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Lecture Notes in Computer Science
Petri Net, Theory and Applications
In the present paper, a kind of temporal linear logic, called linear-time linear logic, is used to describe timed Petri nets with timed tokens. ... Tanabe's temporal linear logic (Tanabe, 1997) is used as a base logic for timed Petri net specifications. ... A Linear Logic Based Approach to Timed Petri Nets, Petri Net, Theory and Applications, Vedran Kordic (Ed.), ISBN: 978-3-902613-12-7, InTech, Available from: http://www.intechopen.com/books/petri_net_theory_and_applications ...doi:10.5772/5319 fatcat:gw25kquocnemtn3d5kfpenlqb4
Soundness of the logic with respect to timed Petri net interpretation is shown. Finally, examples show how to express properties of timed Petri nets by temporal linear logic.” ... Next, temporal linear logic is introduced, which has timed Petri nets as its models, i.e., whose formulas can be interpreted as sets of timed markings of a timed Petri net. ...
Beside the usual graphic editing and simulation facilities, the software tool Tina may build a number of state space abstractions for Petri nets or Time Petri nets, preserving certain classes of properties ... For Petri nets, these abstractions help preventing combinatorial explosion and rely on so-called partial order techniques such as covering steps and/or persistent sets. ...  preserves markings of the TPN and all its properties one can express in linear time temporal logics like¨¨. ...doi:10.1109/qest.2006.56 dblp:conf/qest/BerthomieuV06 fatcat:exonlwr2i5eobc5tjdg36s3fsm
BRICS Report Series
The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics. ... This is a survey of some decidability results for Petri nets, covering the last three decades. ... Acknowledgements Thanks to David de Frutos, Matthias Jantzen, Jean-Luc Lambert and Elisabeth Pelz for providing useful information. ...doi:10.7146/brics.v1i8.21662 fatcat:jyrntthfg5gh5mu77soacgwbsu
Introduction Tina (TIme Petri Net Analyser) 1 is a software environment for the editing and analysis of Petri net and Time Petri net (Merlin and Farber 1976) . ... temporal logic properties, test equivalence), or properties relying on its branching structure (branching time temporal logic properties, bisimulation). ... Introduction Tina (TIme Petri Net Analyser) 1 is a software environment for the editing and analysis of Petri net and Time Petri net (Merlin and Farber 1976) . ...doi:10.1080/00207540412331312688 fatcat:ur4qrvbwvzevnc7othhwilj7f4
As temporal issues can be specified using temporal logics, we provide a short overview of selected temporal logics which can be used to specify the time patterns in business process models. ... We focus on Business Process Model and Notation and provide examples of representing time patterns in this notation. ... Linear Temporal Logic Linear Temporal Logic (LTL)  is a temporal logic system for representing of time linearity. ...doi:10.15439/2016f328 dblp:conf/fedcsis/KluzaJWL16 fatcat:xgzqi6dv7ngkhmxp765bimxhh4
An aim is to use Petri nets to give an understanding of linear logic and give some appraisal of the value of linear logic as a specification logic for Petri nets. ... Intuitionistic linear logic; 3. Proof rules; 4. Quantale interpretation; 5. Petri nets; 6. Quantales from Petri-nets; 7. Petri-net interpretation; 8. Expressing properties of nets; 9. ...
‘Changes to’ is one operator of a temporal proof calculus which combines Petri nets with a UNITY-like temporal logic. ... We extend its applicability to the properties of a temporal logic with a possibility operator. The al- gorithm is based on linear programming. ...
Transactions of the Society of Instrument and Control Engineers
Urquhart: Temporal Logic, 1/97, Springer, (1971) ... Then, based on the general framework called •gtense logic•h dealing with the qualitative properties of time such as transitivity, discreteness and linearity, each proposition representing ...doi:10.9746/sicetr1965.18.1180 fatcat:imipunxvajc7bhn2sk4bffbcve
to NUPNs (Nested-Unit Petri Nets), require certain properties to be computed on Petri nets. ... We notice that, although these properties are theoretically interesting and practically useful, they are not currently implemented in mainstream Petri net tools. ... , Emmanuel Paviot-Adet, Yann Thierry-Mieg, and Karsten Wolf. ...arXiv:2101.05024v2 fatcat:6jqg2qkjljeexc4dcvhcd6ubxu
Lecture Notes in Computer Science
Furthermore we obtain the same results for the linear time temporal logic LTL, which is strictly less expressive than the linear-time -calculus. ... We study the complexity of model-checking Petri Nets w.r.t. the propositional linear-time -calculus. ... The logics we use are linear temporal logics: the well-known propositional linear-time -calculus and the less expressive linear temporal logic (LTL 11] ). ...doi:10.1007/3-540-63139-9_32 fatcat:lblieccp4zf2fiimqqtkli72ny
Summary: “We present a sound and complete tableau system for proving temporal properties of Petri nets, expressed in a propo- sitional modal mu-calculus which subsumes many other temporal logics. ... The algorithm runs in time O(log” n) and requires a linear number of processors. ...
Linear logic (which does not appears in this paper) offers a theoretical framework to interpret the Petri net model and to extract the scenarios. ... The system model is given by a Petri net. To derive critical scenarios and to avoid the state space explosion, the solution is to use directly the Petri net model. ... Linear logic  ,  offers a formal framework to interpret the Petri net model and to extract the scenarios. ...doi:10.1109/icsmc.2009.5346090 dblp:conf/smc/SadouGD09 fatcat:xufeutrlofbunadxhsh6okbzim
lin- ear temporal logic (207-221); Ursula Goltz, Ruurd Kuiper and Wojciech Penczek, Propositional temporal logics and equivalences (222-236); Eric Goubault and Thomas P. ... Jeppesen and Kim Guldstrand Larsen, Model construction for implicit specifications in modal logic (247-261); Orna Bernholtz and Orna Griimberg, Branching time temporal logic and amorphous tree automata ...
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