在本論文中，我們報告了一個整合統一模式語言(UML)和派翠網路(Petri Nets)的方法，此方法主要的目的是去作系統的模式化和分析，在系統模式化方面，我們一開始利用使用案例圖(Use Case Diagrams)去模式化系統需求，然後從使用案例圖依序推導出循序圖、類別圖、活動圖和狀態圖，接著我們再將使用案例圖、循序圖、類別圖、活動圖和狀態圖個別轉成傳統派翠網路、時序派翠網路、彩色派翠網路、傳統派翠網路和階層彩色派翠網路。系統分析方面，我們利用了許多知名的派翠網路來分析系統性質，諸如，可達性(reachability)、保存性(conservativeness)、存在性(liveness)等以及時序性質，諸如，必然性(eventually)、經常性(henceforth)、直到性(until)等，倘若我們發現某些性質派翠網路不能滿足，我們直接在派翠網路作修改。此修改動作一直持續到該派翠網路可以滿足那些性質，然後我們再把派翠網路轉回到統一模式語言的圖，接著再繼續進行下一個階段的統一模式語言的模式化。最後我們根據以上的理論，利用Java語言，實作出了一套工具，叫做NCUPN (National Central University Petri Net toolkit)，可以用來描敘和驗證派翠網路的性質，我們的NCUPN也是可以透過網址http://ncupn.csie.ncu.edu.tw來取得。

In this paper, we present our approach of integrating UML and Petri nets for system modeling and analysis. We begin with a system modeling by utilizing UML use case diagrams to model system requirements, and derive sequence, class, activity, and statechart diagrams from the use case diagrams. We then transform the use case, sequence, class, activity, and statechart diagrams into classical Petri nets, time Petri nets, Coloured Petri nets, classical Petri nets, and hierarchical Coloured Petri nets, respectively. For system analysis, we utilize many well-known Petri nets method for analyzing system properties, such as reachability, conservativeness, liveness, etc and temporal properties, such as eventually, henceforth, until etc. In case we found properties are not satisfied, we make modification directly on the Petri nets. The modification continues until the modified Petri nets can satisfy the specified properties. We then transform the Petri nets back to UML diagrams and proceed with later phases of UML modeling. Finally, according to the above theory, we implement a toolkit called NCUPN (National Central University Petri Net toolkit) in Java for specifying and verifying Petri net properties. NCUPN is available via http://ncupn.csie.ncu.edu.tw.

[bald90] M. Baldassari and G. Bruno, ”PROTOB: An Object Oriented Methodology for Developing Discrete Event Dynamic Systems,” Computer Language, vol. 16, no. 1, pp. 39-63, 1991.
[batt88] E. Battiston, F. D. Cindio, and G. Manri, ”OBJSA Nets: A Class of High-level Nets Having Objects as Domain,” in Advances in Petri nets 1988 (Lecture Notes in Computer Science), vol. 340, G. Rozenberg, Ed. New York: Springer-Verlag, pp. 20-43, 1988.
[bobr98] K. Bobrer, V. Johnson, A. Nilsson, and B. Rubin, “Bussiness Process Components for DISTRIBUTED OBJECT APPLICATIONS,” Commun. ACM, vol. 41, no. 6, Jun. 1998.
[boeh84] B. W. Boehm, “Verifying and Validating Software Requirments and Design Specifiation,” in TRW, pp. 75-88, Jan. 1984.
[boeh88] B. W. Boehm, ”A spiral model of software development and enhancement,“ IEEE Trans. Software Eng., May 1998.
[booc86] G. Booch,”Object-Oriented Development,” IEEE Trans. On Software Eng., vol. SE-12, no. 2, Feb. 1986.
[booc99] G. Booch, J. Rumbaugh, and I. Jacobson, “The Unified Modeling Language User Guide,” Addison-Wesley, 1999.
[broo86] F. P. Brooks, “No Silver Bullet: Essence And Accidents of Software Engineering,” Information Processing ‘86, pp. 10-19, 1986.
[brow95a] A. W. Brown, D. J. Carney, P. C. Clements, B. C. Mayers, D. B. Smith, N.H. Weiderman, and W. G. Wood, “Assessing the Quality of large, Software-Intensive Systems: A Case Study,” in Proc. of the 5th European Software Eng. Conf., 1995.
[brow96b] A. W. Brown and K. C. Wallnau, “A Framework for Systematic Evaluation of Software Technologies,” IEEE Software, Sept. 1996.
[brow96c] A. W. Brown and K. C. Wallnau, “Engineering of Component-Based Systems,” in Proc. of the 2nd IEEE International Conf. on Eng. of Complex Syst., 1996.
[carr89] J. A. Carrasco, ”Automated Construction of Compound Markov Chains from Generalized Stochastic High-level Petri Nets,” in Proc. 3rd Int. Workshop on Petri Nets and Performance Models, IEEE Computer Society Press, pp. 93-102, 1989.
[cheh90] G. Chehaibar, ”Use of Reentrant Nets in Modular Analysis of Colored Nets,” in 11th Int. Conference on Applications and Theory of Petri Nets, pp. 596-617, 1990.
[chen93] Y. Chen, W. T. Tsai, and D. Chao, “Dependency Analysis — A Petri Net Based technique for Synthesizing large concurrent systems,” IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 4, pp. 414-426, Apr. 1993.
[chio??] G. Chiola, C. Dutheillet, G. Franceschinis, and S. Haddad, ”Stochastic Well-Formed Coloured Nets and Multiprocessor Modelling Applications,” (Submitted) to IEEE Trans. Comput., pp. 504-530, 19??.
[chio91] G. Chiola, C. Dutheillet, G. Franceschinis, and S. Haddad, ”On Well-Formed Coloured Nets and Their Symbolic Reachability Graph,” in 11th Int. Conference on Applications and Theory of Petri Nets, pp. 373-396, 1990.
[chio93] G. Chiola, M. A. Marsan, G. Balbo, and G. Conte, ”Generalized stochastic Petri nets: A definition at the net level and its implications,” IEEE Trans. Software Eng., vol. 9, no. 2, pp. ??-??, Feb. 1993.
[chu??] W. C. Chu, L. S. Sun, S. J. Yang, ”A Formal Model To Object-Oriented Program Reuse,” Department of Information Engineering, Feng Chia University, Taichung, Taiwan, ROC, 19??.
[clar86] E. M. Clarke, E. A. Emerson, and A. P. Sistla, “Automatic verification of finite-state concurrent systems using temporal logic specifications,” ACM Transactions on Programming Language and Systems, vol. 8, no. 2, pp. 244-263, Apr. 1986.
[clem95a] P. Clements, “From Subroutines to Subsystems: Component-Based Software Development,” American Programmer, Nov. 1995.
[clem95b] P. Clements, L. Bass, R. Kazman, and G. Abowd, “Predicting Software Quality by Architecture-Level Evaluation,” in Proc. of the 5th International Conf. on Software Quality, 1995.
[clem96a] P. Clements, R. Krut, E. Morris, and K. Wallnau, “The Gadfly: An Approach to Architectural-Level System Comprehension,” in Proc. of the 4th Workshop on Program Comprehension, 1996.
[clem96b] P. C. Clements, and L. N. Northrop, “Software Architechture: An Executive Overview,” IEEE, 1996.
[coad90] P. Coad and E. Yourdon, ”Object-Oriented Analysis,” IEEE, 1990.
[couv90] J. M. Couvreur and J. Martinez, ”Linear Invariants in Commutative High Level Nets,” in Advances in Petri nets 1990, Lecture Notes in Computer Science, vol. 483, G. Rozenberg, Ed. New York: Springer-Verlag, pp. 146-165, 1990.
[deng95] Y. Deng and W. Du, “A Formal Approach for Architectural Modeling and Refinement of Real-Time Systems,” School of Computer Science, Florida International University Miami, FL 33199, 1995.
[emer92] E. A. Emerson, A. K. Mok, A. P. Sistla, and J. Sprinivasan, “Quantitative Temporal Reasoning,” Real-Time Systems, vol. 4, pp. 331-352, 1992.
[feil96] P. H. Feiler, “Reengineering: An Engineering Problem,” IEEE, 1996.
[feld90] F. Feldbrugge and K. Jensen, “Computer Tools for High-level Petri Nets,” in Advances in Petri nets 1989 (Lecture Notes in Computer Science), vol. 424, G. Rozenberg, Ed. New York: Springer-Verlag, pp. 691-717, 1990.
[forg82] C. L. Forgy, “Rete: A fast algorithm for the many pattern/many object pattern match problem,” Dept. of Comput. Sci., Carnegie-Mellon Univ., Pittsburgh, PA 15213, U.S.A., pp ??-??, 1982.
[fowl97] M. Fowel and K. Scoot, “UML Distilled: Applying the Standard Object Modeling Language,” Addison-Wesley, 1997.
[genr86] H. J. Genrich, W. Brauer, W. Reisig, and G. Rozenberg, “Petri nets: Central Models and their properties,“ Lecture Notes in Computer Science, vol. 254, pp. 207-247, 1986.
[gira87] C. Girault, C. Chatelain, and S. Haddad, ”Specification and Properties of a Cache Coherence Protocol Model,” in Advances in Petri nets 1987 (Lecture Notes in Computer Science), vol. 266, G. Rozenberg, Ed. New York: Springer-Verlag, pp. 1-20, 1987.
[hadd90] S. Haddad, ”A Reduction Theory for Coloured Nets,” in Advances in Petri nets 1989 (Lecture Notes in Computer Science), vol. 424, G. Rozenberg, Ed. New York: Springer-Verlag, pp. 209-235, 1990.
[huan96] W. T. Huang, J. Lee and T. L. Kuei, “OBARD: An Object-Based Rapid Application Development Method,” in Joint Conf. Of 1996 Int. Comput. Symp., Inst. of Comput. Sci. and Inf. Eng., National Central Univ., Chung-Li, Taiwan 32054, pp. ??-??, Dec. 19-21, Kaohsiung Taiwan, R.O.C. .
[hube86] P. Huber, A. M. Jensen, L. O. Jepsen, and K. Jensen, ”Reachability Trees for High-level Petri Nets,” Theoretical Computer Science 45, pp. 261-292, 1986.
[hutc9?] D. Hutchison and J. Walpole, “Distributed Systems and Objects,” Lancaster Univ., pp. 223-242, 199?.
[jaco92] I. Jacobson, M. Christerson, P. Jonsson, and G. Orergaard, “Object-Oriented Software Engineering,” Addison-Wesley, 1992.
[jens91] K. Jensen and G. Rozenberg, “High-level Petri Nets: Theory and Application,” Springer-Verlag, 1991.
[jens92] K. Jensen, “Coloured Petri nets: Basic concepts, Analysis methods, and Practical use, volume 1-3,” Springer-Verlag, 1992.
[kram87] B. Kramer and H. W. Schmidt, ”Types and Modules for Net Specifications,” in Advances in Petri nets 1987 (Lecture Notes in Computer Science), K. Voss, H. J. Genrich and G. Rozenberg, Eds. New York: Springer-Verlag, pp. 269-286, 1987.
[lai95] S. T. Lai and C. T. Wu, “Design Criteria of Reusable Class Components,” 1995.
[lee97] J. Lee, K. F. R. Liu, and W. Chiang, “A possibilistic-logic-based approach to integrating imprecise and uncertain information,” Dept. of Comput. Sci. and Inf. Eng., National Central Univ., Chungli, Taiwan 32054, pp. 1-20, 1997.
[lee98] B. H. Lee “Embedded internet systems: Poised for takeoff,” IEEE Internet Computing, Stanford Univ., pp. 24-59, Jun. 1998.
[leve87] N. G. Leveson and J. L. Stolzy, “Safety Analysis Using Petri Nets,” IEEE Trans. on Software Engineering, vol. SE-13, no. 3, pp. 386-397, Mar. 1987.
[leve87] N. G. Leveson and J. L. Stolzy, “Safety Analysis Using Petri Nets,” IEEE Trans. On Software Eng., vol. Se-13, no. 3, Mar. 1987.
[lin88] C. Lin and D. C. Marinescu, ”Stochastic High-level Petri Nets and Applications,” IEEE Trans. Comput., vol. 37, no. 7, pp. 815-825, Jul. 1988.
[luck95a] D. C. Luckham and J. Vera, “An event-based architecture definition language,“ IEEE Trans. Software Eng., vol. 21, no. 9, pp. 717-734, Sept. 1995.
[luck95b] D. C. Luckham, J. J. Kenney, L. M. Augustin, J. Vera, D. Bryan, and W. Mann, “Specification and analysis of system architecture using rapide,” IEEE Trans. Software Eng., vol. 21, no. 4, pp. 336-335, Apr. 1995.
[memm87] G. Memmi and J. Vautherin, ”Analysing Nets by the Invariant Method,” in Advances in Petri nets 1986 (Lecture Notes in Computer Science), vol. 254, W. Braner, W. Reisig, and G. Rozenberg, Eds. New York: Springer-Verlag, pp. 300-336, 1987.
[merl76] P. M. Merlin and D. J. Farber, “Recoverability of Communication Protocols Implications of a Theoretical Study,” IEEE Trans. on Communication, vol. COM-24, no. 9, pp. 1036-1043, Sept. 1976.
[meye85] B. Meyer, “On formalism in specifications,” IEEE, Univ. of California, Santa Barbara, pp. 6-26, 1985.
[mull97] P. A. Muller, “Instant UML,” Wrox Press Ltd., 1997.
[mura89] T. Murata, “Petri Nets: Properties, analysis and applications,“ in Proceeding of The IEEE, vol. 77, no. 4, pp. 541-580, 1989.
[ostr90] J. S. Ostroff, “Deciding properties of timed transition models,” IEEE Trans. Parallel and Distrib. Syst., vol. 1, no. 2, pp. 170-183, Apr. 1990.
[pan99] J. I. Pan, “A Scenario-Driven Approach to Requirements Engineering,” Ph.D. dissertation, Department of Computer Science and Information Engineering, National Central University, Taiwan, ROC, pp. 1-126, 1999.
[pape92] Y. E. Papelis and T. L. Casavant, “Specification and Analysis of Parallel/Distributed Software and Systems by Petri Nets with Transition Enabling Functions,” IEEE Transactions Software Engineering, vol. 18, no. 3, pp. 252-261, Mar. 1992.
[pete81] J. L. Peterson, “Petri net theory and the modeling of systems,” Prentice-hall, Central Book Company, Taipei, Taiwan, 1981.
[pinc90] V. Pinci and R. M. Shapiro, ”An Integrated Software Development Methodology Based on Hierarchical Colored Petri Nets,” in 11th Int. Conference on Applications and Theory of Petri Nets, pp. 649-666, 1990.
[pres92] R. S. Pressman, “Software Engineering: A Practitioner’s Approach,” Third Edition, McGraw-hill International Editions, Computer Science Serious, 1992.
[rama84] C. V. Rammamoorthy, A. Prakash, W. T. Tsai, and Y. Usuda, “Software Engineering: Problems and Perspectives,“ IEEE, Univ. of California, Oct. 1984.
[rama84] C. V. Rammamoorthy, A. Prakash, W. T. Tsai, and Y. Usuda,“Software engineering: Problems and perspectives,“ IEEE, Univ. of California, pp. 191-209, Oct. 1984.
[rati97] Rational, and UML partners, ”UML Summary version 1.1,” http://www.rational.com/uml/resources/documentation/summary/index.jtmpl, 1997.
[reis91] W. Reisig, ”Petri Nets and Algebraic Specification,” Theoretical Computer Science 80, pp. 1-34, 1991.
[roma85] G. C. Roman, “A Taxonomy of Current Issues in Requirements Engineering,” IEEE, Washington Univ., St. Louis, pp. ??-??, Apr. 1985.
[rumb91] J. Rumbaugh, M. Blaha, W. Premerlani, F. Eddy, and W. Lorensen, “Object-Oriented Modeling and Design,” Prentice-Hall, 1991.
[salq96] Y. Y. A. Salqan and C. K. Chang, “Temporal relations and synchronization agents,” IEEE, West Virginia Univ., pp. 30-39, Summer 1996.
[sha96] L. Sha, R. Rajkumar, and M. Gagliardi, “Evolving Dependable Real Time Systems,” in Proc. of the IEEE Aerospace Application Conf., 1996.
[shap91] R. M. Shapiro, ”Validation of a VLSI Chip Using Hierarchical Colored Petri Nets,” Microelectronics and Reliability, Special Issue on Petri Nets, Pergamoa Press, pp. 667-687, 1991.
[shaw92] A. C. Shaw, “Communicating Real-Time State Machines,“ IEEE Trans. Software Eng., vol. 18, no. 9, Sep. 1992.
[shaw95] M. Shaw, “Comparing architectural design styles,“ IEEE, Carnegie Mellon Univ., pp. 27-41, Nov. 1995.
[shel95] F. T. Sheldon, K. M. Kavi, and F. A. Kamangar, “Analysis of real-time concurrent system specifications with timing failure probability and cost-benefit,“ Special Issue on Software Eng. for Distrib. Comput., pp. 1-23, Mar. 1, 1995.
[silv85] M. Silva, J. Martinez, P. Ladet, and H. Alla, ”Generalized Inverses and the Calculation of Symbolic Invariants for Coloured Petri Nets,” Technique et Science Informatiques, vol. 4, no. 1, pp. 113-126, 1985.
[spiv90] J. M. Spivey, “Specifying a real-time kernel,“ IEEE Software, Tektronix, pp. 21-28, Sept. 1990.
[suzu89] I. Suzuki and H. Lu, “Temporal Petri Nets and Their Application to Modeling and Analysis of a HandShake Daisy Chain Arbiter,“ IEEE Trans. on Computer, vol. 38, no. 5, pp. 696-704, May 1989.
[till96] S. Tilley and D. Smith, ”Coming Attractions in Program Understanding,” in Proc. of CASCON''96, 1996.
[wall96a] E. Wallace, P. C. Clements, and K. C. Wallnau, “Discovering a System Modernization Decision Framework: A Case Study in Migrating to Distributed Object Technology,” in Proc. of the International Conf. on Software Maintenance, 1996.
[wall96b] K. Wallnau, F. Long, and A. Earl, “Toward a Distributed, Mediated Architecture for Workflow Management,” in Proc. of NSF Workshop on Workflow and Process Automation in Information Systems: State-of-the-Art and Future Directions, 1996.
[wing90] J. M. Wing, “A specifier''s introduction to formal methods,“ IEEE, Carnegie Mellon Univ., pp. 9-24, 1990.
[yang97a] S. J. H. Yang, K. F. R. Liu, S. Lin, J. Lee, and W. T. Huang, “Object-Oriented Development of a Petri Nets Modeling and Analysis System,“ Dept. Computer Science Information Engineering, National Central Univ., Taiwan, ROC, pp. 1-6, 1997.
[yang97b] S. J. H. Yang and J. J. P. Tsai, “Specifying and Verifying Timing Constraints Using Petri Nets and Temporal Logic,” Dept. of Comput. Sci. and Inf. Eng. National Central Univ., Taiwan, R.O.C., pp. 1-37, 1997.
[yang97c] S. J. H. Yang, “Modeling and Analysis Using Time Petri Nets and Temporal Logic,“ Dept. Comput. Sci. and Inf. Eng., National Central Univ., Taiwan, ROC, pp. 1-17, 1997.
[yang98a] S. J. H. Yang, C. C. Chen, J. Lee, and W. T. Huang, “NCUPN: A Petri Nets Modeling and Analysis Toolkit,” Department of Computer Science and Information Engineering, National Central University, Taiwan ROC, 1998.
[yang98b] S. J. H. Yang, W. Chu, S. Lin, and J. Lee, “Specifying and Verifying Temporal Behavior of High Assurance Systems Using Reachability Tree Logic,“ in Proceedings of the 3rd IEEE International High-Assurance Systems Engineering Symposium, pp. 150-156, 1998.