Symbolic concurrent semantics of safe petri nets
Download
1 / 28

Symbolic Concurrent Semantics of Safe Petri nets - PowerPoint PPT Presentation


  • 119 Views
  • Uploaded on

Symbolic Concurrent Semantics of Safe Petri nets. Application to Time Petri Nets. Claude Jard, ENS Cachan / IRISA, Rennes, France & Thomas Chatain, ENS Cachan / LSV, Cachan, France. Why are we interested in PN and unfoldings?.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Symbolic Concurrent Semantics of Safe Petri nets' - conor


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Symbolic concurrent semantics of safe petri nets

Symbolic Concurrent Semantics of Safe Petri nets

Application to Time Petri Nets

Claude Jard, ENS Cachan / IRISA, Rennes, France

&

Thomas Chatain, ENS Cachan / LSV, Cachan, France


Why are we interested in pn and unfoldings
Why are we interested in PN and unfoldings?

  • Supervision and diagnosis: inferring causal dependencies from observations in a distributed system (guided unfolding) -> already in use on Alcatel platforms

  • Composition of QoS contracts in WS orchestrations (need a partial order view of the behaviours) -> concurrent semantics for ORC

    In such application domains, we do not need strong decidability results and thus consider extensions of PN with data, time, probas, …


Focus of the talk
Focus of the talk

  • Generalize our symbolic approach about unfoldings of time Petri nets

  • Better understand time specificities in a concurrent setting

    • Safe colored PN with linear real constraints

    • Concurrent semantics for such nets

    • Translations of Time PN


Background pns
Background: PNs

  • Places P = {a,b,c}, Transitions T = {u,v,w}

    Consumed (pre(p,t)), read (cont(p,t)) or written (post(p,t)) by transitions

  • Marking: p M(p)  {0,1},

    • initially: M0(a)= M0(b)=1, M0(c)=0

  • t fireable iff ppre(t)cont(t), M(p)=1

  • Sequential move by firing t:

    • p, M(p):=M(p)-pre(p,t)+post(p,t)


Why do we need read arcs
Why do we need read arcs?

  • To be able to test the presence of tokens without serialisation







Concurrent semantics processes
Concurrent semantics: processes

  • v and w can be executed concurrently

Processes

(partially ordered

executions):



Notion of conflict
Notion of conflict

  • fg = (f ≤ g)  (cont(f)  pre(g)  )

  • Conflict(F) =

    •  f,g  F, pre(f)  pre(g)  

      or

    •  (fi)i[1,n]  F, fn=f1  i[1,n-1] fi fi+1








Unfolding the puzzle game6
Unfolding: the puzzle game

Maximal co-sets of places

correspond to markings

-> notion of

finite complete prefix

-> bounded in space by the

size of the marking graph

(can be exponentially smaller)

-> but the time complexity

can be exponential

(size of the prefix to the power

of the degree of concurrency)

w


Representation as a set of events event structure
Representation as a set of events: event structure

e=(e,e,Me)


Our safe colored pns
Our Safe Colored PNs

  • Places P: finite set of real variables

  • Transitions T: labeled (G(t)) with linear expressions over pre(t)+cont(t)+post(t)’

  • Initial expression: ζ0


Concurrent semantics
Concurrent semantics

  • Set of events:

  • U={e=(e,e,Ce,Me)}

  • ⊥=(∅ζ0[x/x⊥]x∈M0, M0) ∈ U

  • pre(e)  cont(e)  f∈e Mf

  • Me=post(e)

  • Ce=G(e)[x/xe]x∈pre(e)cont(e) [x’/xe]x∈post(e)

  • e is conflict-free

    f∈e Cf  Ce satisfiable

 e∈ U


Unfolding process trace
Unfolding / Process / Trace

  • Unfolding is the union of processes

  • Processes are the conflict-free and downward-causally-closed subsets of the unfolding

  • Linear extensions of processes are the sequential traces

  • No hope to obtain in general a complete finite prefix


Safe time pns
Safe Time PNs

  • Syntax:

  • TPN=(P,T,pre,post,efd,lfd,M0)

  • efd: T|R

  • lfd: T |R{}

  • Sequential semantics:

  • dob: P|R

  • (M,dob) -t,-> (M’,dob’) iff

  • - pre(t)M

  • - maxppre(t) dob(p) + efd(t) ≤ 

  • - t’T, pre(t’)M   ≤ maxppre(t’) dob(p) + lfd(t’)

  • - maxpPdob(p) ≤ 

  • M’=(M\pre(t))  post(t)

  • dob’(p)= if ppost(t), dob(p) otherwise


Symbolic concurrent semantics of safe petri nets

PE(u) = {bc}, PE(v) = {a,ab}, PE(w)={b,ab,bc}

Note:

Conflict(abw,abv)

Conflict(bcw,abv)


Symbolic concurrent semantics of safe petri nets

TPN to CPN : read arcs are added to take into account

the time dependencies

-> duplication of transitions

-> try to minimize the number of read arcs


Short term perspectives
Short term perspectives

  • Experiments

  • Existence of finite complete prefixes ? OK

  • Coding of some TPN extensions ? Stopwatches, parametric PNs…

  • Study a similar approach for networks of Timed Automata. Experiment with different semantics for time.