Week-1: Introduction to model checking B. Srivathsan Chennai - PowerPoint PPT Presentation

Week-1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute NPTEL-course July - November 2015 1 / 30

Module 4: Modeling concurrent systems 2 / 30

Concurrent systems Independent Shared variables Shared actions 3 / 30

red TrLight 1 green red TrLight 2 green 4 / 30

red TrLight 1 green red TrLight 2 green What is the transition system for the joint behaviour ? 4 / 30

red TrLight 1 green red TrLight 2 green 5 / 30

red TrLight 1 green red TrLight 2 green red , red 5 / 30

red TrLight 1 green red TrLight 2 green red , red green , red red , green 5 / 30

red TrLight 1 green red TrLight 2 green red , red green , red red , green green , green 5 / 30

red TrLight 1 green red TrLight 2 green red , red green , red red , green green , green 5 / 30

red TrLight 1 green red TrLight 2 green red , red green , red red , green green , green 5 / 30

red TrLight 1 green red TrLight 2 green red , red TrLight 1 ||| TrLight 2 green , red red , green green , green 5 / 30

red TrLight 1 green red TrLight 2 green red , red TrLight 1 ||| TrLight 2 green , red red , green ||| : Interleaving operator green , green 5 / 30

q 1 l 1 y := y-2 x := x+1 ... ... y:= y-2 x:= x+1 q 2 l 2 PG 1 PG 2 6 / 30

α q 1 β l 1 y := y-2 x := x+1 ... ... y:= y-2 x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : y=7 l 1 : x=0 α β q 2 : y=5 l 2 : x=1 TS 1 TS 2 ( initially x=0 ) ( initially y=7 ) 6 / 30

α q 1 β l 1 y := y-2 x := x+1 ... ... y:= y-2 x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : y=7 l 1 : x=0 x=0 , y=7 β α α β x=1 , y=7 x=0 , y=5 α β x=1 , y=5 q 2 : y=5 l 2 : x=1 TS 1 TS 1 ||| TS 2 TS 2 ( initially x=0 ) ( initially y=7 ) 6 / 30

a a q 1 q 2 ||| l 1 l 3 b a b l 2 7 / 30

a a q 1 q 2 ||| l 1 l 3 b a b l 2 l 1 , q 1 l 2 , q 1 l 3 , q 1 l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

a a q 1 q 2 ||| l 1 l 3 b a b l 2 a l 1 , q 1 l 2 , q 1 l 3 , q 1 a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a a a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a a a a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a a a a b b b b l 1 , q 2 l 2 , q 2 l 3 , q 2 a a 7 / 30

Multiple systems TS 1 ||| TS 2 ||| ... ||| TS n 8 / 30

Multiple systems TS 1 ||| TS 2 ||| ... ||| TS n Exercise: Try out an example of interleaving three systems 8 / 30

Concurrent systems Independent Shared variables Interleaving TS 1 ||| TS 2 ||| ... ||| TS n Shared actions 9 / 30

q 1 x:= 2 · x l 1 x:= x+1 ... ... x := 2 · x x:= x+1 q 2 l 2 PG 1 PG 2 10 / 30

α q 1 x:= 2 · x β l 1 x:= x+1 ... ... x := 2 · x x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : x=3 l 1 : x=3 α β q 2 : x=4 l 2 : x=6 TS 1 TS 2 ( initially x=3 ) ( initially x=3 ) 10 / 30

α q 1 x:= 2 · x β l 1 x:= x+1 ... ... x := 2 · x x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : x=3 l 1 : x=3 x=3 , x=3 β α α β x=6 , x=3 x=3 , x=4 α β q 2 : x=4 l 2 : x=6 x=6 , x=4 TS 1 TS 1 ||| TS 2 TS 2 ( initially x=3 ) ( initially x=3 ) 10 / 30

q 1 l 1 x := 2 · x x := x+1 q 2 l 2 PG 1 PG 2 11 / 30

l 1 , q 1 q 1 l 1 x:=2 · x x:=x+1 ||| x := 2 · x l 2 , q 1 l 1 , q 2 x := x+1 = q 2 l 2 x:=2 · x x:=x+1 l 2 , q 2 PG 1 PG 2 PG 1 ||| PG 2 11 / 30

l 1 , q 1 α q 1 β l 1 x:=2 · x x:=x+1 ||| x := 2 · x l 2 , q 1 l 1 , q 2 x := x+1 = q 2 l 2 x:=2 · x x:=x+1 l 2 , q 2 PG 1 PG 2 PG 1 ||| PG 2 l 1 , q 1 : x=3 β α TS( PG 1 ||| PG 2 ): l 2 , q 1 : x=6 l 1 , q 2 : x=4 β α l 2 , q 2 : x=7 l 2 , q 2 : x=8 11 / 30

Concurrent systems Independent Shared variables Interleaving TS( PG 1 ||| PG 2 ||| ... ||| PG n ) TS 1 ||| TS 2 ||| ... ||| TS n Shared actions 12 / 30

Coming next: Another example 13 / 30

while x < 200 while x>0 while x=200 x := x+1 x := x-1 x := 0 14 / 30

while x < 200 while x>0 while x=200 x := x+1 x := x-1 x := 0 Is the value of x always between 0 and 200? 14 / 30

while x < 200 while x>0 while x=200 x := x+1 x := x-1 x := 0 m 1 n 1 l 1 x := x+1 x < 200 x:=x-1 x > 0 x:=0 x = 200 m 2 n 2 l 2 Is the value of x always between 0 and 200? 14 / 30

l 1 , m 1 , n 1 x:=x+1 x=200 x:=x-1 x>0 x:=0 x<200 l 2 , m 1 , n 1 l 1 , m 2 , n 1 l 1 , m 1 , n 2 x=200 x:=x+1 x<200 x:=x-1 x>0 x:=x-1 x>0 x=200 x:=x+1 x:=0 x<200 x:=0 l 2 , m 2 , n 1 l 2 , m 1 , n 2 l 1 , m 2 , n 2 x=200 x:=x+1 x:=x-1 x>0 x:=0 x<200 l 2 , m 2 , n 2 15 / 30

l 1 , m 1 , n 1 x:=x+1 x=200 x:=x-1 x>0 x:=0 x<200 l 2 , m 1 , n 1 l 1 , m 2 , n 1 l 1 , m 1 , n 2 x=200 x:=x+1 x<200 x:=x-1 x>0 x:=x-1 x>0 x=200 x:=x+1 x:=0 x<200 x:=0 l 2 , m 2 , n 1 l 2 , m 1 , n 2 l 1 , m 2 , n 2 x=200 x:=x+1 x:=x-1 x>0 x:=0 x<200 l 2 , m 2 , n 2 15 / 30

l 1 , m 1 , n 1 x:=x+1 x=200 x:=x-1 x>0 x:=0 x<200 l 2 , m 1 , n 1 l 1 , m 2 , n 1 l 1 , m 1 , n 2 x=200 x:=x+1 x<200 x:=x-1 x>0 x:=x-1 x>0 x=200 x:=x+1 x:=0 x<200 x:=0 l 2 , m 2 , n 1 l 2 , m 1 , n 2 l 1 , m 2 , n 2 x=200 x:=x+1 x:=x-1 x>0 x:=0 x<200 l 2 , m 2 , n 2 Is the value of x always between 0 and 200? No 15 / 30

Coming next: Mutual exclusion 16 / 30

... P 1 P 2 P n S HARED R ESOURCE (variable, printer, ... ) Mutual Exclusion: No two processes can access the resource simultaneously 17 / 30

Goal: Modeling the protocols used for mutual exclusion 18 / 30

P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . request request critical section critical section release release . . . . *non-critical actions* *non-critical actions* . . end loop end loop 19 / 30

P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . request request critical section critical section release release . . . . *non-critical actions* *non-critical actions* . . end loop end loop PG 1 PG 2 noncrit 1 noncrit 2 wait 1 wait 2 crit 1 crit 2 19 / 30

P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . 〈 if y>0 : y:=y-1 〉 〈 if y>0 : y:=y-1 〉 *request* *request* critical section critical section y:=y+1 y:=y+1 *release* *release* . . . . *non-critical actions* *non-critical actions* . . end loop end loop PG 1 PG 2 noncrit 1 noncrit 2 wait 1 wait 2 y:= y+1 y:= y+1 y>0:y:=y-1 y>0:y:=y-1 crit 1 crit 2 19 / 30

P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . 〈 if y>0 : y:=y-1 〉 〈 if y>0 : y:=y-1 〉 *request* *request* critical section critical section y:=y+1 y:=y+1 *release* *release* . . . . *non-critical actions* *non-critical actions* . . end loop end loop PG 1 PG 2 noncrit 1 noncrit 2 atomic wait 1 wait 2 y:= y+1 y:= y+1 y>0:y:=y-1 y>0:y:=y-1 crit 1 crit 2 19 / 30

PG 1 ||| PG 2 noncrit 1 , noncrit 2 y:=y+1 y:=y+1 wait 1 , noncrit 2 noncrit 1 , wait 2 y:=y+1 y>0: y>0: y:=y-1 y:=y-1 crit 1 , noncrit 2 wait 1 , wait 2 noncrit 1 , crit 2 y>0: crit 1 , wait 2 wait 1 , crit 2 y:=y-1 y:=y+1 y:=y+1 crit 1 , crit 2 20 / 30

TS( PG 1 ||| PG 2 ) n 1 , n 2 , y=1 w 1 , n 2 , y=1 n 1 , w 2 , y=1 c 1 , n 2 , y=0 w 1 , w 2 , y=1 n 1 , c 2 , y=0 c 1 , w 2 , y=0 w 1 , c 2 , y=0 21 / 30

TS( PG 1 ||| PG 2 ) n 1 , n 2 , y=1 w 1 , n 2 , y=1 n 1 , w 2 , y=1 c 1 , n 2 , y=0 w 1 , w 2 , y=1 n 1 , c 2 , y=0 c 1 , w 2 , y=0 w 1 , c 2 , y=0 Both processes cannot be in critical section simultaneously 21 / 30

Concurrent systems Independent Shared variables Interleaving TS( PG 1 ||| PG 2 ||| ... ||| PG n ) TS 1 ||| TS 2 ||| ... ||| TS n Mutual Exclusion Shared actions 22 / 30

Coming next: Book-keeping system in a supermarket 23 / 30

Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 24 / 30

Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 000 24 / 30

Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 scan 100 000 24 / 30

Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 scan 100 000 check_price 010 24 / 30

Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 scan 100 000 001 prt_cmd check_price 010 24 / 30

Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 101 print check_price scan prt_cmd print print scan scan 100 000 001 110 111 011 scan prt_cmd print check_price 010 24 / 30