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Forward analysis for petri nets with name creation

機(jī)譯：具有名稱創(chuàng)建的Petri網(wǎng)的正向分析

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Pure names are identifiers with no relation between them, except equality and inequality. In previous works we have extended P/T nets with the capability of creating and managing pure names, obtaining ν-APNs and proved that they are strictly well structured (WSTS), so that coverability and boundedness are decidable. Here we use the framework recently developed by Finkel and Goubault-Larrecq for forward analysis for WSTS, in the case of ν-APNs, to compute the cover, that gives a good over approximation of the set of reachable markings. We prove that the least complete domain containing the set of markings is effectively representable. Moreover, we prove that in the completion we can compute least upper bounds of simple loops. Therefore, a forward Karp-Miller procedure that computes the cover is applicable. However, we prove that in general the cover is not computable, so that the procedure is non-terminating in general. As a corollary, we obtain the analogous result for Transfer Data nets and Data Nets. Finally, we show that a slight modification of the forward analysis yields decidability of a weak form of boundedness called width-boundedness.
機(jī)譯：純名稱是標(biāo)識(shí)符，除相等和不相等外，它們之間沒有任何關(guān)系。在以前的工作中，我們擴(kuò)展了P / T網(wǎng)絡(luò)，使其具有創(chuàng)建和管理純名稱，獲取ν-APN的能力，并證明它們具有嚴(yán)格的結(jié)構(gòu)化（WSTS），因此可確定性和可確定性。在這里，我們使用Finkel和Goubault-Larrecq最近開發(fā)的框架（在ν-APN的情況下）對(duì)WSTS進(jìn)行正向分析，以計(jì)算覆蓋率，這可以很好地逼近可到達(dá)標(biāo)記集。我們證明了包含標(biāo)記集的最不完整的域是有效可表示的。此外，我們證明了在完成過程中，我們可以計(jì)算出簡(jiǎn)單循環(huán)的最小上限。因此，適用于計(jì)算覆蓋率的正向Karp-Miller程序。但是，我們證明封面通常是不可計(jì)算的，因此該過程通??常不會(huì)終止。因此，我們獲得了傳輸數(shù)據(jù)網(wǎng)和數(shù)據(jù)網(wǎng)的類似結(jié)果。最后，我們表明對(duì)正向分析的輕微修改會(huì)產(chǎn)生一種確定性，該弱化形式的有界性稱為寬度有界性。

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