SHARED OBJECTS 1.1 incr_count 1.1.1 set_count_1 AND 1.1.2 - PowerPoint PPT Presentation

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 G ARDENS , HIERARCHY TREE Top 1 turnstile1 SHARED OBJECTS 1.1 incr_count 1.1.1 set_count_1 AND 1.1.2 set_count_2 MUTEX 1.1.3 set_count_3 - 1.1.4 set_count_4 2 set_count_to_0 BOTANICAL GARDEN 3 turnstile2 3.1 incr_count 3.1.1 set_count_1 3.1.2 set_count_2 3.1.3 set_count_3 3.1.4 set_count_4 4 next_run Y:\Documents\teaching\course-concurrency\skript-sources\nl_skript_fm\nl05_mutex_garden.sld.fm 5 - 1 / 20 monika.heiner@b-tu.de 5 - 2 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 G ARDENS , TOP LEVEL G ARDENS 1. turnstile1 begin 2. set_count_to_0 process_begin1 cobegin turnstile1 cobegin T1_loop co_loop1 process_begin1 process_begin2 loop1 (2) 1. turnstile1 3. turnstile2 begin_for end_for process_end1 process_end2 T1_in_loop process_end1 1.1. incr_count coend write 4. next_run write end pnt: ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N Y N N N N Y Y N N N N N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S ? Y Y Y Y N N ? Y N N N N cnt: ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N Y N N N N Y Y N N N N N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S WL CL ? Y Y Y Y N N ? Y N N N N N Y monika.heiner@b-tu.de 5 - 3 / 20 monika.heiner@b-tu.de 5 - 4 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 G ARDENS G ARDENS T1_read_4F count_4 1.1.1. set_count_1 1.1. incr_count T1_fact fact T1_set_1 1.1.4. set_count_4 T1_read_3 count_3 T1_set_4 count_0 count_1 count_2 count_3 count_4 T1_read_2 count_2 T1_set_3 1.1.3. set_count_3 count_1 count_1 count_1 count_1 count_1 T1_read_1 count_1 T1_set_2 1.1.2. set_count_2 T1_loop T1_read_0 count_0 T1_set_1 T1_in_loop 1.1.1. set_count_1 T1_loop monika.heiner@b-tu.de 5 - 5 / 20 monika.heiner@b-tu.de 5 - 6 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 G ARDENS 1 4. next_run end next_run reset_loop1 reset_loop2 (2) (2) loop1 loop2 loop2_set loop1_set begin AND THEN THERE WAS COLOUR monika.heiner@b-tu.de 5 - 7 / 20 monika.heiner@b-tu.de 5 - 8 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 C OLOUR , C OLOUR , B OOLEAN OPERATIONS CONTROL FLOW swap swap swap 1`T 1`F 1`F Boolean x x x Boolean Boolean +x +x +x A B C A 1`false B 1`false C 1`false Boolean Boolean Boolean not_fun(a) not_fun(a) not_fun(a) a 1`false a a C Boolean z notB notC 1`false notA 1`false Dot Dot B B Boolean y y Boolean x x A 1`false A 1`false A := B A := B and C Boolean Boolean y y&z in Dot Dot 1`T 1`F dot 1`F Boolean Boolean Boolean A B p3 C Dot dot b c a 1`false 1`false 1`false 1`false or_fun(b,c) Boolean Boolean assign Boolean Boolean Dot A := B or C Dot A A A A dot 1`false 1`false if_A if_AandB B B Boolean x Boolean T F x p4 y y Dot [!(x&y)] [x&y] then else then else dot Dot Dot out endif endif monika.heiner@b-tu.de 5 - 9 / 20 monika.heiner@b-tu.de 5 - 10 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 C OLOUR C OLOUR dot 2`dot papaya p_salat pre_p_salat dot [y=t1]2`p++ 3`dot dot [y=t2]1`p++ bananas 4 fruit_salat [y=t2]3`b++ prep_fruit_salat 2`dot [y=t2]2`m++ dot dot [y=t3]1`m mango mango_salat prep_mango_salat Edibles 8 edibles preps 4`b++ [y=t1]1`ps++ 1`ps 2`p 2`m++ [y=t2]1`fs++ pre_p_salat 2`p [y=t3]1`ms p++ Fruits Salats 1`fs 3`b++ fruits salat 8 2`m it should be possible to combine equal guards. prep_fruit_salat 4`b++ 2`m++ m 1`ms 2`p prep_mango_salat [y=t1]2`p++ [y=t2](1`p++ 3`b++ 2`m)++ 1`ps [y=t3]1`m pre_p_salat 2`p p++ 3`b++ Edibles Edibles 8 2`m edibles prep_fruit_salat edibles 8 preps 1`fs 4`b++ [y=t1]1`ps++ 4`b++ 2`m++ m [y=t2]1`fs++ 2`m++ 2`p [y=t3]1`ms prep_mango_salat 2`p 1`ms monika.heiner@b-tu.de 5 - 11 / 20 monika.heiner@b-tu.de 5 - 12 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 C OLOURED GARDEN C OLOURED GARDEN Dot 1`dot begin Dot set_count_to_0 process_begin1 Dot cobegin turnstile1 cobegin T1_loop Dot Dot Dot 1`2 Loop process_begin2 process_begin1 loop1 x-1 0 turnstile2 x turnstile1 T1_end_for [x<>0] 0 T1_begin_for process_end1 process_end2 Dot Dot Dot Dot T1_in_loop coend incr_count process_end1 Dot write write next_run end Dot monika.heiner@b-tu.de 5 - 13 / 20 monika.heiner@b-tu.de 5 - 14 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 C OLOURED GARDEN C OLOURED GARDEN Dot Dot begin T1_in_loop 1`dot 1`0 x Count T1_read x x 1`0 count Count x set_0 count 0 Count T1_set x y 1`0 Count Dot T1_incr count x+1 cobegin Dot T1_loop monika.heiner@b-tu.de 5 - 15 / 20 monika.heiner@b-tu.de 5 - 16 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 C OLOURED GARDEN COLOURED NETS , OBSERVATIONS ❑ coloured Petri nets may serve as a short-hand notation for place/transition Petri nets Dot ❑ a coloured place has (like a program variable) end -> a name next_run1 -> a colour set = data type = set of values (colours) Dot Dot reset_loop1 ❑ reset_loop2 any token on a given place has a specific colour of the place‘s colour set i i Loop Loop loop2 loop1 ❑ a coloured place contains generally reset_loop2 reset_loop1 2 1`2 2 1`2 a multiset (bug) of coloured tokens Dot Dot loop2_set loop1_set ❑ the arc inscriptions consist of next_run2 -> constants Dot -> “formal sums” of coloured tokens begin -> variables 1`dot -> functions . . . or a combination of all those ❑ arc inscriptions’s readability = net readability ! monika.heiner@b-tu.de 5 - 17 / 20 monika.heiner@b-tu.de 5 - 18 / 20

dependability engineering & Petri nets October 2018 dependability engineering & Petri nets October 2018 COLOURED COLOURED PETRI NETS , PETRI NETS , SUMMARY ANALYSIS ❑ by unfolding ❑ information-preserving transformation -> reuse of all P/T net analysis techniques folding -> symmetrically reduced rg coloured Petrinetz Petrinetz ❑ without unfolding Petri net Petri net -> reachability graph (CPN - occurrence graph) unfolding -> invariants (tools ?) -> CTL model checking (tools ?) ❑ folding needs user interaction ❑ -> partitions of transition set and place set dedicated notion of liveness: collectively live transitions -> all transition colours of ❑ trivial transformation: a given coloured transition only one colour (black colour) guarantee together the liveness -> no structure compression -> very useful for control flow models -->> garden example ❑ any Petri net may be transformed into -->> mutex examples -> all structure information in arc inscriptions monika.heiner@b-tu.de 5 - 19 / 20 monika.heiner@b-tu.de 5 - 20 / 20