A Uniform Framework for Timed Automata and Beyond

Timed automata, and machines alike, currently lack a general mathematical characterisation. This work introduces a uniform understanding of these devices that encompasses known behavioural equivalences such as timed bisimulations and timed language equivalences as well as their weak and time-abstract counterparts. All these notions of equivalence between systems are naturally organised in expressiveness spectra based on their discriminating power; these spectra are shown to be independent from any particular computational effect expressed by the systems under scrutiny. As an application, timed automata and their quantitative extensions such as probabilistic ones are studied.

[1]  Amr Sabry,et al.  Monadic encapsulation of effects: a revised approach (extended version) , 2001, J. Funct. Program..

[2]  A. Kock.  Strong functors and monoidal monads , 1972 .

[3]  Alexandra Silva,et al.  Trace semantics via determinization , 2015, J. Comput. Syst. Sci..

[4]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[5]  S. Lack.  A 2-Categories Companion , 2007, math/0702535.

[6]  Nick Benton,et al.  Monads and Effects , 2000, APPSEM.

[7]  Alexandra Silva,et al.  A Coalgebraic View of ε-Transitions , 2013, CALCO.

[8]  Joost-Pieter Katoen,et al.  Time-Abstracting Bisimulation for Probabilistic Timed Automata , 2008, 2008 2nd IFIP/IEEE International Symposium on Theoretical Aspects of Software Engineering.

[9]  Philip Wadler,et al.  Combining Monads , 1992 .

[10]  Gordon D. Plotkin,et al.  Towards a mathematical operational semantics , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[11]  Marino Miculan,et al.  Behavioural equivalences for coalgebras with unobservable moves , 2014, J. Log. Algebraic Methods Program..

[12]  Ana Sokolova,et al.  Generic Trace Semantics via Coinduction , 2007, Log. Methods Comput. Sci..

[13]  Davide Sangiorgi,et al.  The Pi-Calculus - a theory of mobile processes , 2001 .

[14]  Marco Peressotti,et al.  A Uniform Framework for Timed Automata , 2016, CONCUR.

[15]  J. Golan.  Semirings and their applications , 1999 .

[16]  Marino Miculan,et al.  On the Bisimulation Hierarchy of State-to-Function Transition Systems , 2016, ICTCS.

[17]  Tomasz Brengos.  On Coalgebras with Internal Moves , 2014, CMCS.

[18]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[19]  Eugenio Moggi,et al.  Notions of Computation and Monads , 1991, Inf. Comput..

[20]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[21]  Sam Staton.  Relating Coalgebraic Notions of Bisimulation , 2009, CALCO.

[22]  Giorgio Bacci,et al.  Structural operational semantics for continuous state stochastic transition systems , 2015, J. Comput. Syst. Sci..

[23]  Marco Peressotti,et al.  Endofunctors modelling higher-order behaviours , 2016, ArXiv.

[24]  Tomasz Brengos.  Lax functors and coalgebraic weak bisimulation , 2014 .

[25]  Bartek Klin,et al.  Bialgebras for structural operational semantics: An introduction , 2011, Theor. Comput. Sci..

[26]  Glynn Winskel,et al.  Distributing probability over non-determinism , 2006, Mathematical Structures in Computer Science.

[27]  Peter Aczel,et al.  A Final Coalgebra Theorem , 1989, Category Theory and Computer Science.

[28]  Irina Virbitskaite,et al.  A Categorical View of Timed Weak Bisimulation , 2010, TAMC.

[29]  Ichiro Hasuo,et al.  Generic Forward and Backward Simulations , 2006, CONCUR.

[30]  Philip S. Mulry,et al.  Lifting Theorems for Kleisli Categories , 1993, MFPS.

[31]  A. Kock.  Monads on symmetric monoidal closed categories , 1970 .

[32]  Wang Yi,et al.  Time-abstracted Bisimulation: Implicit Specifications and Decidability , 1997, Inf. Comput..

[33]  Bart Jacobs,et al.  Coalgebraic Trace Semantics for Combined Possibilitistic and Probabilistic Systems , 2008, CMCS.

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

[35]  Pawel Sobocinski,et al.  Relational presheaves, change of base and weak simulation , 2015, J. Comput. Syst. Sci..

[36]  Alexandra Silva,et al.  Generalizing determinization from automata to coalgebras , 2013, Log. Methods Comput. Sci..

[37]  Danièle Beauquier.  On probabilistic timed automata , 2003, Theor. Comput. Sci..

[38]  Tomasz Brengos,et al.  Weak bisimulation for coalgebras over order enriched monads , 2013, Log. Methods Comput. Sci..

[39]  Barbara König,et al.  Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems , 2013, Log. Methods Comput. Sci..

[40]  Eugenio Moggi,et al.  Computational lambda-calculus and monads , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[41]  K. I. Rosenthal.  The Theory of Quantaloids , 1996 .

[42]  Alexandra Silva,et al.  Algebra-coalgebra duality in brzozowski's minimization algorithm , 2014, ACM Trans. Comput. Log..

[43]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[44]  Dirk Pattinson,et al.  Coalgebraic Weak Bisimulation from Recursive Equations over Monads , 2014, ICALP.

[45]  R. Segala,et al.  Automatic Verification of Real-Time Systems with Discrete Probability Distributions , 1999, ARTS.

[46]  Jurriaan Rot,et al.  Coinduction up-to in a fibrational setting , 2014, CSL-LICS.