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Abstract Interpretation of FIFO channels

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(1)Abstract Interpretation of FIFO channels Bertrand Jeannet, Thierry Jéron, Tristan Le Gall. To cite this version: Bertrand Jeannet, Thierry Jéron, Tristan Le Gall. Abstract Interpretation of FIFO channels. [Research Report] RR-5784, INRIA. 2005, pp.25. �inria-00070237�. HAL Id: inria-00070237 https://hal.inria.fr/inria-00070237 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Abstract Interpretation of FIFO channels Bertrand Jeannet, Thierry Jéron & Tristan Le Gall. N˚5784 December 2005. ISSN 0249-6399. ISRN INRIA/RR--5784--FR+ENG. Systèmes communicants. apport de recherche.

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(76) o6[‚SSU`’~‘aX

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(78) [9]TUo]T[,—;TUqrX

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(84) TUqrX=S'X1T

(85) [,—SUT'b,TXJS˜TUqƒb,T

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(92) $%

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(207) TUqrX1_ TUqrX f X`aS q ∈ Q˜ q ∈ Q˜ SU]rZq TUqƒb,T ¤ k qrX=pX/•r_`’TU`a[9_ª[,—ˆTUqrX=ZJ[9‘a[ f — ]_rZ1TU`a[9_ªX1_rSU] f XJS˜TUqƒb,T q `aS

(208) b,‘aS[\b,_¥`’_`’TU`žb,‘¶SUT'b,TX}[,— M ™S[ a `aS (q , a, q) ∈ → bo f X/•¬¥[,—‘a˜X1_„‚TUq A=[,— L ¤ k [$X1_rpMTUqrX*o f [P[,—U™wšmXo f [7”wX*~PR\`’_rp]rZ1TU`a[9_±TUqƒb,Tc™d`–—¶TUqrX f X*`aS­b$SXJP]rX1_rZJX q → q → . . . → q b,‘’‘a[cš­XJp±~PR TUqrX$d]r[9TU`aX1_PT€b,]TNb,T[9_¶™š˜`’TUq q ∈ Q˜ b,_rp l ≤ k ™TUqrX1_ TUqrX f X$b f X l + 1 SUT'b,TXJS q ∈ q , q ∈ q , . . . , q q SU]rZ'qªTUqƒb,jT F q → q → . . . → q `aSb,‘’‘a[cšmXJpª~dR M = [9~d”!`a[9]rS˜—´[ f k = 0>/¤ D X1T q → q → . . . → q ~ X¥b“SXJP]rX1_rZJX©”wX f `–—IR!`’_„¨TUqrX±ZJ[9_rp`’TU`a[9_rSc¤ k qrX1_®TUqrX f Xªb f X l SUT'b,TXJS q ∈ S]rZq¥TUqƒb,jT F q → . . . → q `aSb,‘’‘a[7š­XJp ~dR M = `’_rp]rZ1TU`a[9_«qdR!o6[9TUqrXJSU`aS >/¤ q ,...,q ∈ q ·[ f XJ[c”wX f ™ ∃q ∈ q , q ∈ q , q → q = pX/— _`’TU`a[9_«[,—TUqrX^d]r[9TU`aX1_PT€b,]TNb,T[9_ >/¤mQ![Yš­X=qƒbc”wX=T§šm[NSUT'b,TXJS ¦ ZJZJ[ f p`’_„“T[ªTUqrX\• f ST$pX/•r_`’TU`a[9_®[,— ≈ ™SU`’_rZJX |a . . . a | ≤ k ™ ∃q ∈ q . . . q ∈ q SU]rZ'qATUqƒb,T q ≈ q `aSb,‘’‘a[7š­XJp ~dR M ¤mQ![ q → q → . . . → q ¤ q → ... → q 0. 0. f. k. k. 0. k. 0. 0. 0. a1. 1. 2 a2. 1 a1. 1. 2. f. 2 k 0 a2 2. 0 2. ak. a2. a1. f. 2. f a2. al. 2. 0 a1 1. 2. 0 1. 1. 0 2. . ‘s‘“’•” –—˜1™. 0 f. 1. 2. 2. f f. 2. f 0 2. 2. k. al. f. 1. f. f. al. f. al. a2. 2. 0 a1 1. 0 a2 2. al. 0 f. l. 0 3. 3. 0 f. f. f.

(209) !a !b. ?a ?b. b b a. Ÿ`’„‚] f X‹A  F k qrX=`’_•r_`’TX=~] (;X f WY[!pX1‘ u . . *;8:2•}|. y /

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