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
Haar, A., Cohen, P.R,. Feigenbaum, E.A.: The handbook of artificial intelligence 4 Addison Wesley (1989)
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
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
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
Brown E.M.: Boolean reasoning. Kluwer Academic Publishers, Dordrecht (1990)
Desel, J., Reisig, W.: The synthesis problem of Petri nets. Acta Inf. 3/34 (1996) 297–315
Ehrenfeucht, A., Rozenberg, G.: Partial 2-structures Part II. State space of concurrent systems. Acta Inf. 27 (1990) 348–368
Hack, M.: Decidability questions for Petri nets. Ph.D thesis. Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge MA (1975)
Hurley, R.B.: Decision tables in software engineering. Van Nostrad Reinhold Company, New York (1983)
Janicki, R.: Transforming sequential systems into concurrent systems. Theoretical Comp. Sci. 36 (1985) 27–58
Karp, R.M., and Miller, R.E.: Parallel program schemata. Journal of Computer and System Science 34 (1969) 167–195
Kodratoff, Y., Michalski, R. (eds.): Machine learning 3 Morgan Kaufmann Publishers, San Mateo CA (1990)
Krieg, B.: Petrinetze und Zustandsgraphen. IFI-Bericht B-29/77 Institut für Informatik, Universität Hamburg (1977)
Lengauer, C., Hehner, E.C.R.: A methodology for programming with concurrency: an informal presentation. Sci. Comp. Progr. 2 (1982) 1–18
Michalski, R., Carbonell, J.G., Mitchell, T.M. (eds.): Machine learning: an artificial intelligence approach 1 Tioga/Morgan Kaufmann Publishers, Los Altos CA (1983)
Michalski, R., Carbonell, J.G., Mitchell, T.M. (eds.): Machine learning: an artificial intelligence approach 2 Morgan Publishers, Los Altos CA (1986)
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
Milner, R.: Communication and concurrency. Prentice-Hall, Englewood Cliffs, NJ (1989)
Mukund, M.: Petri nets and step transition systems. Int. Journal of Foundations of Computer Science 34 (1992) 443–478
Murata, T.: Petri nets: properties, analysis and applications. In: Proc. of the IEEE 77/4 (1989) 541–580
Nadler, M., Smith, E.P: Pattern recognition engineering. John Wiley and Sons, New York (1993)
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
Nguyen, H. Son: Discretization of real value attributes: Boolean reasoning approach. Ph.D thesis, Warsaw University, Warsaw (1997) 1–90
Nielsen, M., Rozenberg, G., Thiagarajan, P.S.: Elementary transition systems. Theoretical Comp. Sci. 961 (1992) 3–33
Pawlak, Z.: Rough sets — Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlalc, Z.: Concurrent versus sequential: The rough sets perspective. Bulletin of the EATCS 48 (1992) 178–190
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
Pawlalc, Z.: Some remarks on explanation of data and specification of concurrent processes. Bulletin of International Rough Set Society 11 (1996) 1–4
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)
Reisig, W.: Petri nets. An introduction. Springer-Verlag, Berlin (1985)
Shapiro, S.C., Eckroth, D.: Encyclopedia of artificial intelligence 1 Wiley, New York (1987) 18–35
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
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)
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
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
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
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
Skowron, A., and Suraj, Z.: A rough set approach to the real-time state identification. Bulletin of the EATCS 50 (1993) 264–275
Skowron, A., and Suraj, Z.: Rough sets and concurrency. Bull. Polish Acad. Sci., Ser. Sci. Tech. 413 (1993) 237–254
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)
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)
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)
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
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
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
Slowinski, R. (ed.): Intelligent decision support — Handbook of applications and advances of the rough sets theory. Kluwer Academic Publishers, Dordrecht (1992)
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
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
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
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
Wegener, I.: The complexity of Boolean functions. Wiley and B.G. Teubner, Stuttgart (1987)
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
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)
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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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