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Graph transformation systems, Petri nets and Semilinear Sets: Checking for the Absence of Forbidden Paths in Graphs

Barbara Koenig
2007
This technique is based on the approximation of graph transformation systems by Petri nets and on semilinear sets of markings. An important application is deadlock analysis in distributed systems.  ...  We introduce an analysis method that checks for the absence of (Euler) paths or cycles in the set of graphs reachable from a start graph via graph transformation rules.  ...  Furthermore I would like to thank Vitali Kozioura for developing and maintaining the AUGUR tool. Bibliography  ... 
doi:10.14279/tuj.eceasst.2.26.25 fatcat:ksurfo2etzgizd3ioyus7devhu

Recursive Petri nets

Serge Haddad, Denis Poitrenaud
2007 Acta Informatica  
Here we present and develop the theory of such a model, the recursive Petri nets.  ...  Furthermore, we prove that these patterns cannot be modelled by ordinary Petri nets. Then we study the decidability of some problems: reachability, finiteness and bisimulation.  ...  Sequential Recursive Petri Nets Definitions Preliminaries: As our model relies heavily on semilinear sets, we briefly introduce their definition and properties.  ... 
doi:10.1007/s00236-007-0055-y fatcat:ekrl3z2juzdijdlg26xjif2bma

Verification of Graph Transformation Systems with Context-Free Specifications [chapter]

Barbara König, Javier Esparza
2010 Lecture Notes in Computer Science  
The technique is based on the approximation of graph transformation systems by Petri nets and on semilinear sets of markings.  ...  An important application is deadlock analysis for interaction nets and we specifically show how to apply the technique to an infinite-state dining philosopher's system.  ...  and for their help with the implementation.  ... 
doi:10.1007/978-3-642-15928-2_8 fatcat:rbgio22yj5h4fbwofk7yohw5my

Deciding the Existence of Cut-Off in Parameterized Rendez-Vous Networks

Florian Horn, Arnaud Sangnier, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
We study networks of processes which all execute the same finite-state protocol and communicate thanks to a rendez-vous mechanism.  ...  We provide decidability and complexity results of this problem under various assumptions, such as absence/presence of a leader or symmetric/asymmetric rendez-vous.  ...  Every periodic subset P ⊆ N is semilinear. We now recall some connections between Petri nets and semilinear sets.  ... 
doi:10.4230/lipics.concur.2020.46 dblp:conf/concur/0001S20 fatcat:pi5o3lpqxze4lnyjtek6dimcj4

Deciding the existence of cut-off in parameterized rendez-vous networks [article]

Florian Horn, Arnaud Sangnier
2020 arXiv   pre-print
We study networks of processes which all execute the same finite-state protocol and communicate thanks to a rendez-vous mechanism.  ...  We provide decidability and complexity results of this problem under various assumptions, such as absence/presence of a leader or symmetric/asymmetric rendez-vous.  ...  By Lemma 3, we get that P is semilinear. We now recall some connections between Petri nets and semilinear sets.  ... 
arXiv:2007.05789v1 fatcat:b3rtdhaj35g7lpozzqpljbx5am

An Algorithm for the General Petri Net Reachability Problem

Ernst W. Mayr
1984 SIAM journal on computing (Print)  
An algorithm is presented for the general Petri net reachability problem based on ;■: generalization of the basic reachability construction which is symmetric with respect to the initial and final marking  ...  Sets of transition sequences described by finite automata are used for approximations to firing sequences, and the approximation error is assessed by uniformly constructable Presburger expressions.  ...  Whereas these methods fail for the general case as they rely on semilinear reachability sets-to id there are Petri nets with si> places and non-semilinear reachability sets-the general reachability problem  ... 
doi:10.1137/0213029 fatcat:bjtyu2cnnffkrmrfvl5qvzvle4

An algorithm for the general Petri net reachability problem

Ernst W. Mayr
1981 Proceedings of the thirteenth annual ACM symposium on Theory of computing - STOC '81  
An algorithm is presented for the general Petri net reachability problem based on ;■: generalization of the basic reachability construction which is symmetric with respect to the initial and final marking  ...  Sets of transition sequences described by finite automata are used for approximations to firing sequences, and the approximation error is assessed by uniformly constructable Presburger expressions.  ...  Whereas these methods fail for the general case as they rely on semilinear reachability sets-to id there are Petri nets with si> places and non-semilinear reachability sets-the general reachability problem  ... 
doi:10.1145/800076.802477 dblp:conf/stoc/Mayr81 fatcat:hbogciuta5cnfj47r2ijrugnva

Robustness of Expressivity in Chemical Reaction Networks [chapter]

Robert Brijder, David Doty, David Soloveichik
2016 Lecture Notes in Computer Science  
Both results are proven via a generalized framework that simultaneously captures several definitions, directly inspired by a recent Petri net result of Esparza, Ganty, Leroux, and Majumder [CONCUR 2015  ...  The latter define output by majority vote among "yes" and "no" voters.  ...  R.B. thanks Grzegorz Rozenberg for interesting and useful discussions regarding chemical reaction networks. D.D. thanks Ryan James for suggesting the democratic CRD model.  ... 
doi:10.1007/978-3-319-43994-5_4 fatcat:kaqecb4ib5cbhjmgknrgi5z43m

On Computing Reachability Sets of Process Rewrite Systems [chapter]

Ahmed Bouajjani, Tayssir Touili
2005 Lecture Notes in Computer Science  
a Petri net).  ...  sets based) procedures for the analysis of Petri nets in order to analyze PRS models.  ...  of Petri nets using semilinear sets (or linear arithmetics) to a procedure for symbolic reachability analysis of PRS.  ... 
doi:10.1007/978-3-540-32033-3_35 fatcat:6phqzdvpfbaidoz7ydv52gmawi

Refinement and Asynchronous Composition of Modal Petri Nets [chapter]

Dorsaf Elhog-Benzina, Serge Haddad, Rolf Hennicker
2012 Lecture Notes in Computer Science  
For any modal Petri net, we define its generated modal language specification which abstracts away silent transitions.  ...  As an important application scenario of our approach we consider I/O-Petri nets and their asynchronous composition which typically leads to an infinite state system.  ...  We are very grateful to all reviewers of the submitted version of this paper who have provided detailed reports with many valuable hints and suggestions.  ... 
doi:10.1007/978-3-642-29072-5_4 fatcat:5xxosy3lqvdzrci37xivjzyi5y

Automatic Verification of Multi-queue Discrete Timed Automata [chapter]

Pierluigi San Pietro, Zhe Dang
2003 Lecture Notes in Computer Science  
Due to careful restrictions on queue usage, the binary reachability (the set of all pairs of configurations (¦ § © of an MQDTA such that ¦ can reach © through zero or more transitions) is effectively semilinear  ...  The MQDTA model can be used to specify and verify various systems with unbounded queues, such as a real-time scheduler.  ...  Most of the works have concentrated on very few models, such as Petri Nets (PN), Pushdown Automata (PA) and Timed Automata (TA), and have studied the decidability and complexity of model-checking various  ... 
doi:10.1007/3-540-45071-8_18 fatcat:dktetd4myvfotf4dzhruo7vhaq

Verification of Infinite State Systems [chapter]

Ahmed Bouajjani
2003 Lecture Notes in Computer Science  
The development of our modern societies needs more and more involvement of computers in managing highly complex and (safety-)critical tasks, e.g., in telecommunication, chemical and physical process control  ...  It is essential to be able to produce reliable hardware and software systems, since any erroneous behaviour can have catastrophic (economical and human) consequences.  ...  We show how unfoldings can be extended to the context of infinite-state Petri nets.  ... 
doi:10.1007/978-3-540-45220-1_7 fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m

Hierarchical System Design Using Refinable Recursive Petri Net

Messaouda Bouneb, Djamel Eddine Saidouni, Jean Michel Ilie
2018 Computing and informatics  
For this purpose we propose the model of Refinable Recursive Petri Nets (RRPN) under a maximality semantics. In this model a notion of undefined transitions is considered.  ...  This paper is in the framework of the specification and verification of concurrent dynamic systems.  ...  REFINABLE RECURSIVE PETRI NETS A refinable recursive Petri net is a recursive Petri net on which all transitions are labeled by actions and abstract transitions may be labeled by ⊥ (the abstract transitions  ... 
doi:10.4149/cai_2018_3_635 fatcat:3zayqytdhfazxblymsisy2ehya

Democratic, Existential, and Consensus-Based Output Conventions in Stable Computation by Chemical Reaction Networks [article]

Robert Brijder and David Doty and David Soloveichik
2017 arXiv   pre-print
Both results are proven via a generalized framework that simultaneously captures several definitions, directly inspired by a Petri net result of Esparza, Ganty, Leroux, and Majumder [CONCUR 2015].  ...  The CRNs using the latter output convention define output by majority vote among "yes" and "no" voters.  ...  R.B. thanks Grzegorz Rozenberg for useful comments on an earlier version of this paper and for useful discussions regarding CRNs in general.  ... 
arXiv:1604.03687v2 fatcat:nyxanndb4jc3zm53smi3ociqg4

Flatness and Complexity of Immediate Observation Petri Nets [article]

Mikhail Raskin, Chana Weil-Kennedy, Javier Esparza
2020 arXiv   pre-print
We show that, while BIO nets are no longer globally flat, and their sets of reachable markings may be non-semilinear, they are still locally flat.  ...  This makes BIO nets the first natural net class with non-semilinear reachability relation for which the reachability problem is provably simpler than for general Petri nets.  ...  A relation on N n is semilinear if it is semilinear as a set of N 2n . All these notions extend to sets of multisets. Place/transition Petri nets with weighted arcs.  ... 
arXiv:2001.09966v3 fatcat:puyfuc56izgdbepoe6xc226luq
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