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pn2mc:pt_cp_model_checking [2014/11/24 22:38] jbiernacki [nuXmv] | pn2mc:pt_cp_model_checking [2021/09/23 08:51] (current) | ||
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- '' | - '' | ||
- '' | - '' | ||
- | - '' | + | - '' |
- | - '' | + | - '' |
These formulae can be added to the nuXmv code file: | These formulae can be added to the nuXmv code file: | ||
Line 179: | Line 179: | ||
< | < | ||
- | NuSMV > check_ltlspec | + | nuXmv > check_ltlspec |
-- specification G ( F p5) is false | -- specification G ( F p5) is false | ||
-- as demonstrated by the following execution sequence | -- as demonstrated by the following execution sequence | ||
Line 208: | Line 208: | ||
p7 = FALSE | p7 = FALSE | ||
</ | </ | ||
- | Analogical counterexamples are generated for forulas | + | Analogical counterexamples are generated for formulae |
< | < | ||
Line 218: | Line 218: | ||
-- specification G (((((!p0 & !p1) & !p2) & !p3) & !p4) -> ((((p5 | p6) | | -- specification G (((((!p0 & !p1) & !p2) & !p3) & !p4) -> ((((p5 | p6) | | ||
p7) | p8) | p9)) is true | p7) | p8) | p9)) is true | ||
- | NuSMV > check_ctlspec | + | nuXmv > check_ctlspec |
-- specification EF p5 is true | -- specification EF p5 is true | ||
-- specification EF p6 is true | -- specification EF p6 is true | ||
Line 244: | Line 244: | ||
===== CP-net model checking - Producer–consumer example ===== | ===== CP-net model checking - Producer–consumer example ===== | ||
+ | Producer–consumer problem will serve as an explanatory example showing capabilities of the presented approach for coloured Petri nets. | ||
==== Problem ==== | ==== Problem ==== | ||
- | ---- | + | This is a classic problem related to the synchronization of concurrent processes. In the system there are two types of processes: producers who produce some data and consumers who receive these data from producers. Between producers and consumers there is a buffer of a certain capacity. The problem is how to synchronise the two types of processes in such a way that: |
- | ==== nuXmv ==== | + | - Consumers do not try to receive data from empty buffer, |
+ | - Producers do not try to send data to full buffer, | ||
+ | - There is no possibility of starvation of a consumer, | ||
+ | - There is no possibility of starvation of a producer, | ||
+ | - There are no deadlocks | ||
+ | A coloured Petri net model was prepared for this problem. To make this example as easy as possible. there is only one producer and one consumer. Number of consumers and producers can be easily changed for this model. | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 3 enumeration colour sets were defined: | ||
+ | * '' | ||
+ | * '' | ||
+ | * '' | ||
+ | |||
+ | Places '' | ||
+ | |||
+ | In order to verify the properties of the created model of the system, reachability graph of the net was generated in CPN Tools. Its representation is shown below. | ||
+ | |||
+ | {{: | ||
---- | ---- | ||
+ | ==== nuXmv ==== | ||
+ | Using PetriNet2ModelChecker to translate reachability graph into description of the system in nuXmv code, the following file was generated: | ||
+ | |||
+ | < | ||
+ | MODULE main | ||
+ | VAR | ||
+ | s: {s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11, s12}; | ||
+ | P5_client : 0..2; | ||
+ | P6_bufSpace : 0..2; | ||
+ | P4_client : 0..2; | ||
+ | P1_factory : 0..2; | ||
+ | P3_bufSpace : 0..2; | ||
+ | P2_factory : 0..2; | ||
+ | ASSIGN | ||
+ | init(s) := s1; | ||
+ | next(s) := case | ||
+ | s = s1 : s2; | ||
+ | s = s2 : s3; | ||
+ | s = s3 : {s5, s4}; | ||
+ | s = s4 : {s7, s6}; | ||
+ | s = s5 : {s1, s7}; | ||
+ | s = s6 : {s8, s9}; | ||
+ | s = s7 : {s2, s9}; | ||
+ | s = s8 : s10; | ||
+ | s = s9 : {s3, s10}; | ||
+ | s = s10 : {s4, s11}; | ||
+ | s = s11 : {s6, s12}; | ||
+ | s = s12 : s8; | ||
+ | esac; | ||
+ | P5_client := case | ||
+ | s = s10 : 1; | ||
+ | s = s11 : 1; | ||
+ | s = s5 : 1; | ||
+ | s = s9 : 1; | ||
+ | s = s7 : 1; | ||
+ | s = s12 : 1; | ||
+ | TRUE : 0; | ||
+ | esac; | ||
+ | P6_bufSpace := case | ||
+ | s = s10 : 1; | ||
+ | s = s1 : 2; | ||
+ | s = s4 : 1; | ||
+ | s = s2 : 2; | ||
+ | s = s5 : 2; | ||
+ | s = s9 : 1; | ||
+ | s = s7 : 2; | ||
+ | s = s3 : 1; | ||
+ | TRUE : 0; | ||
+ | esac; | ||
+ | P4_client := case | ||
+ | s = s1 : 1; | ||
+ | s = s8 : 1; | ||
+ | s = s6 : 1; | ||
+ | s = s4 : 1; | ||
+ | s = s2 : 1; | ||
+ | s = s3 : 1; | ||
+ | TRUE : 0; | ||
+ | esac; | ||
+ | P1_factory := case | ||
+ | s = s11 : 1; | ||
+ | s = s1 : 1; | ||
+ | s = s6 : 1; | ||
+ | s = s5 : 1; | ||
+ | s = s9 : 1; | ||
+ | s = s3 : 1; | ||
+ | TRUE : 0; | ||
+ | esac; | ||
+ | P3_bufSpace := case | ||
+ | s = s10 : 1; | ||
+ | s = s11 : 2; | ||
+ | s = s8 : 2; | ||
+ | s = s6 : 2; | ||
+ | s = s4 : 1; | ||
+ | s = s9 : 1; | ||
+ | s = s12 : 2; | ||
+ | s = s3 : 1; | ||
+ | TRUE : 0; | ||
+ | esac; | ||
+ | P2_factory := case | ||
+ | s = s10 : 1; | ||
+ | s = s8 : 1; | ||
+ | s = s4 : 1; | ||
+ | s = s2 : 1; | ||
+ | s = s7 : 1; | ||
+ | s = s12 : 1; | ||
+ | TRUE : 0; | ||
+ | esac; | ||
+ | </ | ||
+ | |||
+ | |||
+ | To verify specified properties of the system, the following LTL formulae were created: | ||
+ | |||
+ | - Consumer do not try to receive data from empty buffer, \\ \\ '' | ||
+ | - Producer do not try to send data to full buffer, \\ \\ '' | ||
+ | - There is no possibility of starvation of a consumer, \\ \\ '' | ||
+ | - There is no possibility of starvation of a producer, \\ \\ '' | ||
+ | - There are no deadlocks \\ \\ '' | ||
+ | |||
+ | These formulae can be added to the previously generated nuXmv code for the model: | ||
+ | |||
+ | < | ||
+ | LTLSPEC (P3_bufSpace=0 & P4_client=1) -> !X(P5_client=1) | ||
+ | LTLSPEC (P6_bufSpace=0 & P2_factory=1) -> !X(P1_factory=1) | ||
+ | LTLSPEC G F (P4_client=1) -> G F (P5_client=1) | ||
+ | LTLSPEC G F (P2_factory=1) -> G F (P1_factory=1) | ||
+ | LTLSPEC G F (P2_factory=1) & G F (P1_factory=1) & G F (P4_client=1) & G F (P5_client=1) | ||
+ | </ | ||
+ | |||
+ | Verification of satisfiability of these formulae can be performed in nuXmv tool: | ||
+ | |||
+ | < | ||
+ | nuXmv > check_ltlspec | ||
+ | -- specification ( G ( F P4_client = 1) -> G ( F P5_client = 1)) is true | ||
+ | -- specification ( G ( F P2_factory = 1) -> G ( F P1_factory = 1)) is true | ||
+ | -- specification ((P3_bufSpace = 0 & P4_client = 1) -> !( X P5_client = 1)) | ||
+ | is true | ||
+ | -- specification ((P6_bufSpace = 0 & P2_factory = 1) -> !( X P1_factory = | ||
+ | 1)) is true | ||
+ | -- specification ((( G ( F P2_factory = 1) & G ( F P1_factory = 1)) & G ( F | ||
+ | P4_client = 1)) & G ( F P5_client = 1)) is true | ||
+ | </ | ||
+ | ---- | ||
==== CADP ==== | ==== CADP ==== | ||