Accelerations for the Coverability Set of Petri Nets with Names

Rosa-Velardo, Fernando; Martos-Salgado, María; Frutos-Escrig, David de

doi:10.3233/fi-2011-611

Cited by 7 publications

(5 citation statements)

References 18 publications

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“…The first indicator that reachability may be decidable for UDPN is a characterization of the coverability set established in the paper [18], in the same paper, as a conclusion, the place-boundedness problem is proven to be decidable. The recent development in other classes proposed in [22] can be found in papers [33,32,31,18], all those results are focused on better understanding of the coverability relation.…”

Section: Related Research and Motivationmentioning

confidence: 99%

“…Unordered data nets extend the classical model of Petri nets by allowing each token to carry a datum from a countable set D. We recall the definition from [33,32]. A multiset over some set X is a function M : X → N. The set X ⊕ of all multisets over X is ordered pointwise, and the multiset union of Similarly, flow function provides multisets F (p, t) and F (t, p) over the variables Var, so we can associate to each transition t the corresponding data vectors F (•, t) and F (t, •) : The complexity of checking state equations for UDPN thus matches that of the same problem for ordinary Petri nets (via linear programming).…”

Section: Unordered Data Petri Netsmentioning

confidence: 99%

Section: Unordered Data Petri Netsmentioning

confidence: 99%

“…We show two applications to the reachability analysis of counter programs extended with data (in Section 6). The first involves finding state invariants for unordered data Petri nets [22,33,18] and the second aplication is the reachability problem for blind counter automata [15] extended with data.…”

Section: Introductionmentioning

confidence: 99%

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Linear combinations of unordered data vectors

Hofman

Leroux

Totzke

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question if a given data vector can be expressed as a finite sum of others, only assuming that 1) the domain is countable and 2) the given set of base vectors is finite up to permutations of the domain.Based on a succinct representation of the involved permutations as integer linear constraints, we derive that positive instances can be witnessed in a bounded subset of the domain.For data vectors over a group we moreover study when a data vector is reversible, that is, if its inverse is expressible using only nonnegative coefficients. We show that if all base vectors are reversible then the expressibility problem reduces to checking membership in finitely generated subgroups. Moreover, checking reversibility also reduces to such membership tests.These questions naturally appear in the analysis of counter machines extended with unordered data: namely, for data vectors over (Z d , +) expressibility directly corresponds to checking state equations for Coloured Petri nets where tokens can only be tested for equality. We derive that in this case, expressibility is in NP, and in P for reversible instances. These upper bounds are tight: they match the lower bounds for standard integer vectors (over singleton domains). ACM Subject Classification F.1.1 Models of Computation Keywords and phrases Computation with atoms, vector addition systemsDigital Object Identifier 10.4230/LIPIcs.xxx.yyy.p IntroductionFinite collections of named values are basic structures used in many areas of theoretical computer science. They can be used for instance to model databases snapshots or define the operational semantics of programming languages. We can formalize these as functions v : D → X from some countable domain D of names or data, into some value space X, and call such functions (X-valued) data vectors. Often the actual names used are not relevant and instead one is interested in data vectors up to renaming, i.e., one wants to consider vectors v and w equivalent if v = w • θ for some permutation θ : D → D of the domain. We consider the case where the value space X has additional algebraic structure. Namely, we focus on data vectors where the values are from some commutative monoid (M, +, 0) and where all but finitely many names are mapped to the neutral element. A natural question then asks if a given data vector is expressible as a sum of vectors from a given set, where the monoid operation is lifted to data vectors pointwise.

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Section: Related Research and Motivationmentioning

confidence: 99%

Section: Unordered Data Petri Netsmentioning

confidence: 99%

Section: Unordered Data Petri Netsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linear combinations of unordered data vectors

Hofman

Leroux

Totzke

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…Repeated control-state reachability is undecidable for general WSTS, but decidable for Petri nets by use of the Karp-Miller coverability tree [KM67] and the detection of increasing sequences. That technique fails on well-structured extensions of Petri nets: generating the Karp-Miller tree does not always terminate on ν-Petri nets [RMdF11], on reset Petri nets [DFS98], on transfer Petri nets, on broadcast protocols, and on the depth-bounded π-calculus [HMM14, RM12,ZWH12] which can simulate reset Petri nets. This is perhaps why little research has been conducted on coverability tree algorithms and model checking of liveness properties for general WSTS.…”

mentioning

confidence: 99%

Forward Analysis for WSTS, Part III: Karp-Miller Trees

Blondin,

Finkel,

Goubault-Larrecq

2017

Preprint

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This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and "Forward Analysis for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward reachability analyses of WSTS, using finite representations of downwards-closed sets. We further develop this framework to obtain a generic Karp-Miller algorithm for the new class of very-WSTS. This allows us to show that coverability sets of very-WSTS can be computed as their finite ideal decompositions. Under natural effectiveness assumptions, we also show that LTL model checking for very-WSTS is decidable. The termination of our procedure rests on a new notion of acceleration levels, which we study. We characterize those domains that allow for only finitely many accelerations, based on ordinal ranks.

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The Ideal Theory for WSTS

Finkel

2016

Lecture Notes in Computer Science

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Accelerations for the Coverability Set of Petri Nets with Names

Cited by 7 publications

References 18 publications

Linear combinations of unordered data vectors

Linear combinations of unordered data vectors

Forward Analysis for WSTS, Part III: Karp-Miller Trees

The Ideal Theory for WSTS

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