rv~adC ak!q(l9qRv9.q_ad

9 v~¢lxZ v%(¸I

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t!dckzv~a aQ°<q(lxqdc(_l9t#qk7cv~bezv~adc2q kl9Zq!d~

Y Ê (m Ê kCl9£dc<nabedctlxqdc%{«q}rzdc k! ~lxtl9a9 a H&maI ~H& Ê U QÆ Æ

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q_ad¢vcoCadcdcQqv®¢dt!dckdZqm½}&qkM9lx nad k

Ê QÆ ÆQ³Ød~Âa»q_adcv~t!t!dckzv~a a

q_ad dZdZ k¢anq±q_ad7 dZdZ¦_adct!d7q_ad

Ê QÆ ÆRcv~aadcZqv~t±¢dZ v~a~km QÆ Æ

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9lx nad± knakdZ?na¢dcml9nak(dM?v~t ak!q(l9acd. \°<q(lxqdcb\lxqd~¨<l7k!q(lxqd.b\lcrRcv~q(lx CÆ (

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k!q(lxqdW kdcqdct!dc)°< bRl9t#r¦q_+Æ ))(O ¨q_adW~lx nad H& Ê U knak(dc¦_adc´ dmlc% a

lRk!q(lxqd" +°<q(lxqdcb\lxqd~

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