Rough set methods for the synthesis and analysis of concurrent processes

Abstract. In this Chapter rough set methods for the modeling of concurrent processes are considered. The research is motivated by the problems coming from the domains such as, for example: knowledge discovery systems, data mining, control design, decomposition of information systems, object identification in real-time. this Chapter includes, in particular, the description of automatic methods for the modeling and analysis of concurrent systems specified by information systems. In this Chapter the following problems are considered: 1. The synthesis problem of concurrent systems specified by information systems. 2. The problem of discovering concurrent data models from experimental tables. 3. The re-engineering problem for cooperative information systems. 4. The real-time decision making problem. 5. The control design problem for discrete event systems.

[1]  K. Mani Chandy,et al.  Parallel program design - a foundation , 1988 .

[2]  Andrea Maggiolo-Schettini,et al.  An Algebra of Processes , 1987, J. Comput. Syst. Sci..

[3]  B. Natarajan Machine Learning: A Theoretical Approach , 1992 .

[4]  Oscar N. Garcia,et al.  Knowledge-based systems : fundamentals and tools , 1991 .

[5]  Jan M. Zytkow,et al.  Discovery of Equations: Experimental Evaluation of Convergence , 1992, AAAI.

[6]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[7]  Andrzej Szałas,et al.  Time and Logic: A Computational Approach , 1995 .

[8]  René David,et al.  Petri nets and grafcet - tools for modelling discrete event systems , 1992 .

[9]  Zdzisław Pawlak,et al.  Decision tables and decision algorithms , 1985 .

[10]  Yi Deng,et al.  A G-Net Model for Knowledge Representation and Reasoning , 1990, IEEE Trans. Knowl. Data Eng..

[11]  H.-M. Hanisch,et al.  Analysis of signal/event nets , 1997, 1997 IEEE 6th International Conference on Emerging Technologies and Factory Automation Proceedings, EFTA '97.

[12]  Pascal Raymond,et al.  The synchronous data flow programming language LUSTRE , 1991, Proc. IEEE.

[13]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[14]  James F. Peters,et al.  Approximate Time Rough Control: Concepts and Application to Satellite Attitude Control , 1998, Rough Sets and Current Trends in Computing.

[15]  Roman Slowinski,et al.  Rough-Set Reasoning about Uncertain Data , 1996, Fundam. Informaticae.

[16]  Antoni W. Mazurkiewicz,et al.  Introduction to Trace Theory , 1995, The Book of Traces.

[17]  Józef Winkowski Concatenable Weighted Pomsets and Their Applications to Modelling Processes of Petri Nets , 1996, Fundam. Informaticae.

[18]  Wolfgang Reisig,et al.  Lectures on Petri Nets I: Basic Models , 1996, Lecture Notes in Computer Science.

[19]  Wolfgang Reisig,et al.  Petri Nets: Applications and Relationships to Other Models of Concurrency , 1986, Lecture Notes in Computer Science.

[20]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[21]  Colin Stirling,et al.  Verifying Temporal Properties of Processes , 1990, CONCUR.

[22]  John N. Warfield,et al.  SOCIETAL SYSTEMS Planning, Policy and Complexity , 1978 .

[23]  Carl G. Looney,et al.  Fuzzy Petri nets for rule-based decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[24]  Alan A. Desrochers,et al.  Applications of Petri Nets in Manufacturing Systems: Modeling, Control, and Performance Analysis , 1994 .

[25]  C. Reutenauer The Mathematics of Petri Nets , 1990 .

[26]  Michel Hack,et al.  Decidability Questions for Petri Nets , 1975, Outstanding Dissertations in the Computer Sciences.

[27]  Herbert A. Simon,et al.  The Sciences of the Artificial , 1970 .

[28]  Glynn Winskel,et al.  Relationships between Models of Concurency , 1993 .

[29]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[30]  Keith Edwards,et al.  Real-Time Structured Methods: Systems Analysis , 1993 .

[31]  Andrzej Skowron,et al.  The Discernibility Matrices and Functions in Information Systems , 1992, Intelligent Decision Support.

[32]  Horst Eggert,et al.  Petri-Netz-Methoden und -Werkzeuge: Hilfsmittel zur Entwurfsspezifikation und -validation von Rechensystemen , 1989, Informatik-Fachberichte.

[33]  Luca Bernardinello,et al.  Synthesis of Net Systems , 1993, Application and Theory of Petri Nets.

[34]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[35]  Stanislaw Budkowski,et al.  An Introduction to Estelle: A Specification Language for Distributed Systems , 1987, Comput. Networks.

[36]  Matthias Jarke,et al.  Distributed Information Systems Engineering , 1996, ISMIS.

[37]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[38]  Jiacun Wang,et al.  Timed Petri Nets , 1998, The Kluwer International Series on Discrete Event Dynamic Systems.

[39]  Michio Sugeno,et al.  Fuzzy systems theory and its applications , 1991 .

[40]  Zbigniew Suraj,et al.  Reconstruction of Cooperative Information Systems under Cost Constraints: A Rough Set Approach , 1998, Inf. Sci..

[41]  Mordechai Ben-Ari,et al.  The temporal logic of branching time , 1981, POPL '81.

[42]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[43]  Wolfgang Reisig,et al.  A Primer in Petri Net Design , 1992, Springer Compass International.

[44]  Ernst-Rüdiger Olderog,et al.  Nets, terms and formulas , 1991 .

[45]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[46]  Adam Mrózek,et al.  Rough Sets in Computer Implementation of Rule-Based Control of Industrial Processes , 1992, Intelligent Decision Support.

[47]  Andrzej Skowron,et al.  Rough sets and current trends in computing : first international conference, RSCTC '98, Warsaw, Poland, June 22-26, 1998 : proceedings , 1998 .

[48]  A. Giordana,et al.  Modelling Production Systems by means of Predicate-Transitions Networks , 1985, Inf. Sci..

[49]  Zdzisław Pawlak,et al.  Rough real functions and rough controllers , 1997 .

[50]  Andrzej Skowron,et al.  Decision Algorithms: A Survey of Rough Set - Theoretic Methods , 1997, Fundam. Informaticae.

[51]  Robert Valette,et al.  Fuzzy Petri Nets: An Overview , 1996 .

[52]  Tsau Young Lin,et al.  Fuzzy Controllers: An Integrated Approach Based on Fuzzy Logic, Rough Sets, and Evolutionary Computing , 1997 .

[53]  Roman Słowiński,et al.  Intelligent Decision Support , 1992, Theory and Decision Library.

[54]  Richard M. Karp,et al.  Parallel Program Schemata , 1969, J. Comput. Syst. Sci..

[55]  Philippe Darondeau,et al.  The Synthesis Problem for Elementary Net Systems is NP-Complete , 1997, Theor. Comput. Sci..

[56]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[57]  Grzegorz Rozenberg,et al.  High-level Petri Nets: Theory And Application , 1991 .

[58]  Andrzej Skowron,et al.  Synthesis of Decision Systems from Data Tables , 1997 .

[59]  Barbara Hayes Roth Architectural foundations for real-time performance in intelligent agents , 1990 .

[60]  Wojciech Ziarko,et al.  Knowledge-Based Process Control Using Rough Sets , 1992, Intelligent Decision Support.

[61]  Eike Best COSY: Its Relation to Nets and CSP , 1986, Advances in Petri Nets.

[62]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains, Part I , 1981, Theor. Comput. Sci..

[63]  Amir Pnueli,et al.  Applications of Temporal Logic to the Specification and Verification of Reactive Systems: A Survey of Current Trends , 1986, Current Trends in Concurrency.

[64]  C. Ramchandani,et al.  Analysis of asynchronous concurrent systems by timed petri nets , 1974 .

[65]  S. Gottwald,et al.  Fuzzy sets, fuzzy logic, fuzzy methods with applications , 1995 .

[66]  A. Mazurkiewicz Concurrent Program Schemes and their Interpretations , 1977 .

[67]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[68]  James F. Peters,et al.  Time and Clock Information Systems: Concepts and Roughly Fuzzy Petri Net Models , 1998 .

[69]  Amir Pnueli,et al.  The temporal logic of programs , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[70]  Tadao Murata,et al.  A Predicate-Transition Net Model for Parallel Interpretation of Logic Programs , 1988, IEEE Trans. Software Eng..

[71]  Hans-Michael Hanisch,et al.  A Signal Extension for Petri Nets and its Use in Controller Design , 2000, Fundam. Informaticae.

[72]  Witold Pedrycz,et al.  Data Mining Methods for Knowledge Discovery , 1998, IEEE Trans. Neural Networks.

[73]  Robert M. Keller,et al.  Formal verification of parallel programs , 1976, CACM.

[74]  Zbigniew Suraj,et al.  The Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems , 1998 .

[75]  Andrzej Skowron,et al.  Boolean Reasoning for Decision Rules Generation , 1993, ISMIS.

[76]  Mogens Nielsen,et al.  Models for Concurrency , 1992 .

[77]  James L. Crowley,et al.  Navigation for an intelligent mobile robot , 1985, IEEE J. Robotics Autom..

[78]  Professor Dr. Wolfgang Reisig Elements of Distributed Algorithms , 1998, Springer Berlin Heidelberg.

[79]  Józef Winkowski An Algebraic Description of System Behaviours , 1982, Theor. Comput. Sci..

[80]  Andrzej Skowron,et al.  Rough sets and concurrency , 1993 .

[81]  Jörg Desel,et al.  Free choice Petri nets , 1995 .

[82]  Madhavan Mukund Petri Nets and Step Transition Systems , 1992, Int. J. Found. Comput. Sci..

[83]  Steven A. Stanton Michael Hammer The Reengineering Revolution , 1996 .

[84]  Grzegorz Rozenberg,et al.  Elementary Transition Systems , 1990, Theor. Comput. Sci..

[85]  Paul R. Manson Petri net theory: a survey , 1988 .

[86]  Rüdiger Valk Self-Modifying Nets, a Natural Extension of Petri Nets , 1978, ICALP.

[87]  Jin-Fu Chang,et al.  Knowledge Representation Using Fuzzy Petri Nets , 1990, IEEE Trans. Knowl. Data Eng..

[88]  Andrzej Skowron,et al.  The rough sets theory and evidence theory , 1990 .

[89]  Zohar Manna,et al.  Temporal Verification of Reactive Systems , 1995, Springer New York.

[90]  C. A. R. Hoare,et al.  A Theory of Communicating Sequential Processes , 1984, JACM.

[91]  Pierre-Jacques Courtois,et al.  On time and space decomposition of complex structures , 1985, CACM.

[92]  Ryszard S. Michalski,et al.  Constructive Induction An Automated Improvement of Knowledge Representation Spaces for Machine Learning , 1993 .

[93]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[94]  J. Kacprzyk,et al.  Incomplete Information: Rough Set Analysis , 1997 .

[95]  Andrzej Skowron,et al.  EXTRACTING LAWS FROM DECISION TABLES: A ROUGH SET APPROACH , 1995, Comput. Intell..

[96]  Ludwik Czaja,et al.  Finite Processes in Cause-Effect Structures and Their Composition , 1989, Inf. Process. Lett..

[97]  E. A. Trachtenberg,et al.  Design automation tools for efficient implementation of logic functions by decomposition , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[98]  Frits Feldbrugge Petri net tool overview 1989 , 1988, European Workshop on Applications and Theory in Petri Nets.

[99]  Kishor S. Trivedi,et al.  Performance And Reliability Analysis Of Computer Systems (an Example-based Approach Using The Sharpe Software , 1997, IEEE Transactions on Reliability.

[100]  Matthew Hennessy,et al.  Algebraic theory of processes , 1988, MIT Press series in the foundations of computing.

[101]  Glynn Winskel,et al.  Models for concurrency: towards a classification , 1996 .

[102]  Tommaso Bolognesi,et al.  Tableau methods to describe strong bisimilarity on LOTOS processes involving pure interleaving and enabling , 1994, FORTE.

[103]  Louchka Popova-Zeugmann,et al.  On Time Petri Nets , 1991, J. Inf. Process. Cybern..

[104]  Witold Pedrycz,et al.  Approximate real‐time decision making: Concepts and rough fuzzy Petri net models , 1999 .

[105]  Yair Wand,et al.  An Automated Approach to Information Systems Decomposition , 1992, IEEE Trans. Software Eng..

[106]  Wojciech Ziarko Acquisition of Control Algorithms from Operation Data , 1992, Intelligent Decision Support.

[107]  Zdzisław Pawlak,et al.  ROUGH CONTROL APPLICATION OF ROUGH SET THEORY TO CONTROL , 1996 .

[108]  Edward Ochmanski Recognizable Trace Languages , 1995, The Book of Traces.

[109]  Frits Feldbrugge,et al.  Petri net tools , 1985, Applications and Theory in Petri Nets.

[110]  P. H. Starke On the mutual simulatability of different types of Petri nets , 1987 .

[111]  Ryszard Janicki,et al.  Transforming Sequential Systems into Concurrent Systems , 1985, Theor. Comput. Sci..

[112]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[113]  A. Mrozek,et al.  The methodology of rough controller synthesis , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[114]  Andrzej Skowron,et al.  A rough set approach to real-time state identification , 1993, Bull. EATCS.

[115]  William Frawley,et al.  Knowledge Discovery in Databases , 1991 .

[116]  Simon Peck,et al.  Practice of Petri Nets in Manufacturing , 1993 .

[117]  Kurt Jensen,et al.  Petri Net Tool Overview 1986 , 1986, Advances in Petri Nets.

[118]  Tin A. Nguyen,et al.  Knowledge base verification , 1987 .

[119]  Michael R. Genesereth,et al.  Logical foundations of artificial intelligence , 1987 .

[120]  Pedro Meseguer,et al.  Knowledge Based Systems Validation: A State of the Art , 1990, AI Commun..

[121]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[122]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[123]  Peter H. Starke Petri-Netz-Maschine a software tool for analysis and validation of Petri nets , 1985 .

[124]  Witold Pedrycz,et al.  A generalized fuzzy Petri net model , 1994, IEEE Trans. Fuzzy Syst..

[125]  MengChu Zhou,et al.  Petri nets and industrial applications: A tutorial , 1994, IEEE Trans. Ind. Electron..

[126]  Y.Y. Haimes,et al.  Methodology for large-scale systems , 1978, Proceedings of the IEEE.

[127]  Grzegorz Rozenberg,et al.  Advances in Petri Nets 1985 , 1985, Lecture Notes in Computer Science.

[128]  V. S. Subrahmanian,et al.  A Petri Net Model for Reasoning in the Presence of Inconsistency , 1991, IEEE Trans. Knowl. Data Eng..

[129]  Ryszard Janicki,et al.  Specification and Analysis of Concurrent Systems , 1992, EATCS Monographs in Theoretical Computer Science.

[130]  Kurt Jensen,et al.  Computer Tools for High-level Petri Nets , 1991 .

[131]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[132]  Kurt Lautenbach,et al.  System Modelling with High-Level Petri Nets , 1981, Theor. Comput. Sci..

[133]  Tsau Young Lin,et al.  Rough Sets and Data Mining: Analysis of Imprecise Data , 1996 .

[134]  Glynn Winskel,et al.  Event Structures , 1986, Advances in Petri Nets.

[135]  Gérard Berry,et al.  The Esterel Synchronous Programming Language: Design, Semantics, Implementation , 1992, Sci. Comput. Program..

[136]  Marco Ajmone Marsan,et al.  Performance models of multiprocessor systems , 1987, MIT Press series in computer systems.

[137]  Toshinori Munakata,et al.  Rough Control: A Perspective , 1997 .

[138]  Wlodzimierz M. Zuberek,et al.  Timed Petri nets definitions, properties, and applications , 1991 .

[139]  Jaegeol Yim,et al.  A Predicate-Transition Net Model for Multiple Agent Planning , 1991, Inf. Sci..

[140]  Kurt Lautenbach Linear Algebraic Techniques for Place/Transition Nets , 1986, Advances in Petri Nets.

[141]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[142]  B. Chandrasekaran,et al.  Real-time disturbance control , 1991, CACM.

[143]  David W. Payton,et al.  Intelligent real-time control of robotic vehicles , 1991, CACM.

[144]  Janette Cardoso,et al.  Petri nets with uncertain markings , 1991, Applications and Theory of Petri Nets.

[145]  Grzegorz Rozenberg,et al.  Petri Nets: Basic Notions, Structure, Behaviour , 1986, Current Trends in Concurrency.

[146]  C. R. Snow Concurrent programming , 1992, Cambridge computer science texts.

[147]  G. Harhalakis,et al.  Petri nets for manufacturing information systems , 1993 .

[148]  Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[149]  Marcel Schoppers Real-time knowledge-based control systems , 1991, CACM.

[150]  Jiacun Wang,et al.  Timed Petri Nets: Theory and Application , 1998 .

[151]  Dan C. Marinescu,et al.  Logical Inference of Horn Clauses in Petri Net Models , 1993, IEEE Trans. Knowl. Data Eng..

[152]  Morton Nadler,et al.  Pattern recognition engineering , 1993 .

[153]  Peter H. Starke,et al.  Analyse von Petri-Netz-Modellen , 1990, Leitfäden und Monographien der Informatik.

[154]  Kurt Jensen,et al.  Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 2, Analysis Methods , 1992 .

[155]  Zdzisław Pawlak,et al.  The idea of a rough fuzzy controller and its application to the stabilization of a pendulum-car system , 1995 .

[156]  Charles L. Forgy,et al.  Rete: A Fast Algorithm for the Many Patterns/Many Objects Match Problem , 1982, Artif. Intell..

[157]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[158]  Glynn Winskel,et al.  Events in computation , 1980 .

[159]  Boudewijn R. Haverkort Performance of computer communication systems , 1998 .

[160]  Derek L. Nazareth,et al.  Investigating the Applicability of Petri Nets for Rule-Based System Verification , 1993, IEEE Trans. Knowl. Data Eng..

[161]  R. Yasdi Rough Sets: State of the Art and Perspectives: Poznan-Kiekrz, Poland, 2-4 September 1992 , 1992 .

[162]  MengChu Zhou,et al.  Petri net synthesis for discrete event control of manufacturing systems , 1992, The Kluwer international series in engineering and computer science.

[163]  John H. Reif,et al.  Synthesis of Parallel Algorithms , 1993 .

[164]  Eike Best,et al.  Nonsequential Processes: A Petri Net View , 1988 .

[165]  Anastasia Pagnoni,et al.  Project Engineering: Computer-Oriented Planning and Operational Decision Making , 1990 .

[166]  E. Ott Chaos in Dynamical Systems: Contents , 1993 .

[167]  J. Baeten Applications of process algebra , 1990 .

[168]  Jan M. Zytkow,et al.  Interactive Mining of Regularities in Databases , 1991, Knowledge Discovery in Databases.

[169]  Ali Bulent Cambel,et al.  Applied Chaos Theory: A Paradigm for Complexity , 1992 .

[170]  Michael K. Molloy Performance Analysis Using Stochastic Petri Nets , 1982, IEEE Transactions on Computers.

[171]  David Harel,et al.  Statecharts: A Visual Formalism for Complex Systems , 1987, Sci. Comput. Program..

[172]  Marek Antoni Bednarczyk,et al.  Categories of asynchronous systems , 1987 .

[173]  Performance Models Proceedings of the Fourth International Workshop on Petri Nets and Performance Models (PNPM91), December 2-5, 1991, Melbourne, Australia , 1991 .

[174]  Zdzislaw Pawlak Concurrent versus sequential - the rough sets perspective , 1992, Bull. EATCS.

[175]  Ingo Wegener,et al.  The complexity of Boolean functions , 1987 .

[176]  Tadao Murata,et al.  Temporal Uncertainty and Fuzzy-Timing High-Level Petri Nets , 1996, Application and Theory of Petri Nets.

[177]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[178]  Gérard Berthelot Transformations and Decompositions of Nets , 1986 .

[179]  Karl Martin Schmidt-Reindl,et al.  Notations and terminology on Petri Net theory , 1987 .

[180]  Wolfgang Reisig,et al.  Petri Nets: Central Models and Their Properties , 1986, Lecture Notes in Computer Science.

[181]  Brian D. Ripley,et al.  Pattern Recognition and Neural Networks , 1996 .

[182]  Jan M. Zytkow,et al.  Automatic Theorem Generation in Plane Geometry , 1993, ISMIS.

[183]  Joseph Fong,et al.  Information systems reengineering , 1997 .

[184]  V. S. Subrahmanian,et al.  Paraconsistent Logic Programming , 1987, Theor. Comput. Sci..

[185]  Andrzej Skowron,et al.  Rough set rudiments , 1995 .

[186]  Adam Mrózek,et al.  Knowledge Representation in Fuzzy and Rough Controllers , 1997, Fundam. Informaticae.

[187]  James Gleick Chaos: Making a New Science , 1987 .

[188]  André Arnold,et al.  Finite transition systems , 1994 .

[189]  Philip M. Johnson Reengineering inspection , 1998, CACM.

[190]  Christian Lengauer,et al.  A Methodology for Programming with Concurrency: An Informal Presentation , 1982, Sci. Comput. Program..

[191]  Andrzej Skowron,et al.  Rough-Fuzzy Hybridization: A New Trend in Decision Making , 1999 .

[192]  Witold Pedrycz,et al.  Fuzzy sets engineering , 1995 .

[193]  Zbigniew Suraj,et al.  Discovery of Concurrent Data Models from Experimental Tables: A Rough Set Approach , 1995, Fundam. Informaticae.

[194]  Performance Models,et al.  Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM 1989, Kyoto, Japan, December 11-13, 1989 , 1989, PNPM.

[195]  Andrzej Skowron,et al.  Dynamic Reducts as a Tool for Extracting Laws from Decisions Tables , 1994, ISMIS.

[196]  Robert Valette,et al.  Software Implementation of Petri nets and compilation of rule-based systems , 1990, Applications and Theory of Petri Nets.

[197]  Philip D. Wasserman,et al.  Advanced methods in neural computing , 1993, VNR computer library.

[198]  Ryszard Janicki,et al.  Specification and Analysis of Concurrent Systems: The Cosy Approach , 1992 .