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The Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems

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Rough Sets in Knowledge Discovery 2

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 19))

Abstract

We discuss the synthesis problem of concurrent systems from observations or specification encoded in data table (information system) [Pawlak,1991]. In the paper we first introduce a new notion of a so-called dynamic information system, and then we apply this notion as a tool for specification of concurrent systems behaviour [Pawlak,1992], [Pawlak,1997]. Finally, we present two methods of construction from any dynamic information system DS with its underlying system S, and transition system TS describing the behaviour of DS, a concurrent model in the form of an elementary net system N [Thiagarajan,1987] with the following property: a given transition system TS is isomorphic to the transition system associated with the constructed net system N. In the first method we assume that the data table representing a given dynamic information system DS contains the whole knowledge about the observed or specified behaviour of the system. For this setting, we adopt a method of construction a solution of the synthesis problem of concurrent system models suggested by [Desel and Reisig,1996]. A solution of the synthesis problem is any net which is constructed using the concept of regions of transition systems, introduced in [Ehrenfeucht and Rozenberg,1990]. The second method presented in the paper is based on approach that a given data table consists of only partial knowledge about the system behaviour. Thus, we at first compute an extension DS′ of the dynamic information system DS, i.e. the system in which the set of all global states of DS′ is consistent with all rules true in the underlying information system S of DS, and the set of all global states of DS′ represents the largest extension of S consistent with the knowledge represented by S. Next, for finding a solution of the synthesis problem considered here we use the first method. This approach is based on rough set theory [Pawlak,1991] and Boolean reasoning [Brown,1990]. We have implemented program on IBM PC generating a net model from a dynamic information system.

In our approach we also use a modification of the process independence definition presented in [Pawlak,1992]. This paper is an attempt to present a new approach to concurrency based on the rough set philosophy.

We illustrate our ideas by an intuitive example of traffic signal control [Pawlak, 1997].

We assume that the reader is familiar with the basic ideas of concurrent systems [Milner, 1989], Petri nets [Murata, 1989], [Reisig, 1985] and information systems [Pawlak, 1991].

Our results seem to have some significance for methods of explanation of the system behavior. Besides, the proposed approach can be seen as basis for a certain class of control system design [Pawlak, 1997], and it could be also used for software specification [Hurley, 1983].

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References

  1. Haar, A., Cohen, P.R,. Feigenbaum, E.A.: The handbook of artificial intelligence 4 Addison Wesley (1989)

    Google Scholar 

  2. Bazan, J., Skowron, A., Synak, P.: Dynamic reducts as a tool for extracting laws from decision tables. In: Z. W. Ras, M. Zemankova (eds.), Proceedings of the Eighth Symposium on Methodologies for Intelligent Systems, Charlotte, NC, October 16–19, Lecture Notes in Artificial Intelligence 869, Springer-Verlag (1994) 346–355

    Google Scholar 

  3. Bazan, J., Skowron, A., Synak, P.: Discovery of decision rules from experimental data. In: T.Y. Lin (ed.), Proc. of the Third International Workshop on Rough Sets and Soft Computing, San Jose CA, November 10–12 (1994) 526–533

    Google Scholar 

  4. Bernadinello, L.: Synthesis of net systems. In: Proc. of the Application and Theory of Petri Nets. Lecture Notes in Comput. Sci. 691, Springer-Verlag, Berlin (1993) 89–105

    Google Scholar 

  5. Brown E.M.: Boolean reasoning. Kluwer Academic Publishers, Dordrecht (1990)

    Book  Google Scholar 

  6. Desel, J., Reisig, W.: The synthesis problem of Petri nets. Acta Inf. 3/34 (1996) 297–315

    Article  Google Scholar 

  7. Ehrenfeucht, A., Rozenberg, G.: Partial 2-structures Part II. State space of concurrent systems. Acta Inf. 27 (1990) 348–368

    Google Scholar 

  8. Hack, M.: Decidability questions for Petri nets. Ph.D thesis. Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge MA (1975)

    Google Scholar 

  9. Hurley, R.B.: Decision tables in software engineering. Van Nostrad Reinhold Company, New York (1983)

    Google Scholar 

  10. Janicki, R.: Transforming sequential systems into concurrent systems. Theoretical Comp. Sci. 36 (1985) 27–58

    Article  Google Scholar 

  11. Karp, R.M., and Miller, R.E.: Parallel program schemata. Journal of Computer and System Science 34 (1969) 167–195

    Google Scholar 

  12. Kodratoff, Y., Michalski, R. (eds.): Machine learning 3 Morgan Kaufmann Publishers, San Mateo CA (1990)

    Google Scholar 

  13. Krieg, B.: Petrinetze und Zustandsgraphen. IFI-Bericht B-29/77 Institut für Informatik, Universität Hamburg (1977)

    Google Scholar 

  14. Lengauer, C., Hehner, E.C.R.: A methodology for programming with concurrency: an informal presentation. Sci. Comp. Progr. 2 (1982) 1–18

    Article  Google Scholar 

  15. Michalski, R., Carbonell, J.G., Mitchell, T.M. (eds.): Machine learning: an artificial intelligence approach 1 Tioga/Morgan Kaufmann Publishers, Los Altos CA (1983)

    Google Scholar 

  16. Michalski, R., Carbonell, J.G., Mitchell, T.M. (eds.): Machine learning: an artificial intelligence approach 2 Morgan Publishers, Los Altos CA (1986)

    Google Scholar 

  17. Michalski, R.S., Kerschberg, L., Kaufman, K.A., and Ribeiro, J.S.: Mining for knowledge in databases: The INLEN architecture, initial implementation and first results. Intelligent Information Systems: Integrating Artificial Intelligence and Database Technologies 11 (1992) 85–113

    Article  Google Scholar 

  18. Milner, R.: Communication and concurrency. Prentice-Hall, Englewood Cliffs, NJ (1989)

    Google Scholar 

  19. Mukund, M.: Petri nets and step transition systems. Int. Journal of Foundations of Computer Science 34 (1992) 443–478

    Article  Google Scholar 

  20. Murata, T.: Petri nets: properties, analysis and applications. In: Proc. of the IEEE 77/4 (1989) 541–580

    Google Scholar 

  21. Nadler, M., Smith, E.P: Pattern recognition engineering. John Wiley and Sons, New York (1993)

    Google Scholar 

  22. Nguyen, H. Son, Skowron, A.: Quantization of real value attributes. In: P.P. Wang (ed.), Second Annual Joint Conference on Information Sciences (JCIS’95), September 28–October 1, Wrightsville Beach, North Carolina, USA (1995) 34–37

    Google Scholar 

  23. Nguyen, H. Son: Discretization of real value attributes: Boolean reasoning approach. Ph.D thesis, Warsaw University, Warsaw (1997) 1–90

    Google Scholar 

  24. Nielsen, M., Rozenberg, G., Thiagarajan, P.S.: Elementary transition systems. Theoretical Comp. Sci. 961 (1992) 3–33

    Article  Google Scholar 

  25. Pawlak, Z.: Rough sets — Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)

    Google Scholar 

  26. Pawlalc, Z.: Concurrent versus sequential: The rough sets perspective. Bulletin of the EATCS 48 (1992) 178–190

    Google Scholar 

  27. Pawlak, Z, and Skowron, A.: A rough set approach for decision rules generation. In: Proceedings of the Workshop W12: The Management of Uncertainty in AI at 13th IJCAI, Chambery Savoie, France, August 30, see also: ICS Research Report 23/93 Warsaw University of Technology (1993) 1–19

    Google Scholar 

  28. Pawlalc, Z.: Some remarks on explanation of data and specification of concurrent processes. Bulletin of International Rough Set Society 11 (1996) 1–4

    Google Scholar 

  29. Petri, C.A.: Kommunikation mit Automaten. Bonn: Inst. Inst.um.Math., Schr. IIM 3 (1962). Also in English: Communication with automata, Griffith Air Force Base. Tech. Rep. RADC-Tr-65–377 1 Suppl. 1 (1966)

    Google Scholar 

  30. Reisig, W.: Petri nets. An introduction. Springer-Verlag, Berlin (1985)

    Google Scholar 

  31. Shapiro, S.C., Eckroth, D.: Encyclopedia of artificial intelligence 1 Wiley, New York (1987) 18–35

    Google Scholar 

  32. Skowron, A.: Boolean reasoning for decision rules generation. In: J. Komorowski, Z.W. Ras (eds.), Proceedings of of the Seventh International Symposium on Methodologies for Intelligent Systems (ISMIS’93), Trondheim, Norway, June 1518, 1993, Lecture Notes in Computer Science 689 (1993) 295–305

    Google Scholar 

  33. Skowron, A.: A synthesis of decision rules: applications of discernibility matrix properties. In: Proc. of the Conference Intelligent Information Systems, Augustów, Poland, June 7–11 (1993)

    Google Scholar 

  34. Skowron, A: Synthesis of adaptive decision systems from experimental data (invited talk). In: A. Aamodt, J. Komorowski (eds.), Proceedings of the Fifth Scandinavian Conference on Artificial Intelligence (SCAI’95), May 29–31, 1995, Trondheim, Norway, IOS Press, Amsterdam (1995) 220–238

    Google Scholar 

  35. Skowron, A., Polkowski, L., Komorowski, J.: Learning tolerance relations by Boolean descriptors: automatic feature extraction from data tables. In: S. Tsumoto, S. Kobayashi, T. Yokomori, H. Tanaka, and A. Nakamura (eds.): Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (RSFD’96), The University of Tokyo, November 6–8 (1996) 11–17

    Google Scholar 

  36. Skowron, A., and Rauszer, C.: The discernibility matrices and functions in information systems. In: R. Slowinski (ed.), Intelligent decision support — Handbook of applications and advances of the rough sets theory. Kluwer Academic Publishers, Dordrecht (1992) 331–362

    Chapter  Google Scholar 

  37. Skowron, A., and Stepaniuk, J.: Decision rules based on discernibility matrices and decision matrices. In: T.Y. Lin (ed.), Proc. of The Third International Workshop on Rough Sets and Soft Computing, San Jose CA, November 10–12 (1994) 156–163

    Google Scholar 

  38. Skowron, A., and Suraj, Z.: A rough set approach to the real-time state identification. Bulletin of the EATCS 50 (1993) 264–275

    Google Scholar 

  39. Skowron, A., and Suraj, Z.: Rough sets and concurrency. Bull. Polish Acad. Sci., Ser. Sci. Tech. 413 (1993) 237–254

    Google Scholar 

  40. Skowron, A., and Suraj, Z.: Synthesis of concurrent systems specified by information systems Part 1. Institute of Computer Science Report 4/93, Warsaw University of Technology (1993)

    Google Scholar 

  41. Skowron, A., and Suraj, Z.: Synthesis of concurrent systems specified by information systems Part 2. Examples of synthesis. Institute of Computer Science Report 38/93, Warsaw University of Technology (1993)

    Google Scholar 

  42. Skowron, A., and Suraj, Z.: Synthesis of concurrent systems specified by information systems. Institute of Computer Science Report 39/94, Warsaw University of Technology (1994)

    Google Scholar 

  43. Skowron, A., and Suraj, Z.: Discovery of concurrent data models from experimental tables: a rough set approach. In: U.M. Fayyad, R. Uthurusamy (eds.), Proceedings of the First International Conference on Knowledge Discovery and Data Mining (KDD’95), August 20–21, 1995, Montreal, AAAI Press, Menlo Park CA (1995) 288–293

    Google Scholar 

  44. Skowron, A., and Suraj, Z.: A Parallel algorithm for real-time decision making: A rough set approach. Journal of Intelligent Information Systems 7 (1996) 5–28

    Article  Google Scholar 

  45. Smith, D.R.: The synthesis of LISP programs from examples: a survey. In: A. Bierman, G. Guiho, Y. Kodratoff (eds.), Automatic program construction techniques, Macmillan, New York (1984) 307–324

    Google Scholar 

  46. Slowinski, R. (ed.): Intelligent decision support — Handbook of applications and advances of the rough sets theory. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  47. Suraj, Z.: Tools for generating and analyzing concurrent models specified by information systems. In: T.Y. Lin (ed.): Proceedings of the Third International Workshop on Rough Sets and Soft Computing (RSSC’94), San Jose State University, San Jose CA, November 10–12 (1994) 610–617

    Google Scholar 

  48. Suraj, Z.: PN-tools: environment for the design and analysis of Petri nets. Control and Cybernetics (published by Systems Research Institute of Polish Academy of Sciences) 242 (1995) 199–222

    Google Scholar 

  49. Suraj, Z.: An application of rough set methods to cooperative information systems re-engineering. In: S. Tsumoto, S. Kobayashi, T. Yokomori, H. Tanaka, and A. Nakamura (eds.): Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (RSFD’96), The University of Tokyo, November 6–8 (1996) 364–371

    Google Scholar 

  50. Thiagarajan, P.S.: Elementary net systems. Advances in Petri nets 1986 Part I. Lecture Notes in Computer Science 254 Springer-Verlag, Berlin (1987) 26–59

    Google Scholar 

  51. Wegener, I.: The complexity of Boolean functions. Wiley and B.G. Teubner, Stuttgart (1987)

    Google Scholar 

  52. Ziarko, W., and Shan, N.: An incremental learning algorithm for constructing decision rules. In: W. Ziarko (ed.): Proceedings of the Second International Workshop on Rough Sets and Knowledge Discovery (RSKD’93), Banff, Alberta, Canada, October 12–15 (1993) 335–346

    Google Scholar 

  53. Zytkow, J.: Interactive mining of regularities in databases. In: G. PiatetskyShapiro and W. Frawley (eds.), Knowledge Discovery in Databases, The AAAI Press, Menlo Park CA (1991)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Pedagogical University, Rejtana 16A, 35-310, Rzeszów, Poland

    Zbigniew Suraj

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  1. Zbigniew Suraj
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Editors and Affiliations

  1. Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-665, Warsaw, Poland

    Lech Polkowski

  2. Polish-Japanese Institute of Computer Techniques, Koszykowa 86, 02-008, Warsaw, Poland

    Lech Polkowski

  3. Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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Suraj, Z. (1998). The Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems. In: Polkowski, L., Skowron, A. (eds) Rough Sets in Knowledge Discovery 2. Studies in Fuzziness and Soft Computing, vol 19. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1883-3_22

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  • DOI: https://doi.org/10.1007/978-3-7908-1883-3_22

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2459-9

  • Online ISBN: 978-3-7908-1883-3

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