2020
DOI: 10.1007/s10009-020-00586-9
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PolyGraph: a data flow model with frequency arithmetic

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Cited by 4 publications
(2 citation statements)
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“…Indeed, at each step, c l`1 i " c 1 i `f γ ij `f 1 γ ik where f and f 1 are the number of firings, resp., of v j and v k in the prefix of length l `1 in σ. At most one of γ ij and γ ik is not an integer 4 ; by symmetry, we can assume γ ik P Z. Then in the first sum we have tc l`1 i u " tc 1 i `f γ ij u for all l, that implies the proposed rewriting.…”
Section: Additional Properties Of Polygraph Executionsmentioning
confidence: 88%
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“…Indeed, at each step, c l`1 i " c 1 i `f γ ij `f 1 γ ik where f and f 1 are the number of firings, resp., of v j and v k in the prefix of length l `1 in σ. At most one of γ ij and γ ik is not an integer 4 ; by symmetry, we can assume γ ik P Z. Then in the first sum we have tc l`1 i u " tc 1 i `f γ ij u for all l, that implies the proposed rewriting.…”
Section: Additional Properties Of Polygraph Executionsmentioning
confidence: 88%
“…If P is live from a state s 1 , by Th. 2 in [5,4] there is a minimal live execution σ, such that σr1s " s 1 . Moreover, any other live execution σ 1 with σ 1 r1s " s 1 is equivalent to l repetitions of σ (for some l ě 1), that is, x σ 1 " l ¨xσ [4, Cor.…”
Section: Definition 3 (Polygraph State)mentioning
confidence: 99%