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View all- Tredup RErofeev E(2021)On the parameterized complexity of the synthesis of Boolean nets with restricted place environmentsTheoretical Computer Science10.1016/j.tcs.2021.08.014890:C(36-69)Online publication date: 12-Oct-2021
Occupancy Number Restricted Boolean Petri Net Synthesis: A Fixed-Parameter Algorithm
Pages 143 - 160
Abstract
Let be a Boolean type of net. For a given transition system A and a natural number , the problem occupancy-restricted-synthesis (ORS) is the task to decide whether there is a Boolean Petri net N of type whose reachability graph is isomorphic to A and, moreover, every place of N contains a token in at most reachable markings. In case of a positive decision, N should be constructed. In this paper, we argue that ORS is fixed-parameter tractable when parameterized by .
References
[1]
van der Aalst WMP Process Mining 2011 Heidelberg Springer
[2]
Badouel E, Bernardinello L, and Darondeau P The synthesis problem for elementary net systems is NP-complete Theor. Comput. Sci. 1997 186 1–2 107-134
[3]
Badouel E, Bernardinello L, and Darondeau P Petri Net Synthesis 2015 Heidelberg Springer
[4]
Badouel E and Darondeau P Trace nets and process automata Acta Inf. 1995 32 7 647-679
[5]
Baldan P, Bruni A, Corradini A, König B, Rodríguez C, and Schwoon S Efficient unfolding of contextual Petri nets Theor. Comput. Sci. 2012 449 2-22 http://www.sciencedirect.com/science/article/pii/S0304397512004318, descriptional Complexity of Formal Systems (DCFS 2011)
[6]
Best E and Devillers R Dediu A-H, Martín-Vide C, Sierra-Rodríguez J-L, and Truthe B Characterisation of the state spaces of live and bounded marked graph Petri nets Language and Automata Theory and Applications 2014 Cham Springer 161-172
[7]
Best E, Hujsa T, and Wimmel H Sufficient conditions for the marked graph realisability of labelled transition systems Theor. Comput. Sci. 2018 750 101-116
[8]
Carmona J, Cortadella J, and Kishinevsky M Dumas M, Reichert M, and Shan M-C A region-based algorithm for discovering Petri nets from event logs Business Process Management 2008 Heidelberg Springer 358-373
[9]
Chatain T, Haar S, Kolcák J, Paulevé L, and Thakkar A Concurrency in Boolean networks Nat. Comput. 2020 19 1 91-109
[10]
Cortadella J, Kishinevsky M, Kondratyev A, Lavagno L, and Yakovlev A Logic Synthesis of Asynchronous Controllers and Interfaces 2002 Heidelberg Springer
[11]
Cygan M et al. Parameterized Algorithms 2015 Cham Springer
[12]
Devillers, R.R., Erofeev, E., Hujsa, T.: Synthesis of weighted marked graphs from circular labelled transition systems. In: van der Aalst, W.M.P., Bergenthum, R., Carmona, J. (eds.) ATAED@Petri Nets/ACSD 2019, Aachen, Germany, June 25, 2019. CEUR Workshop Proceedings, vol. 2371, pp. 6–22. CEUR-WS.org (2019). http://ceur-ws.org/Vol-2371/ATAED2019-6-22.pdf
[13]
Devillers R, Erofeev E, and Hujsa T Koutny M, Pomello L, and Kristensen LM Synthesis of weighted marked graphs from constrained labelled transition systems: a geometric approach Transactions on Petri Nets and Other Models of Concurrency XIV 2019 Heidelberg Springer 172-191
[14]
Erofeev, E.: Characterisation of a class of Petri net solvable transition systems. Ph.D. thesis, University of Oldenburg, Germany (2018)
[15]
Gannon T and Shapiro S An optimal approach to fault tolerant software systems design IEEE Trans. Softw. Eng. 1978 SE–4 390-409
[16]
Lorenz, R., Mauser, S., Juhas, G.: How to synthesize nets from languages - a survey, pp. 637–647 (January 2008).
[17]
Montanari U and Rossi F Schneider HJ and Ehrig H Contextual occurrence nets and concurrent constraint programming Graph Transformations in Computer Science 1994 Heidelberg Springer 280-295
[18]
Montanari U and Rossi F Contextual nets Acta Inf. 1995 32 6 545-596
[19]
Pietkiewicz-Koutny M Azéma P and Balbo G Transition systems of elementary net systems with inhibitor arcs Application and Theory of Petri Nets 1997 1997 Heidelberg Springer 310-327
[20]
Institute for Quality, Safety and Transportation: -tool (2013). http://www.iqst.de
[21]
Schlachter, U.: Bounded Petri net synthesis from modal transition systems is undecidable. In: Desharnais, J., Jagadeesan, R. (eds.) 27th International Conference on Concurrency Theory, CONCUR 2016, August 23–26, 2016, Québec City, Canada. LIPIcs, vol. 59, pp. 15:1–15:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016).
[22]
Schlachter, U.: Petri net synthesis and modal specifications. Ph.D. thesis, University of Oldenburg, Germany (2018)
[23]
Schlachter, U., Wimmel, H.: k-bounded Petri net synthesis from modal transition systems. In: CONCUR. LIPIcs, vol. 85, pp. 6:1–6:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2017).
[24]
Schmitt V Puech C and Reischuk R Flip-flop nets STACS 96 1996 Heidelberg Springer 515-528
[25]
Shapiro S A stochastic Petri net with applications to modelling occupancy times for concurrent task systems Networks 1979 9 4 375-379
[26]
Tredup, R.: The complexity of synthesizing nop-equipped Boolean nets from g-bounded inputs (technical report) (2019)
[27]
Tredup R Filiot E, Jungers R, and Potapov I Synthesis of structurally restricted b-bounded Petri nets: complexity results Reachability Problems 2019 Cham Springer 202-217
[28]
Tredup R et al. Chatzigeorgiou A et al. Parameterized complexity of synthesizing b-bounded (m, n)-T-systems SOFSEM 2020: Theory and Practice of Computer Science 2020 Cham Springer 223-235
[29]
Tredup, R., Erofeev, E.: On the parameterized complexity of d-restricted Boolean net synthesis. In: Chen, J., Feng, Q., Xu, J. (eds.) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science, vol. 12337. Springer, Cham (2020).
[30]
Tredup, R., Rosenke, C.: Narrowing down the hardness barrier of synthesizing elementary net systems. In: CONCUR. LIPIcs, vol. 118, pp. 16:1–16:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018).
[31]
Tredup, R., Rosenke, C.: The complexity of synthesis for 43 boolean petri net types. In: Gopal, T.V., Watada, J. (eds.) TAMC 2019. LNCS, vol. 11436, pp. 615–634. Springer, Cham (2019).
[32]
Tredup R, Rosenke C, and Wolf K Khomenko V and Roux OH Elementary net synthesis remains NP-complete even for extremely simple inputs Application and Theory of Petri Nets and Concurrency 2018 Cham Springer 40-59
[33]
Vogler W, Semenov A, and Yakovlev A Sangiorgi D and de Simone R Unfolding and finite prefix for nets with read arcs CONCUR 1998 Concurrency Theory 1998 Heidelberg Springer 501-516
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Published In
Nov 2020
326 pages
ISBN:978-3-030-64275-4
DOI:10.1007/978-3-030-64276-1
- Editors:
- Violet Ka I Pun,
- Volker Stolz,
- Adenilso Simao
© Springer Nature Switzerland AG 2020.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 30 November 2020
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View all- Tredup RErofeev E(2021)On the parameterized complexity of the synthesis of Boolean nets with restricted place environmentsTheoretical Computer Science10.1016/j.tcs.2021.08.014890:C(36-69)Online publication date: 12-Oct-2021