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Coverability, Termination, and Finiteness in Recursive Petri Nets [article]

Alain Finkel, Serge Haddad, Igor Khmelnitsky
2021 arXiv   pre-print
Although Recursive Petri nets strictly extend Petri nets and context-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable  ...  In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets.  ...  We thank the reviewers very much for their deep, detailed and insightful reviews, which helped us a lot in order to simplify and clarify this paper.  ... 
arXiv:2109.06804v2 fatcat:2kn4hx7msbcwjfljzjc764zz34

Nonprimitive recursive complexity and undecidability for Petri net equivalences

Petr Jančar
2001 Theoretical Computer Science  
Sci. 148 (1995) 281-301] can be immediately extended for the whole range of equivalences (and preorders) on labelled Petri nets.  ...  Secondly, it shows that restricting our attention to nets with ÿnite reachable space, the respective (decidable) problems are nonprimitive recursive; this approach also applies to Mayr and Meyer's result  ...  Any reasonable preorder is undecidable for labelled Petri nets. Theorem 4. Any reasonable preorder is not primitive recursive for r-ÿnite labelled Petri nets.  ... 
doi:10.1016/s0304-3975(00)00100-6 fatcat:a3jdzuu5vba6pljcpfe65fiv3u

The Ordinal-Recursive Complexity of Timed-arc Petri Nets, Data Nets, and Other Enriched Nets

Serge Haddad, Sylvain Schmitz, Philippe Schnoebelen
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
We show how to reliably compute fast-growing functions with timed-arc Petri nets and data nets.  ...  This construction provides ordinal-recursive lower bounds on the complexity of the main decidable properties (safety, termination, regular simulation, etc.) of these models.  ...  A Petri Data Net (PDN) is a Petri net where each token carries an identity from a linearly ordered and dense domain D.  ... 
doi:10.1109/lics.2012.46 dblp:conf/lics/HaddadSS12 fatcat:vyeh46lnhnen3dj3us5lrgkdmq

Petri Meta-Compiler - A Recursive Approach to System Design and Development

Piotr Chrzastowski-Wachtel, Michal Dolezek, Pawel Greipner, Tomasz Wójcicki
2019 Applications and Theory of Petri Nets  
We gain a common language 110 PNSE'19 -Petri Nets and Software Engineering  ...  We propose a framework for the definition of Petri Net models in the Petri net approach. All the components: places, transitions, arcs are defined as Petri net objects.  ...  General scheme Chrząstowski-Wachtel Petri Meta-Compiler -a Recursive Approach PNSE'19 -Petri Nets and Software Engineering  ... 
dblp:conf/apn/Chrzastowski-Wachtel19 fatcat:rwr5azyairhe7jrfanqw23dy5q

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

Maximality Semantic For Recursive Petri Nets

Djamel-Eddine Saidouni, Messaouda Bouneb, Jean-Michel Ilie
2013 ECMS 2013 Proceedings edited by: Webjorn Rekdalsbakken, Robin T. Bye, Houxiang Zhang  
For this purpose, we propose a maximality operational semantic for recursive Petri nets.  ...  As an illustration, a system of filling medical bottles is specified in terms of recursive Petri net and translated to a maximality-based labeled transition system.  ...  RECURSIVE PETRI NETS Recursive Petri Nets (RPN) has been proposed for the specification and analysis of dynamic systems (S. Haddad and D. Poitrenaud, 2007) (S. Haddad and D.  ... 
doi:10.7148/2013-0544 dblp:conf/ecms/SaidouniBI13 fatcat:abrvtdkic5fpflxyg526apey4q

Checking linear temporal formulas on sequential recursive Petri nets

S. Haddad, D. Poitrenaud
Proceedings Eighth International Symposium on Temporal Representation and Reasoning. TIME 2001  
Recursive Petri nets (RPNs) have been introduced to model systems with dynamic structure.  ...  In this work, we introduce a submodel of RPNs called sequential recursive Petri nets (SRPNs) and we study the model checking of the action-based linear time logic on SRPNs.  ...  At last, we have studied the language family of SRPNs and proved that this family strictly includes the union of Petri nets and context-free languages.  ... 
doi:10.1109/time.2001.930718 dblp:conf/time/HaddadP01 fatcat:y5oldmpt7raqhis6p6jzih3e6a

Using Net Refinement to Compute the Fixpoint of a Recursive Expression

Eike Best, Maciej Koutny
1995 Electronical Notes in Theoretical Computer Science  
The talk illustrates the general Petri net semantics of equations such a s X = term(X) using a basic CCS-like process algebra without restriction, synchronisation and relabelling.  ...  In Petri nets, transition re nement p l a ys a similar role. More precisely, l e t a recursive equation of the form X = term(X) (1) be given, where term(X) m a y c o n tain variable X freely.  ...  The talk illustrates the general Petri net semantics of equations such a s ( 1 ) using a basic CCS-like process algebra without restriction, synchronisation and c 1995 Elsevier Science B. V.  ... 
doi:10.1016/s1571-0661(05)80177-x fatcat:kveh3bh2n5hvrjwz62mrtyryn4

Page 7285 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
(RS-AOS-PG; Pereslavl’ Zalesskiy) Nested Petri nets: multi-level and recursive systems. (English summary) Special issue on concurrency specification and programming (Berlin, 2000). Fund.  ...  Here we con- sider multi-level and recursive NP-nets, for which decidability of termination and some other properties are proved.  ... 

Petri nets semantics of π-calculus

Zhenhua Yu, Yuanli Cai, Haiping Xu
2008 Frontiers of Electrical and Electronic Engineering in China  
concurrency, choice and recursive modules.  ...  As p-calculus based on the interleaving semantics cannot depict the true concurrency and has few supporting tools, it is translated into Petri nets. p-calculus is divided into basic elements, sequence,  ...  In this paper, p-calculus is divided into basic elements, recursive, sequence, concurrency and choice modules. These modules are translated into Petri nets, and then construct a complicated system.  ... 
doi:10.1007/s11460-008-0050-2 fatcat:w2crgev3gzf55n6ddhkb526tce

Cyclic Petri Net Reachability Sets are Semi-linear Effectively Constructible

Zakaria Bouziane, Alain Finkel
1997 Electronical Notes in Theoretical Computer Science  
We p r o ve that cyclic Petri net reachability sets are nite unions of linear combinations of integer vectors whose sizes are exponential in the size of the cyclic Petri net.  ...  Theorem 4.4 The cyclicity problem and the reachability, the coverability, the boundedness, the liveness, the regularity and the inclusion problems for cyclic Petri nets are decidable in space 2 c:n:log  ...  However, the proposed algorithms are not primitive recursive and, up to now, we don't even know whether the reachability problem for Petri nets is primitive recursive or not.  ... 
doi:10.1016/s1571-0661(05)80423-2 fatcat:dejw3etms5gnhlptt2ovxygyjm

Petri Net Approach for Algorithms Design and Implementation

Peter Jakubčo, Slavomír Šimoňák
2011 Acta Electrotechnica et Informatica  
A class of Petri nets, suitable for the purpose is proposed within the paper, based on Colored Petri nets.  ...  The paper deals with the design of a new hybrid RISC computer architecture, with the computation driven by a Petri net.  ...  Petri nets.  ... 
doi:10.2478/v10198-011-0042-7 fatcat:wnhlhhi32jbcdhv23yhjvyiisq

A note on petri net languages

D. Mandrioli
1977 Information and Control  
Hack (1975) showed that if a particular class of "Petri Net languages" were effectively closed under complementation, then the answer to the problem of recursiveness of Petri Nets would be negative: in  ...  INTRODUCTION Most of the research efforts (see any of the references) in the field of mathematical properties of Petri Nets have been devoted to state whether this formalism is recursive or not (this problem  ... 
doi:10.1016/s0019-9958(77)80013-2 fatcat:6spq7yxrqngrjiu6mkb6qstcvy

Completeness Results for Single-Path Petri Nets

R.R. Howell, P. Jancar, L.E. Rosier
1993 Information and Computation  
., boundedness, reachability, containment, and equivalence) for single-path Petri nets are PSPACE-complete in the strong sense.  ...  We de ne a new subclass of persistent Petri nets called single-path Petri nets.  ...  Furthermore, even the problem of recognizing a persistent Petri net | a problem that is also PSPACE-hard Jones, Landweber, and Lien, 1977] | is not known to be primitive recursive (cf.  ... 
doi:10.1006/inco.1993.1055 fatcat:phbfc5552zahvicv4yflr2pvjq

Translating Workflow Nets to Process Trees: An Algorithmic Approach

Sebastiaan J. van Zelst, Sander J. J. Leemans
2020 Algorithms  
Hence, in this paper, we present such an algorithm, i.e., it detects whether a WF-net corresponds to a process tree, and, if so, constructs it.  ...  A process tree is a (mathematical) tree-based model of a process, in which internal vertices represent behavioral control-flow relations and leaves represent process activities.  ...  ., in Figure 3 , and . We lift the •-notation to the level of sets, i.e., given , and . Let be a Petri net and let , and . The Petri net is a subnet of N , written .  ... 
doi:10.3390/a13110279 fatcat:oat3iqopvngmhigiufcnbbnxxa
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