Modal Specifications for Probabilistic Timed Systems

Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinem ent and compositional reasoning. In recent years, quantitative variants of modal automata were introduced for specifying and reasoning about component-based designs for embedded and mobile systems. These respectively generalize modal specification theories for timed and probabilistic sy stems. In this paper, we define a modal specification language for combined probabilistic timed sy stems, called abstract probabilistic timed automata, which generalizes existing formalisms. We introduce appropriate syntactic and semantic refinement notions and discuss consistency of our specificat ion language, also with respect to timedivergence. We identify a subclass of our models for which we define the fundamental operations for

[1]  Marta Z. Kwiatkowska,et al.  Revisiting Timed Specification Theories: A Linear-Time Perspective , 2012, FORMATS.

[2]  Kim G. Larsen,et al.  Abstract Probabilistic Automata , 2011, VMCAI.

[3]  Kim G. Larsen,et al.  A modal process logic , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[4]  Bengt Jonsson,et al.  A Compositional Specification Theory for Component Behaviours , 2012, ESOP.

[5]  Bengt Jonsson,et al.  Assume-Guarantee Reasoning for Safe Component Behaviours , 2012, FACS.

[6]  Kim G. Larsen,et al.  On Modal Refinement and Consistency , 2007, CONCUR.

[7]  Joost-Pieter Katoen,et al.  Compositional Abstraction Techniques for Probabilistic Automata , 2012, IFIP TCS.

[8]  Kim G. Larsen,et al.  Timed I/O automata: a complete specification theory for real-time systems , 2010, HSCC '10.

[9]  Nathalie Bertrand,et al.  Modal event-clock specifications for timed component-based design , 2012, Sci. Comput. Program..

[10]  Thomas A. Henzinger,et al.  Event-Clock Automata: A Determinizable Class of Timed Automata , 1999, Theor. Comput. Sci..

[11]  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.

[12]  Frits W. Vaandrager,et al.  Root Contention in IEEE 1394 , 1999, ARTS.

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

[14]  Kim G. Larsen,et al.  Constraint Markov Chains , 2011, Theor. Comput. Sci..

[15]  Axel Legay,et al.  A Robust Specification Theory for Modal Event-Clock Automata , 2012, FIT.

[16]  Jeremy Sproston.  Strict Divergence for Probabilistic Timed Automata , 2009, CONCUR.

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

[18]  Marta Z. Kwiatkowska,et al.  Automatic verification of real-time systems with discrete probability distributions , 1999, Theor. Comput. Sci..

[19]  Axel Legay,et al.  General Quantitative Specification Theories with Modalities , 2012, CSR.