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pn2mc:pt_cp_model_checking [2014/11/24 22:58]
jbiernacki [Problem] 		pn2mc:pt_cp_model_checking [2021/09/23 08:51] (current)
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 <code> <code>
-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 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 255: Line 255:
   - There are no deadlocks   - 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.
  
-----+{{:pn2mc:mc:prodkons.png?600|}}
  
-==== nuXmv ====+3 enumeration colour sets were defined: 
 +  * ''PR'' - denoting a producer. In the example it has only one possible colour - ''factory''. 
 +  * ''CON'' - denoting a consumer. In the example it has only one possible colour - ''client''. 
 +  * ''BUF'' - denoting a buffer. Number of tokens of this type refers to amount of free and occupied slots in the buffer. This colour set has also only one possible colour - ''bufSpace''.
  
 +Places ''P1'' and ''P2'' refer to producers, ''P3'' and ''P6'' refer to the buffer, ''P4'' and ''P5'' refer to consumers. Tokens in places ''P1'' and ''P5'' denote activity of a producer and a consumer, respectively. Tokens in places ''P2'' and ''P4'' denote waiting for access to the buffer. Occupied slots in the buffer are represented by the tokens in place ''P3'' and free slots are represented by the tokens in place ''P6''.
 +
 +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.
 +
 +{{:pn2mc:mc:prodkons_rg.png?600|}}
 ---- ----
 +==== nuXmv ====
  
 +Using PetriNet2ModelChecker to translate reachability graph into description of the system in nuXmv code, the following file was generated:
 +
 +<code>
 +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;
 +</code>
 +
 +
 +To verify specified properties of the system, the following LTL formulae were created:
 +
 +  - Consumer do not try to receive data from empty buffer, \\ \\ ''(P3_bufSpace = 0 Λ P4_client = 1) ⇒ ¬X(P5_client = 1)'' \\ \\ 
 +  - Producer do not try to send data to full buffer, \\ \\ ''(P6_bufSpace = 0 Λ P2_factory = 1) ⇒ ¬X(P1_factory = 1)'' \\ \\ 
 +  - There is no possibility of starvation of a consumer, \\ \\ ''GF(P4_client = 1) ⇒ GF(P5_client = 1)'' \\ \\ 
 +  - There is no possibility of starvation of a producer, \\ \\ ''GF(P2_factory = 1) ⇒ GF(P1_factory = 1)'' \\ \\ 
 +  - There are no deadlocks \\ \\ ''GF(P2_factory = 1) Λ GF(P1_factory = 1) Λ GF(P4_client = 1) Λ GF(P5_client = 1)'' \\ \\ 
 +
 +These formulae can be added to the previously generated nuXmv code for the model:
 +
 +<code>
 +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)
 +</code>
 +
 +Verification of satisfiability of these formulae can be performed in nuXmv tool:
 +
 +<code>
 +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
 +</code>
 +----
 ==== CADP ==== ==== CADP ====
  
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