Fast verification of the class of stop-and-wait protocols modelled by coloured Petri nets

Most protocols contain parameters, such as the maximum number of retransmissions in an error recovery protocol. These parameters are instantiated with values that depend on the operating environment of the protocol. We would therefore like our formal specification or model of the system to include these parameters symbolically, where in general each parameter will have an arbitrary upper limit. The inclusion of parameters results in an infinite family of finite state systems, which makes verification difficult. However, techniques and tools are being developed for the verification of parametric and infinite state systems. We explore the use of one such tool, FAST, for automatically verifying several properties (such as channel bounds and the stop-and-wait property of alternating sends and receives) of the stop-and-wait class of protocols, where the maximum number of retransmissions and the maximum sequence number are considered as unbounded parameters. Coloured Petri nets (CPNs), an expressive language for representing protocols, is used to model this stop-and-wait class. However, FAST'S foundation is counter systems, automata where states are a vector of non-negative integers and with operations limited to Presburger arithmetic. We therefore also present some first steps in transforming CPNs to counter systems in the context of stop-and-wait protocols operating over unbounded FIFO channels.

[1]  Kurt Jensen,et al.  Coloured Petri nets (2nd ed.): basic concepts, analysis methods and practical use: volume 1 , 1996 .

[2]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[3]  Jonathan Billington,et al.  A Coloured Petri Net Approach to Protocol Verification , 2003, Lectures on Concurrency and Petri Nets.

[4]  Jonathan Billington,et al.  PROTEAN: A High-Level Petri Net Tool for the Specification and Verification of Communication Protocols , 1988, IEEE Trans. Software Eng..

[5]  Laure Petrucci,et al.  From PNML to counter systems for accelerating Petri Nets with FAST , 2004 .

[6]  Michel Diaz,et al.  Modeling and Analysis of Communication and Cooperation Protocols Using Petri Net Based Models , 1982, Comput. Networks.

[7]  Jérôme Leroux The Affine Hull of a Binary Automaton is Computable in Polynomial Time , 2003, INFINITY.

[8]  Ichiro Suzuki,et al.  Formal Analysis of the Alternating Bit Protocol by Temporal Petri Nets , 1990, IEEE Trans. Software Eng..

[9]  Keith A. Bartlett,et al.  A note on reliable full-duplex transmission over half-duplex links , 1969, Commun. ACM.

[10]  Alain Finkel,et al.  On the verification of broadcast protocols , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[11]  Parosh Aziz Abdulla,et al.  Symbolic Verification of Lossy Channel Systems: Application to the Bounded Retransmission Protocol , 1999, TACAS.

[12]  Jeffrey D. Ullman,et al.  Introduction to automata theory, languages, and computation, 2nd edition , 2001, SIGA.

[13]  Antti Valmari,et al.  Unbounded verification results by finite-state compositional techniques: 10/sup any/ states and beyond , 1998, Proceedings 1998 International Conference on Application of Concurrency to System Design.

[14]  Laurent Fribourg,et al.  Reachability Analysis of (Timed) Petri Nets Using Real Arithmetic , 1999, CONCUR.

[15]  Kenneth J. Turner,et al.  Using Formal Description Techniques: An Introduction to Estelle, Lotos, and SDL , 1993 .

[16]  Parosh Aziz Abdulla,et al.  Using Forward Reachability Analysis for Verification of Lossy Channel Systems , 2004, Formal Methods Syst. Des..

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

[18]  Hubert Comon-Lundh,et al.  Diophantine Equations, Presburger Arithmetic and Finite Automata , 1996, CAAP.

[19]  Alain Finkel,et al.  How to Compose Presburger-Accelerations: Applications to Broadcast Protocols , 2002, FSTTCS.

[20]  Marco Ajmone Marsan,et al.  A LOTOS extension for the performance analysis of distributed systems , 1994, TNET.

[21]  Laure Petrucci,et al.  FAST: Fast Acceleration of Symbolikc Transition Systems , 2003, CAV.

[22]  Wolfgang Reisig,et al.  Distributed algorithms: modeling and analysis with Petri nets , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[23]  Kurt Jensen,et al.  Coloured Petri Nets , 1997, Monographs in Theoretical Computer Science An EATCS Series.

[24]  Jonathan Billington,et al.  Using Parametric Automata for the Verification of the Stop-and-Wait Class of Protocols , 2005, ATVA.

[25]  Lars Michael Kristensen,et al.  A Generalised Sweep-Line Method for Safety Properties , 2002, FME.

[26]  Pierre Wolper,et al.  On the Construction of Automata from Linear Arithmetic Constraints , 2000, TACAS.

[27]  Piotr Kosiuczenko,et al.  A timed rewriting logic semantics for SDL: A case study of alternating bit protocol , 1998, WRLA.