Reversing Computations Modelled by Coloured Petri Nets

Reversible computation is an unconventional form of computing where any sequence of performed operations can be executed in reverse order at any point during computation. It has recently been attracting increasing attention as on the one hand it promises low-power computation and on the other hand it is inherent or of interest in a variety of applications. In this paper we propose a structural way of translating reversing Petri nets (RPNs), a formalism that embeds the three main forms of reversibility (backtracking, causal reversing and out-of-causalorder reversing), to Coloured Petri Nets (CPNs), an extension of traditional Petri Nets, where tokens carry data values. The translation into the CPN model uses additional places and transitions in order to capture the machinery employed in the RPN framework and demonstrates that the abstract model of RPNs, and thus the principles of reversible computation, can be emulated in CPNs. The transformation can be automated and utilized for the analysis of reversible systems using CPN Tools.

[1]  Maciej Koutny,et al.  Reversible computation vs. reversibility in Petri nets , 2016, Sci. Comput. Program..

[2]  Ivan Lanese,et al.  Reversibility in the higher-order π-calculus , 2016, Theor. Comput. Sci..

[3]  Irek Ulidowski,et al.  A Reversible Process Calculus and the Modelling of the ERK Signalling Pathway , 2012, RC.

[4]  Vincent Danos,et al.  Transactions in RCCS , 2005, CONCUR.

[5]  Iain C. C. Phillips,et al.  Reversing algebraic process calculi , 2006, J. Log. Algebraic Methods Program..

[6]  Maciej Koutny,et al.  Reversing Transitions in Bounded Petri Nets , 2016, CS&P.

[7]  Irek Ulidowski,et al.  Concurrency and Reversibility , 2014, RC.

[8]  Lars Michael Kristensen,et al.  Coloured Petri Nets - Modelling and Validation of Concurrent Systems , 2009 .

[9]  Irek Ulidowski,et al.  A Calculus for Local Reversibility , 2016, RC.

[10]  Vincent Danos,et al.  Reversible Communicating Systems , 2004, CONCUR.

[11]  Wolfgang Reisig,et al.  Understanding Petri Nets Modeling Techniques, Analysis Methods, Case Studies , 2013, Bull. EATCS.

[12]  Cosimo Laneve,et al.  Reversible structures , 2011, CMSB.

[13]  Michael Westergaard,et al.  CPN Tools for Editing, Simulating, and Analysing Coloured Petri Nets , 2003, ICATPN.

[14]  Irek Ulidowski,et al.  Modelling of Bonding with Processes and Events , 2013, RC.

[15]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[16]  Vincent Danos,et al.  Formal Molecular Biology Done in CCS-R , 2007, Electron. Notes Theor. Comput. Sci..

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

[18]  Anna Philippou,et al.  Reversible Computation in Petri Nets , 2018, RC.