Compositionality for Quantitative Specifications

We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.

[1]  Joseph Sifakis,et al.  A vision for computer science — the system perspective , 2011, Central European Journal of Computer Science.

[2]  Kim G. Larsen,et al.  Refinement and Difference for Probabilistic Automata , 2012, QEST.

[3]  Luca Aceto,et al.  Reactive Systems: Figures and tables , 2007 .

[4]  Kim G. Larsen,et al.  Real-time specifications , 2013, International Journal on Software Tools for Technology Transfer.

[5]  Thomas A. Henzinger,et al.  Quantifying Similarities Between Timed Systems , 2005, FORMATS.

[6]  Luca de Alfaro,et al.  Linear and Branching System Metrics , 2009, IEEE Transactions on Software Engineering.

[7]  Thomas A. Henzinger,et al.  Interface automata , 2001, ESEC/FSE-9.

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

[9]  Luca Cardelli,et al.  A Spatial Logic for Concurrency , 2001, TACS.

[10]  David de Frutos Escrig,et al.  Defining distances for all process semantics , 2012 .

[11]  Luca Aceto,et al.  On the specification of modal systems: A comparison of three frameworks , 2013, Sci. Comput. Program..

[12]  Kim G. Larsen,et al.  Consistency and refinement for Interval Markov Chains , 2012, J. Log. Algebraic Methods Program..

[13]  Dexter Kozen,et al.  RESULTS ON THE PROPOSITIONAL’p-CALCULUS , 2001 .

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

[15]  Kim G. Larsen,et al.  Robust synthesis for real-time systems , 2014, Theor. Comput. Sci..

[16]  Kim G. Larsen,et al.  Robust Specification of Real Time Components , 2011, FORMATS.

[17]  Thomas A. Henzinger,et al.  Timed Interfaces , 2002, EMSOFT.

[18]  Luca Cardelli,et al.  A spatial logic for concurrency (part I) , 2003, Inf. Comput..

[19]  Luca Aceto,et al.  Reactive Systems: Frontmatter , 2007 .

[20]  Axel Legay,et al.  Sound Merging and Differencing for Class Diagrams , 2014, FASE.

[21]  Kim G. Larsen,et al.  Modular Markovian Logic , 2011, ICALP.

[22]  Kim Guldstrand Larsen,et al.  Specification and refinement of probabilistic processes , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[23]  Radha Jagadeesan,et al.  Metrics for labelled Markov processes , 2004, Theor. Comput. Sci..

[24]  Jean-Baptiste Raclet,et al.  Residual for Component Specifications , 2008, Electron. Notes Theor. Comput. Sci..

[25]  Axel Legay,et al.  The quantitative linear-time-branching-time spectrum , 2011, Theor. Comput. Sci..

[26]  Axel Legay,et al.  Generalized Quantitative Analysis of Metric Transition Systems , 2013, APLAS.

[27]  Bart Jacobs,et al.  A Logic for the Java Modeling Language JML , 2001, FASE.

[28]  David de Frutos-Escrig,et al.  Distances between Processes: A Pure Algebraic Approach , 2012, WADT.

[29]  Axel Legay,et al.  General quantitative specification theories with modal transition systems , 2014, Acta Informatica.

[30]  Jeannette M. Wing,et al.  A behavioral notion of subtyping , 1994, TOPL.

[31]  Ivana Cerná,et al.  Modal Transition Systems: Composition and LTL Model Checking , 2011, ATVA.

[32]  Marsha Chechik,et al.  Merging partial behavioural models , 2004, SIGSOFT '04/FSE-12.

[33]  Axel Legay,et al.  Structural Refinement for the Modal nu-Calculus , 2014, ICTAC.

[34]  Kim G. Larsen,et al.  Moving from Specifications to Contracts in Component-Based Design , 2012, FASE.

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

[36]  Axel Legay,et al.  Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory , 2013, CONCUR.

[37]  Kim G. Larsen,et al.  Extending modal transition systems with structured labels , 2012, Mathematical Structures in Computer Science.

[38]  David de Frutos-Escrig,et al.  Defining Distances for All Process Semantics , 2012, FMOODS/FORTE.

[39]  Sebastián Uchitel,et al.  Merging Partial Behaviour Models with Different Vocabularies , 2013, CONCUR.

[40]  Kim G. Larsen,et al.  Weighted modal transition systems , 2012, Formal Methods Syst. Des..

[41]  Kim G. Larsen,et al.  Equation solving using modal transition systems , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[42]  Michael Huth,et al.  Quantitative analysis and model checking , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[43]  Kim G. Larsen,et al.  Graphical Versus Logical Specifications , 1990, Theor. Comput. Sci..

[44]  Vladimiro Sassone,et al.  Structural operational semantics for stochastic and weighted transition systems , 2013, Inf. Comput..

[45]  Axel Legay,et al.  The quantitative linear-time-branching-time spectrum , 2014, Theor. Comput. Sci..

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

[47]  Kim G. Larsen,et al.  Taking It to the Limit: Approximate Reasoning for Markov Processes , 2012, MFCS.

[48]  Kim G. Larsen,et al.  On determinism in modal transition systems , 2009, Theor. Comput. Sci..

[49]  Matteo Mio.  Probabilistic Modal μ-Calculus with Independent Product , 2011, FoSSaCS.

[50]  Sophie Pinchinat,et al.  Modal Specifications for the Control Theory of Discrete Event Systems , 2007, Discret. Event Dyn. Syst..

[51]  Louis-Marie Traonouez.  A Parametric Counterexample Refinement Approach for Robust Timed Specifications , 2012, FIT.

[52]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[53]  Thomas A. Henzinger,et al.  The Embedded Systems Design Challenge , 2006, FM.

[54]  Matthew Hennessy,et al.  Acceptance trees , 1985, JACM.

[55]  Kim G. Larsen,et al.  Quantitative Refinement for Weighted Modal Transition Systems , 2011, MFCS.

[56]  James Worrell,et al.  A behavioural pseudometric for probabilistic transition systems , 2005, Theor. Comput. Sci..

[57]  Kim G. Larsen,et al.  Proof Systems for Satisfiability in Hennessy-Milner Logic with Recursion , 1990, Theor. Comput. Sci..

[58]  Thomas A. Henzinger,et al.  Model checking discounted temporal properties , 2005, Theor. Comput. Sci..