Abstract
We define and study a quantitative generalization of the traditional boolean framework of model-based specification and verification. In our setting, propositions have integer values at states, and properties have integer values on traces. For example, the value of a quantitative proposition at a state may represent power consumed at the state, and the value of a quantitative property on a trace may represent energy used along the trace. The value of a quantitative property at a state, then, is the maximum (or minimum) value achievable over all possible traces from the state. In this framework, model checking can be used to compute, for example, the minimum battery capacity necessary for achieving a given objective, or the maximal achievable lifetime of a system with a given initial battery capacity. In the case of open systems, these problems require the solution of games with integer values.
Quantitative model checking and game solving is undecidable, except if bounds on the computation can be found. Indeed, many interesting quantitative properties, like minimal necessary battery capacity and maximal achievable lifetime, can be naturally specified by quantitative-bound automata, which are finite automata with integer registers whose analysis is constrained by a bound function f that maps each system K to an integer f(K). Along with the linear-time, automaton-based view of quantitative verification, we present a corresponding branching-time view based on a quantitative-bound μ-calculus, and we study the relationship, expressive power, and complexity of both views.
Chapter PDF
Similar content being viewed by others
References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49, 672–713 (2002)
Bianco, A., de Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Bouyer, P., Petit, A., Thérien, D.: An algebraic approach to data languages and timed languages. Information & Computation 182, 137–162 (2003)
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. Information & Computation 98, 142–170 (1992)
Chakrabarti, A., de Alfaro, L., Henzinger, T.A., Stoelinga, M.: Resource interfaces. In: Alur, R., Lee, I. (eds.) EMSOFT 2003. LNCS, vol. 2855, pp. 117–133. Springer, Heidelberg (2003)
Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)
Dam, M.: CTL* and ECTL* as fragments of the modal μ-calculus. Theoretical Computer Science 126, 77–96 (1994)
de Alfaro, L., Henzinger, T.A., Majumdar, R.: From verification to control: Dynamic programs for ω-regular objectives. In: LICS, pp. 279–290. IEEE, Los Alamitos (2001)
de Alfaro, L., Majumdar, R.: Quantitative solution of concurrent games. J. Computer & Systems Sciences 68, 374–397 (2004)
Emerson, E.A., Lei, C.: Efficient model checking in fragments of the propositional μ-calculus. In: LICS, pp. 267–278. IEEE, Los Alamitos (1986)
Holzmann, G.J.: Design and Validation of Computer Protocols. Prentice-Hall, Englewood Cliffs (1991)
Huth, M., Kwiatkowska, M.: Quantitative analysis and model checking. In: LICS, pp. 111–122. IEEE, Los Alamitos (1997)
Ibarra, O.H., Su, J., Dang, Z., Bultan, T., Kemmerer, R.A.: Counter machines: Decidable properties and applications to verification problems. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 426–435. Springer, Heidelberg (2000)
Kozen, D.: Results on the propositional μ-calculus. Theoretical Computer Science 27, 333–354 (1983)
McIver, A., Morgan, C.: Games, probability, and the quantitative μ-calculus. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 292–310. Springer, Heidelberg (2002)
Vardi, M.Y.: A temporal fixpoint calculus. In: POPL, pp. 250–259. ACM, New York (1988)
Xie, G., Dang, Z., Ibarra, O.H., Pietro, P.S.: Dense counter machines and verification problems. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 93–105. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chakrabarti, A., Chatterjee, K., Henzinger, T.A., Kupferman, O., Majumdar, R. (2005). Verifying Quantitative Properties Using Bound Functions. In: Borrione, D., Paul, W. (eds) Correct Hardware Design and Verification Methods. CHARME 2005. Lecture Notes in Computer Science, vol 3725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11560548_7
Download citation
DOI: https://doi.org/10.1007/11560548_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29105-3
Online ISBN: 978-3-540-32030-2
eBook Packages: Computer ScienceComputer Science (R0)Springer Nature Proceedings Computer Science
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.