Earlier, Chao pioneered the very first closed-form solution of the number of reachable and other states for marked graphs and kth-order systems, which is the simplest class of systems of simple sequential processes with resources. This paper progresses one step further by enumerating reachable, forbidden, live and deadlock states for bottom kth-order systems, which have one non-sharing resource place in the bottom position of the right-side process, with a formula depending on parameter k for a subclass of nets with k sharing resources.
ChaoDY (2005) Reachability of nonsynchronized choice Petri nets and its applications. IEEE Transactions on Systems, Man, and Cybernetics A35(6): 1203–1213.
2.
ChaoDY (2006) Computation of elementary siphons in Petri nets for deadlock control. Computer Journal (British Computer Society)49(4): 470–479.
3.
ChaoDY (2011a) Improvement of suboptimal siphon- and FBM-based control model of a well-known S3PR. IEEE Transactions on Automation Science and Engineering8(2): 404–411.
4.
ChaoDY (2011b) Enumeration of lost states of a suboptimal control model of a well-known S3PR. IET Control Theory & Applications5(11): 1277–1286.
5.
ChaoDY (2011c) A simple modification of deadlock prevention policy of S3PR based on elementary siphons. Transactions of the Institute of Measurement and Control33(1): 93–115.
6.
ChaoDYChenJ-TYuF (2012) Enumeration of reachable and other states of simple version of systems of simple sequential processes with resources (S3PR). In: Industrial Electronics Society, 2012 ISIE 2012. The 21th IEEE International Symposium on Industrial Electronics, Hangzhou Tianyuan Tower, 28–31 May. IEEE, pp. 1369–1374.
7.
ChaoDYChenJ-TYuF (2013) A novel liveness condition for S3PGR2. Transactions of the Institute of Measurement and Control35(2): 131–137.
8.
ChaoDYWuK-C (2013) An integrated approach for supervisory control of a subclass of Petri nets. Transactions of the Institute of Measurement and Control35(2): 117–130.
9.
ChaoDY (2012) Recursive solution of number of reachable states of a simple subclass of FMS. International Journal of Systems Science45(3): 702–710.
10.
EzpeletaJJColomMMartinezJ (1995) A Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Transactions on Robotics and Automation11(4): 173–184.
11.
FerrariniL (1994) On the reachability and reversibility problems in a class of Petri nets. IEEE Transactions on Systems, Man and Cybernetics24(10): 1474–1482.
12.
HiraishiKIchikawaA (1988) A class of Petri nets that a necessary and sufficient condition for reachability is obtainable. Transactions of the Society of Instrument and Control Engineers24(6): 635–640.
13.
IchikawaAYokoyamaKKurogiS (1985) Control of event-driven systems – reachability and control of conflict-free Petri nets. Transactions of the Society of Instrument and Control Engineers21(4): 324–330.
14.
KostinAE (2003) Reachability analysis in T-invariant-less Petri nets. IEEE Transactions on Automatic Control48(6): 1019–1024.
15.
LeeDIKumagaiSKodamaS (1990) Reachability of LSFC nets. IEEE International Symposium on Circuits and Systems4(5): 2666–2669.
16.
LeeJSZhouMCHsuPL (2005) An application of Petri nets to supervisory control for human-computer interactive systems. IEEE Transactions on Industrial Electronics52(5/Oct): 1220–1226.
17.
LiangHChaoDY (2012) Enumeration of reachable states for arbitrary marked graphs. IET Control Theory and Applications6(10): 1536–1543.
18.
LiptonRJ (1976) The reachability problem requires exponential space. Research Report 62, Department of Computer Science, Yale University, New Haven, CT.
19.
MiyamotoTHoriguchiK (2011) Modular reachability analysis in fundamental class of multi-agent nets. In: IECON 2011–37th Annual Conference on IEEE Industrial Electronics Society, Crown Conference Centre, 07–10 November. IEEE, pp. 3782–3787.
20.
MizunoNOhtaATsujiK (2007) Reachability problem of marked graphs with batch processing arcs. In: IECON 2007, 33rd Annual Conference of IEEE Industrial Electronics, Grand Hotel, 5–8 November. IEEE, pp. 70–75.
21.
NazeemAReveliotisSAWangY. (2011) Designing compact and maximally permissive deadlock avoidance policies for complex resource allocation systems through classification theory: The linear case. IEEE Transactions on Automatic Control57(7): 1670–1684.
22.
ShihYYChaoDY (2010) Sequence of control in S3PMR. Computer Journal, doi:10.1093/comjnl/bxp081.
23.
StarkePH (1992) INA: Integrated Net Analyzer. Handbuch, Germany.
24.
SunPJiangCJZhouMC (2009) Interactive Web service composition based on Petri net. Transactions of the Institute of Measurement and Control33(1): 116–132.
25.
UzamMZhouMC (2006) An improved iterative synthesis approach for liveness enforcing supervisors of flexible manufacturing systems. International Journal of Production Research44(10): 1987–2030.
26.
WangJZhouXDingJ (2010) Software architectural modelling and verification: a Petri net and temporal logic approach. Transactions of the Institute of Measurement and Control33(1): 168–181.
27.
ZimmermannA (2012) http://www.tu-ilmenau.de/TimeNeT, Technische Universitat Ilmenau, System and Software Engineering, D-98684 Ilmenau, Germany.
