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Department of Computers and Informatics FEEI, Technical University of Košice, S lovak Republic

A SUPPORT TOOL FOR THE REACHABILITY AND OTHER PETRI NETS- RELATED PROBLEMS AND FORMAL DESIGN AND ANALYSIS OF DISCRETE SYSTEMS. Department of Computers and Informatics FEEI, Technical University of Košice, S lovak Republic Štefan HUDÁK, Štefan KOREČKO , Slavomír ŠIMOŇÁK. Contents.

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Department of Computers and Informatics FEEI, Technical University of Košice, S lovak Republic

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  1. A SUPPORT TOOL FOR THE REACHABILITY AND OTHER PETRI NETS- RELATED PROBLEMS AND FORMAL DESIGN AND ANALYSIS OF DISCRETE SYSTEMS Department of Computers and Informatics FEEI, Technical University of Košice, Slovak Republic Štefan HUDÁK, Štefan KOREČKO,Slavomír ŠIMOŇÁK

  2. Contents • PNtool overview • mFDT Environment • Supported Petri nets dialects • PNtool modes and features • PNML support • Interfaces

  3. PNtool overview • Implemented in Java • Supports four Petri nets dialects • Generalized Petri nets (GPN) • Time-basic nets (TB nets) • Evaluative Petri nets (EvPN) • Coloured Petri nets (CPN) • Provides • graphical editor • simulator • formal analyser (invariants, reachability) • import/export from/to PNML • translation to/from Process algebra, B-AMN • Is a part of the mFDT Environment

  4. B-Method (B) is model-oriented. It provides the whole development process from abstract formal specification to implementation. Process algebra (PA) views systems as processes, described in algebraic way. In PA we can deal with de/composition of systems very elegantly. Petri nets (PN) is behavior-oriented method, where the invariants of the system described can be derived automatically. mFDT Environment • multi Formal Description Technique Environment • Integrates 3 formal methods with complementary features

  5. Supported Petri nets dialects • Generalized Petri nets (GPN) • Time-basic nets (TB nets)1) • Evaluative Petri nets (EvPN)2) • Coloured Petri nets (CPN) 1) – time interval semantics introduces by Š. Hudák 2) – developed by Š. Hudák

  6. t Supported Petri nets dialectsGeneralized Petri nets • Also called Place/Transition nets, “basic” type of Petri nets in PNtool • Easy to understand graphical notation - oriented graph with 2 types of vertices: • Places (circles, or ellipses) – hold tokens, represent state of system • Transitions (rectangles) – their execution cause the change of state • Valuable analytical properties • Automatic derivation of invariants • Reachability analysis ... N=(P, T, pre, post) P={p1,p2,p3,p4} T={t} pre(p1,t) = 2, post(p1,t)=0 pre(p3,t) = 0, post(p3,t)=1 m0(p1)=2, m1(p3)=1 m0=(2,1,0,1) [t> m1=(0,0,1,4)

  7. t Supported Petri nets dialectsTime - basic nets • Extension of GPN, incorporates the concept of the time • Chronos (timestamp) • associated with each token • time when the token has been created • semantics: single value (time point) time interval • Time function • associated with each transition • relation between the timestamps of removed and created tokens 5 (5,11) max((4,8),(2,10)) = (4,10) (4,10)+1 = (5,11)

  8. t1 Supported Petri nets dialectsEvaluative Petri nets • Turing-powerful extension of GPN • 3 sets of places : • P – alike the places in GPN (called individual variables ) • Pf– with associatedfunctions over the individual variables • Pe– with associatedpredicates over the individual variables • m(p)<0 allowed for p P  Pf • Transition firing depends also on non-adjacent places P={p1,p2,p3} p1>0 means if m(p1)>0 then m(pe1)=1, else m(pe1)=0 Pe={pe1}, Pf= 2p2means 2* m(p2)

  9. t1 Supported Petri nets dialectsColoured Petri nets • High-level Petri nets • Each token has some value: integer, string, tuple, list of values… • The same expressional and analytical power as GPN • Arc expressions • specify the groups of tokens taken from and delivered to places when transitions are fired • Guarding predicates • associated with transitions • additional conditions of transitions feasibility

  10. PNtool modes and features 1) – GPN only

  11. PNtool modes and featuresGraphical editor • Allows to • draw, • save, • load and • modify a graph of a net. • Offers specialized dialogs for place, transition and arc properties

  12. PNtool modes and featuresSimulator • Enabled transitions and the effect of a transition firing are shown directly in the editor • Allows to • choose a transition to be fired • fire 1, 5 or 50 transitions randomly • go back to the previous or to the initial marking • 3 simulation modes are available for TB nets: • GPN-like mode, • time point semantics mode, • time interval semantics mode. 5 (5,11)

  13. PNtool modes and featuresEditor and simulator in CPN mode

  14. PNtool modes and featuresInvariants-based analyser • Available for GPN • Computes • basic place invariants • basic transition invariants • Implements • Silva method • Gaussian elimination method • It is also possible to use the Adriana plug-in (D.A. Zaitsev)

  15. PNtool modes and featuresReachability analyser • Available for GPN • Implements original reachability problem solution by Š. Hudák: • Construction of an Mw automaton for the given net N. (fully implemented, including a visualisation) • Creation and solving of the integer linear programming problem for Mw and an examined vector q (partially implemented) • Mw automaton • special type of finite automaton • represents the (possibly infinite) state space of N • contains macrostates • constructed only once for a given net

  16. PNtool modes and featuresAnalysers - screenshot

  17. PNML support • Available for GPN and EvPN • PNML • Petri Net Markup Language • XML-based interchange file format for Petri-nets • New elements defined for EvPN • evpnPlace - specifies whether the given place belongs to P, Pe or Pf, • evpnArc - specifies whether a negative value of marking of the place adjacent to this arc is allowed, • relPlace - includes the name of a place, not connected to this arc, which affects the pre or post value of the arc, • capacity - specifies a capacityof the place adjacent to this arc.

  18. PNtool interfaces • Theoretical basis: semantics preserving translations • PN  Algebra of communicating processes (ACP) 1) • Algebra of process components (APC)  PN 1) • EvPN  B-Abstact machine notation (B-AMN) 2) • B-AMN  CPN 2) • Implementation • PN  ACP: standalone tool ACP2PETRI • APC  PN: standalone tool PETRI2APC • EvPN  B-AMN: implemented in PNtool • B-AMN  CPN: partial standalone implementation 1) – defined by S. Šimoňák 2) – defined by Š. Korečko

  19. PNtool interfaces: example EvPN  B-AMN MACHINE EvPNfig3 VARIABLES sv_1, sv_2, sv_3 INVARIANT sv_1:NAT & sv_2:NAT & sv_3:NAT DEFINITIONS grd1== sv_1>0 INITIALISATION sv_1:=1 || sv_2:=2 || sv_3:=0 OPERATIONS op_1= SELECT grd1 & sv_1>=1 THEN sv_1:=sv_1 - 1 || sv_3:=sv_3 + 2*sv_2 END END

  20. Future work • To add a PNML support for TB nets • require another extension of PNML. • To implement the second step of RP algorithm • To be able to load/edit/save a graph of Mw automaton in PNtool • as equivalent P/T net. • To use some 2D graphics framework for the graphical editor and simulator.

  21. Thank you for your patience. Štefan HUDÁK Štefan KOREČKO Slavomír ŠIMOŇÁK

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