Comparison of the expressiveness of Arc, Place and Transition Time - PowerPoint PPT Presentation

Motivation Definition Expressiveness Conclusion Comparison of the expressiveness of Arc, Place and Transition Time Petri Nets Marc Boyer (1) and Olivier (H.) Roux (2) (1) IRIT, Toulouse, France - (2) IRCCyN, Nantes, France june, 28th, 2007 - ICATPN’07 M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 1 / 39

Motivation Definition Expressiveness Conclusion Outline Motivation ◮ Model definitions ◮ Comparing model expressiveness ◮ Conclusion ◮ M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 2 / 39

Motivation Definition Expressiveness Conclusion Outline Motivation ◮ Model definitions ◮ Comparing model expressiveness ◮ Conclusion ◮ M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 3 / 39

Motivation Definition Expressiveness Conclusion Why this study? In 30 years, several models developed: intervals on transitions [Mer74, BD91], places [KDCD96] or arcs [Han93, AN01, dFRA00] each model has its own application domain people are attached to their model when failing to model: user skill or model power? M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 4 / 39

Motivation Definition Expressiveness Conclusion Why this study? In 30 years, several models developed: intervals on transitions [Mer74, BD91], places [KDCD96] or arcs [Han93, AN01, dFRA00] each model has its own application domain people are attached to their model when failing to model: user skill or model power? Previous studies several studies on power of some models: decidability of reachability, covering some comparisons have been done: [CA99], [BV00] but M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 4 / 39

Motivation Definition Expressiveness Conclusion Why this study? In 30 years, several models developed: intervals on transitions [Mer74, BD91], places [KDCD96] or arcs [Han93, AN01, dFRA00] each model has its own application domain people are attached to their model when failing to model: user skill or model power? Previous studies several studies on power of some models: decidability of reachability, covering some comparisons have been done: [CA99], [BV00] but some results are contradictory M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 4 / 39

Motivation Definition Expressiveness Conclusion Comparing what ? With which criterion ? Comparing: Petri nets with time constraint with intervals on transitions [Mer74, BD91], places [KDCD96] or arcs [Han93, AN01, dFRA00] with weak and strong semantics one bounded ( ⇐ ⇒ k-bounded with mono-server semantics) with large and strict intervals bounds ([ a , b ] , [ a , b [ , ] a , b ] , ] a , b [), cf [BV00] M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 5 / 39

Motivation Definition Expressiveness Conclusion Comparing what ? With which criterion ? Comparing: Petri nets with time constraint with intervals on transitions [Mer74, BD91], places [KDCD96] or arcs [Han93, AN01, dFRA00] with weak and strong semantics one bounded ( ⇐ ⇒ k-bounded with mono-server semantics) with large and strict intervals bounds ([ a , b ] , [ a , b [ , ] a , b ] , ] a , b [), cf [BV00] Criterion: weak timed bisimulation “weak bisimulation” is “the same visible actions are possible in both models” M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 5 / 39

Motivation Definition Expressiveness Conclusion Comparing what ? With which criterion ? Comparing: Petri nets with time constraint with intervals on transitions [Mer74, BD91], places [KDCD96] or arcs [Han93, AN01, dFRA00] with weak and strong semantics one bounded ( ⇐ ⇒ k-bounded with mono-server semantics) with large and strict intervals bounds ([ a , b ] , [ a , b [ , ] a , b ] , ] a , b [), cf [BV00] Criterion: weak timed bisimulation “weak bisimulation” is “the same visible actions are possible in both models” “weak timed bisimulation” is “the same visible actions are possible in both models at the same time ” M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 5 / 39

Motivation Definition Expressiveness Conclusion Comparing what ? With which criterion ? Comparing: Petri nets with time constraint with intervals on transitions [Mer74, BD91], places [KDCD96] or arcs [Han93, AN01, dFRA00] with weak and strong semantics one bounded ( ⇐ ⇒ k-bounded with mono-server semantics) with large and strict intervals bounds ([ a , b ] , [ a , b [ , ] a , b ] , ] a , b [), cf [BV00] Criterion: weak timed bisimulation “weak bisimulation” is “the same visible actions are possible in both models” “weak timed bisimulation” is “the same visible actions are possible in both models at the same time ” bisimulation implies language equality M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 5 / 39

Motivation Definition Expressiveness Conclusion Bisimulation a a a a a a ε a c b c c b c b c b M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 6 / 39

Motivation Definition Expressiveness Conclusion Outline Motivation ◮ Model definitions ◮ T-time Petri net Strong vs Weak Semantics P-time Petri net A-time Petri net Comparing model expressiveness ◮ Introduction, previous works Results from [BCH + 05] Weak with strong for P-TPN and A-TPN Something that P-TPN can’t do, and T-TPN does Emulating T-TPN rule with A-TPN Conclusion ◮ M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 7 / 39

Motivation Definition Expressiveness Conclusion Outline Motivation ◮ Model definitions ◮ T-time Petri net Strong vs Weak Semantics P-time Petri net A-time Petri net Comparing model expressiveness ◮ Introduction, previous works Results from [BCH + 05] Weak with strong for P-TPN and A-TPN Something that P-TPN can’t do, and T-TPN does Emulating T-TPN rule with A-TPN Conclusion ◮ M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 8 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): basis Example (Basic: net from L. Gallon) p 1 p 3 • • t 1 t 3 p 2 t 2 M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 9 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): basis Example (Basic: net from L. Gallon) p 1 p 3 • t 1 t 3 p 2 • t 2 M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 9 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): basis Example (Basic: net from L. Gallon) p 1 p 3 • • t 1 [0 , 4] t 3 [5 , 6] p 2 t 2 [3 , 4] M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 9 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): basis Example (Basic: net from L. Gallon) p 1 p 3 • • t 1 [0 , 4] t 3 [5 , 6] p 2 t 2 [3 , 4] { p 1 , p 3 } { p 1 , p 3 } { p 2 , p 3 } { p 2 , p 3 } 4 t 1 1 t 3 ν ( t 1 ) = 0 → ν ( t 1 ) = 4 → ν ( t 2 ) = 0 → ν ( t 2 ) = 1 → · · · ν ( t 3 ) = 0 ν ( t 3 ) = 4 ν ( t 3 ) = 4 ν ( t 3 ) = 5 M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 9 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): properties Example (Priority) p 1 • t 3 [3 , 3] t 1 [1 , 2] p 2 t 2 [3 , 4] Strong semantics ( T-TPN ): t 3 is never fired, t 1 and t 2 always are Weak semantics ( T-TPN ): all t 1 , t 2 and t 3 can be fired, or not M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 10 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): properties Example (Priority) p 1 t 3 [3 , 3] t 1 [1 , 2] p 2 • t 2 [3 , 4] Strong semantics ( T-TPN ): t 3 is never fired, t 1 and t 2 always are Weak semantics ( T-TPN ): all t 1 , t 2 and t 3 can be fired, or not M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 10 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): properties Example (Priority) p 1 t 3 [3 , 3] t 1 [1 , 2] p 2 t 2 [3 , 4] Strong semantics ( T-TPN ): t 3 is never fired, t 1 and t 2 always are Weak semantics ( T-TPN ): all t 1 , t 2 and t 3 can be fired, or not M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 10 / 39

Motivation Definition Expressiveness Conclusion T-time Petri net ( T-TPN ): properties Example (Synchronisation) p 1 p 3 • • t 1 [0 , 4] t 2 [0 , 3] p 2 p 4 t synch [1 , 1] { p 1 , p 3 } ν ( t 1 ) = 0 ν ( t 2 ) = 0 M. Boyer / O.H. Roux (IRIT/IRCCyN) Expressiveness of Time Petri Nets june, 28th, 2007 - ICATPN’07 11 / 39