On the use of unfoldings to abstract communicating automata into sets of scenarios

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Submitted on 19 May 2006

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On the use of unfoldings to abstract communicating automata into sets of scenarios

Thomas Chatain, Loïc Hélouët, Claude Jard

To cite this version:

Thomas Chatain, Loïc Hélouët, Claude Jard. On the use of unfoldings to abstract communicating automata into sets of scenarios. [Research Report] RR-5778, INRIA. 2005, pp.23. �inria-00070243�

ISRN INRIA/RR--5778--FR+ENG

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

On the use of unfoldings to abstract

communicating automata into sets of scenarios

Thomas Chatain, Loïc Hélouët, Claude Jard

N˚5778

Décembre 2005

Systèmes communicants

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l

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B2

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gh[£i \Fe<w<“s`

H = (N,→ ,M, n0, F)^{š7+z<` l `} N gs[ƒi—[F`o\,cj–µf<cLy<`[š

→⊆ N × M ×N ^{gs[ri—\ l} if<[Fg¢\˜gscjf l `“´i¬Ÿ

\˜gscjf›š

M gs[ri—[]`\qc–mt7įY<u#[š

n0

gs[+\˜z<`%gsf<g¢\˜gsij“›f<cLy<`jšOijf<y

F gs[ri—[F`o\qcj–µiaa`w”\˜ghf<ˆ

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l

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H y<`o¶‡f<`[9i[F`o\cj–#w‡i\Fz<[

PH

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p = n₀ −→^M1 n₁ −→^M2 n2. . . −→^Mk nk ∈ PH

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Bp = M1 ◦M2 ◦ · · · ◦Mk

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Ai = hS_i, Σi,→_i, s⁰_ii_i∈I gs[,y<`o¶‡f<`y®ij[it7įY<u

M = (E, Σ, A, Θ)šL+gh\˜z\Fz<`,–Âcd“s“hc¬+ghf<ˆ9w l cdwx` l \Fgs`[ S

g

Σ = S

i∈I

−→i

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e = (ei)i∈I

š"`Xija{z

ei

gh[—cj–\˜z”`³–Âc l _

ei = (e⁰, t)šijf<y¯"`'+gs“s“-y<`f”cj\˜`

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ghg

A = S

i∈I

Σi

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gsghg

Θ(t) =λ(t)

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År[

Σ, A, Θ ^{i l} `—gh_0w<“hgsagh\q–Âc

l

i³ˆdg¢ d`f [F`\9cj–«` j`fQ\˜[

Eš"`—+gh“s“µcj–¹\˜`f®y<`f<cj\˜`

i—t7įY<u

B = (E, Σ, A, Θ) tQZ¯g¢\˜[ƒ[]`\,c–µ` d`fQ\˜[

E^© ¤fQ\˜e<g¢\˜gh j`“¢ZdšOijf¯` j`fQ\

e 6=⊥

l `w l `[]`fQ\˜[:\Fz<`([™Z¡f”a{z l cdf”gXi=\˜gscjf9cj–xijao\˜gscjf<[ cj–‡\Fz<`(ie”\˜cd_0i\Fcdf

Ai

[Fe<a{z9\Fz‡i\

ei 6=•

ijf<y

ei = (e⁰, t) _J`Xijf<['\Fz‡i\’\˜z<`“scLaXi“«ija\Fgscdf°cdf ije”\Fcd_0i\˜cdf

Ai

gh[

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i ∈ I ijf<yV–Âc l ijfQZVa{z‡ijghf

⊥ −→ e¹ = (⊥, t₁)−→e² = (e¹, t2). . .−→e^k = (e^k−1, tk) []e<a{z¦\Fz‡i\

∀j ∈1..k, e^ji 6=•^š¡\˜z<`

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t1.t2. . . tk

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AB ^ijf”y CEX ^c–

5 gsˆde l ` =

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0 =⊥, 3 = ((1,(1, b,2)),•), 1 = ((0,(0, a,1)),•), 4 = (•,(2,(1, e,2))),

2 = (•,(0,(0, c,1))), 5 = ((3,(2, x,0)),(4,(2, x,0)))