Abstract
The usual high degree of assurance in safety-critical systems is being challenged by a new incarnation of distributed systems exposed to the presence of hierarchical computation (e.g., virtualization resources such as container and virtual machine technology). This paper addresses the issue of symbolically specifying and verifying properties of distributed hierarchical systems using rewriting modulo SMT, a symbolic approach for rewriting logic that seamlessly combines rewriting modulo theories, SMT solving, and model checking. It presents a rewrite theory \(\mathcal {R}\) implementing a symbolic executable semantics of an algebraic model of spatially constrained concurrent process with extrusion. The underlying constraint system in \(\mathcal {R}\) is materialized with the help of SMT-solving technology, where the constraints are quantifier-free formulas interpreted over the Booleans and integers, and information entailment is queried via semantic inference. Symbolic rewrite steps with \(\rightarrow _\mathcal {R}\) capture all possible traces from ground instances of the source state to the ground instances of the target state. This approach, as illustrated with some examples in the paper, is well-suited for specifying and proving (or disproving) existential reachability properties of distributed hierarchical systems, such as fault-tolerance, consistency, and privacy.
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References
Agha, G., Meseguer, J., Sen, K.: PMaude: rewrite-based specification language for probabilistic object systems. Electron. Notes Theor. Comput. Sci. 153(2), 213–239 (2006)
Barco, A., Knight, S., Valencia, F.D.: K-Stores: a spatial and epistemic concurrent constraint interpreter. In: 21st Workshop on Functional and Constraint Logic Programming (WFLP2012), Nagoya, Japan. Informal Proceedings (2012)
Barrett, C., Conway, C.L., Deters, M., Hadarean, L., Jovanović, D., King, T., Reynolds, A., Tinelli, C.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171–177. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_14
Braga, C., Meseguer, J.: Modular rewriting semantics in practice. Electron. Notes Theor. Comput. Sci. 117, 393–416 (2005)
Bruni, R., Meseguer, J.: Semantic foundations for generalized rewrite theories. Theor. Comput. Sci. 360(1–3), 386–414 (2006)
Caccamo, M., Buttazzo, G., Sha, L.: Capacity sharing for overrun control. In: 21st IEEE Real-Time Systems Symposium, pp. 295–304. IEEE (2000)
Clavel, M. (ed.): All about Maude - a High-Performance Logical Framework: How to Specify, Program, and Verify Systems in Rewriting Logic. Lecture Notes in Computer Science, vol. 4350. Springer, Berlin (2007). https://doi.org/10.1007/978-3-540-71999-1
Degano, P., Gadducci, F., Priami, C.: A causal semantics for CCS via rewriting logic. Theor. Comput. Sci. 275(1–2), 259–282 (2002)
Durán, F., Rocha, C., Álvarez, J.M.: Towards a Maude formal environment. In: Agha, G., Danvy, O., Meseguer, J. (eds.) Formal Modeling: Actors, Open Systems, Biological Systems. LNCS, vol. 7000, pp. 329–351. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24933-4_17
Dutertre, B.: Yices 2.2. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 737–744. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_49
Estlin, T., Jonsson, A., Pasareanu, C., Simmons, R., Tso, K., Verma, V.: Plan execution interchange language (PLEXIL). Technical report TM-2006-213483, NASA, April 2006
Gutiérrez, R., Meseguer, J., Rocha, C.: Order-sorted equality enrichments modulo axioms. Sci. Comput. Program. 99, 235–261 (2015)
Guzmán, M., Haar, S., Perchy, S., Rueda, C., Valencia, F.D.: Belief, knowledge, lies and other utterances in an algebra for space and extrusion. J. Log. Algebr. Methods Program. 86(1), 107–133 (2017)
Guzmán, M., Valencia, F.D., Herbstritt, M.: On the expressiveness of spatial constraint systems. Technical report, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany (2016)
Knight, S., Palamidessi, C., Panangaden, P., Valencia, F.D.: Spatial and epistemic modalities in constraint-based process calculi. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 317–332. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32940-1_23
Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992)
Meseguer, J., Roşu, G.: The rewriting logic semantics project: a progress report. Inf. Comput. 231, 38–69 (2013)
Ölveczky, P., Meseguer, J.: Real-time maude: a tool for simulating and analyzing real-time and hybrid systems. Electron. Notes Theor. Comput. Sci. 36, 361–382 (2000)
Rocha, C., Meseguer, J., Muñoz, C.: Rewriting modulo SMT and open system analysis. J. Log. Algebr. Methods Program. 86(1), 269–297 (2017)
Romero, M.: Una semántica ejecutable en lógica de reescritura para programación espacial concurrente por restricciones (SCCP). Trabajo de grado 001/522, Escuela Colombiana de Ingenieria Julio Garavito, Bogotá, Colombia, January 2017
Romero, M., Rocha, C.: Reachability analysis for spatial concurrent constraint systems with extrusion (2017). http://camilorocha.info/publications
Saraswat, V.: Concurrent Constraint Programming. Logic programming. MIT Press, Cambridge (1993)
Verdejo, A., Martí-Oliet, N.: Two case studies of semantics execution in Maude: CCS and LOTOS. Formal Methods Syst. Des. 27(1–2), 113–172 (2005)
Viry, P.: Equational rules for rewriting logic. Theor. Comput. Sci. 285(2), 487–517 (2002)
Acknowledgments
The authors would like to thank C. Rueda and F. Valencia for the fruitful discussions on these ideas, and the anonymous referees for their comments that helped in improving the paper. The first author was partially supported by Colciencias’ Convocatoria 761 Jóvenes Investigadores e Innovadores 2016.
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Romero, M., Rocha, C. (2018). Symbolic Execution and Reachability Analysis Using Rewriting Modulo SMT for Spatial Concurrent Constraint Systems with Extrusion. In: Dutle, A., Muñoz, C., Narkawicz, A. (eds) NASA Formal Methods. NFM 2018. Lecture Notes in Computer Science(), vol 10811. Springer, Cham. https://doi.org/10.1007/978-3-319-77935-5_29
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