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Automated calculation of a progress measure for the sweep-line method Karsten Schmidt Humboldt-Universit ät zu Berlin
Sometime it’s good to forget... A)  store only important states - branching  - cover all cycles B) throw away if they cease to be useful (*) -  the sweep-line method [Mailund] (*) by help of a progress measure
Road map ,[object Object],[object Object],[object Object],[object Object]
The sweep-line method (Basic) Idea: state s     progress value p(s) with s  -t    s’     p(s)    p(s’) Not yet seen  Processed p Unprocessed sweep-line
The sweep-line method (extended) If p is  not  monotonous: s s’ p(s’) < p(s) Consequently: not too often  p(s’) < p(s) t ,[object Object],[object Object]
Setting f or our measure ,[object Object],[object Object],[object Object],[object Object],[object Object]
Petri nets 1 0 3 1 1 1 0 1 0 2 if  s  --  r b g y g y     s’  then important: different paths to same state =  linear dependency : s’ = s +   w 1 , s’ = s +   w 2       w 1  –   w 2  =  0 3 2 3 2 0 0 -2 -1 1 + = s’ = s  +  1 •  +  1 •  +  2 •  +  2 •  1 -1 0 0 0 -1 1 3 0 0 0 0 0 1 -1 0 0 -2 -1 1 4 1 7 2 0 0 0 2 1 8 4 1 5 1 1 0 0 0 0 9
The measure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Examples U TU 1 1 1 1 1 1 2 -2 0
Geometric interpretation p 2 p 1 p 3 s U progress p(s) 1
Possible optimizations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Combination with Partial Order Reduction ,[object Object],[object Object],[object Object],[object Object]
Combination with Symmetry Problem: transform state s to canonical representative c(s) so far not guaranteed:  p(s) = p(c(s)) ! Fortunately:  Petri net symmetry induces equivalence on transitions s.t. ,[object Object],s 0 s  t 1  t 2  ... t n c(s) t 1 ’ t 2 ’... t n ’ t i  equivalent t i ’
Availability www.informatik.hu-berlin.de/~kschmidt/lola.html also: integrated into The Model Checking Kit (University of Stuttgart)

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Automated Calculation of a Progress Measure of the Sweep-Line Method

  • 1. Automated calculation of a progress measure for the sweep-line method Karsten Schmidt Humboldt-Universit ät zu Berlin
  • 2. Sometime it’s good to forget... A) store only important states - branching - cover all cycles B) throw away if they cease to be useful (*) - the sweep-line method [Mailund] (*) by help of a progress measure
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  • 4. The sweep-line method (Basic) Idea: state s  progress value p(s) with s -t  s’  p(s)  p(s’) Not yet seen  Processed p Unprocessed sweep-line
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  • 7. Petri nets 1 0 3 1 1 1 0 1 0 2 if s -- r b g y g y  s’ then important: different paths to same state = linear dependency : s’ = s +  w 1 , s’ = s +  w 2   w 1 –  w 2 = 0 3 2 3 2 0 0 -2 -1 1 + = s’ = s + 1 • + 1 • + 2 • + 2 • 1 -1 0 0 0 -1 1 3 0 0 0 0 0 1 -1 0 0 -2 -1 1 4 1 7 2 0 0 0 2 1 8 4 1 5 1 1 0 0 0 0 9
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  • 9. Examples U TU 1 1 1 1 1 1 2 -2 0
  • 10. Geometric interpretation p 2 p 1 p 3 s U progress p(s) 1
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  • 14. Availability www.informatik.hu-berlin.de/~kschmidt/lola.html also: integrated into The Model Checking Kit (University of Stuttgart)