PZ nets a formal method integrating Petri nets with Z

Abstract In this paper, a formal method (called PZ nets) for specifying concurrent and distributed systems is presented. PZ nets integrate two well-known existing formal methods Petri nets and Z such that Petri nets are used to specify the overall structure, control flows, causal relation, and dynamic behavior of a system; and Z is used to define tokens, labels and constrains of the system. The essence, benefits, and problems of the integration are discussed. A set of heuristics and transformations to develop PZ nets and a technique to analyze PZ nets are proposed and demonstrated through a well-known example.

[1]  J. Michael Spivey,et al.  Z Notation - a reference manual (2. ed.) , 1992, Prentice Hall International Series in Computer Science.

[2]  Xudong He,et al.  A Temporal Logic Approach for Analyzing Safety Properties of Predicate Transition Nets , 1992, IFIP Congress.

[3]  Graeme Smith,et al.  Temporal Logic and Z Specifications , 1989, Aust. Comput. J..

[4]  M. Benjamin A Message Passing System. An example of combining CSP and Z , 1989, Z User Workshop.

[5]  Richard A. Kemmerer,et al.  Testing Formal Specifications to Detect Design Errors , 1985, IEEE Transactions on Software Engineering.

[6]  Bowen Alpern,et al.  Defining Liveness , 1984, Inf. Process. Lett..

[7]  John A. N. Lee,et al.  A methodology for constructing predicate transition net specifications , 1991, Softw. Pract. Exp..

[8]  Hartmann J. Genrich Equivalence transformations of PrT-nets , 1988, European Workshop on Applications and Theory in Petri Nets.

[9]  Keijiro Araki,et al.  The state-based CCS semantics for concurrent Z specification , 1997, First IEEE International Conference on Formal Engineering Methods.

[10]  Edward Yourdon,et al.  Modern structured analysis , 1989 .

[11]  Hartmann J. Genrich,et al.  Predicate/Transition Nets , 1986, Advances in Petri Nets.

[12]  Leslie Lamport,et al.  The temporal logic of actions , 1994, TOPL.

[13]  Kees M. van Hee,et al.  Z and High Level Petri Nets , 1991, VDM Europe.

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

[15]  Zohar Manna,et al.  Temporal verification of reactive systems - safety , 1995 .

[16]  Susan Stepney,et al.  Object Orientation in Z , 1992, Workshops in Computing.

[17]  Xudong He,et al.  High-level algebraic Petri nets , 1995, Inf. Softw. Technol..

[18]  Hartmann J. Genrich Predicate/transition nets , 1987 .

[19]  Wolfgang Reisig,et al.  System Design Using Petri Nets , 1983, Requirements Engineering.

[20]  Paul K. Harter Book Review: The Temporal Logic of Reactive and Concurrent Systems, Vol. I Specification by Zahar Manna and Amir Pnueli , 1993, ACM SIGOPS Oper. Syst. Rev..

[21]  Wolfgang Reisig Petri Nets: An Introduction , 1985, EATCS Monographs on Theoretical Computer Science.

[22]  Wilfried Brauer,et al.  A survey of behaviour and equivalence preserving refinements of Petri nets , 1991, Applications and Theory of Petri Nets.

[23]  Jacques Vautherin,et al.  Parallel systems specitications with coloured Petri nets and algebraic specifications , 1986, European Workshop on Applications and Theory of Petri Nets.

[24]  Kurt Jensen Coloured Petri Nets , 1992, EATCS Monographs in Theoretical Computer Science.

[25]  Carroll Morgan,et al.  Programming from specifications , 1990, Prentice Hall International Series in computer science.

[26]  Kurt Jensen Coloured Petri nets , 1986 .

[27]  Edmund M. Clarke,et al.  Formal Methods: State of the Art and Future Directions Working Group Members , 1996 .

[28]  X. He,et al.  Structured analysis using hierarchical predicate transition nets , 1992, [1992] Proceedings. The Sixteenth Annual International Computer Software and Applications Conference.

[29]  Xudong He,et al.  A Formal Definition of Hierarchical Predicate Transition Nets , 1996, Application and Theory of Petri Nets.

[30]  Jeannette M. Wing A specifier's introduction to formal methods , 1990, Computer.

[31]  J. B. Wordsworth,et al.  Software development with Z , 1992 .

[32]  Xudong He A method for analyzing properties of hierarchical predicate transition nets , 1995, Proceedings Nineteenth Annual International Computer Software and Applications Conference (COMPSAC'95).

[33]  Gul Agha,et al.  Concurrent Object-Oriented Programming and Petri Nets , 2001, Lecture Notes in Computer Science.

[34]  Bernd J. Krämer,et al.  Introducing the GRASPIN specification language SEGRAS, , 1991, J. Syst. Softw..

[35]  Andy Evans An Improved Recipe for Specifying Reactive Systems in Z , 1997, ZUM.

[36]  Peter Baumann,et al.  A Framework for the Specification of Reactive and Concurrent Systems in Z , 1995, FSTTCS.

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

[38]  Wolfgang Reisig,et al.  Petri Nets and Algebraic Specifications , 1991, Theor. Comput. Sci..