Abstract
We review Wilhelm’s work on WCET for hard real-time applications and also recent work on analysis of soft-real time systems using probabilistic methods. We then present Probabilistic Abstract Interpretation (PAI) as a quantitative variation of the classical approach; PAI aims to provide close approximations – this should be contrasted to the safe approximations studied in the standard setting. We discuss the relation between PAI and classical Abstract Interpretation as well as average case analysis.
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References
Wilhelm, R.: Timing analysis and timing predictability. In: de Boer, F.S., et al. (eds.) FMCO 2004. LNCS, vol. 3657, pp. 317–323. Springer, Heidelberg (2005)
Shaw, A.: Reasoning about time in higher-level language software. IEEE Transactions on Software Engineering 15, 875–889 (1989)
Lundquist, T., Stenström, P.: Timing anomalies in dynamically scheduled microprocessors. In: 20th IEEE Real-Time Systems Symposium (1999)
Balbo, G.: Introduction to stochastic Petri nets. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) EEF School 2000 and FMPA 2000. LNCS, vol. 2090, pp. 84–155. Springer, Heidelberg (2001)
Bause, F., Kritzinger, P.S.: Stochastic Petri Nets – An Introduction to the Theory, 2nd edn. Vieweg Verlag, Wiesbaden (2002)
Plateau, B., Atif, K.: Stochastic automata network of modeling parallel systems. IEEE Transactions on Software Engineering 17, 1093–1108 (1991)
Norman, G., et al.: Formal analysis and validation of continuous time Markov chain based system level power management strategies. In: Rosenstiel, W. (ed.) Proc. 7th Annual IEEE International Workshop on High Level Design Validation and Test (HLDVT’02), pp. 45–50. IEEE Computer Society Press, Los Alamitos (2002)
Di Pierro, A., Wiklicky, H.: Concurrent Constraint Programming: Towards Probabilistic Abstract Interpretation. In: Gabbrielli, M., Pfenning, F. (eds.) Proceedings of PPDP’00 – Priciples and Practice of Declarative Programming, Montréal, Canada, ACM SIGPLAN, pp. 127–138. Association of Computing Machinery (2000)
Cousot, P., Cousot, R.: Abstract Interpretation and Applications to Logic Programs. Journal of Logic Programming 13, 103–180 (1992)
Abramsky, S., Hankin, C. (eds.): Abstract Interpretation of Declarative Languages. Ellis-Horwood, Chichester (1987)
Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Heidelberg (1999)
Di Pierro, A., Wiklicky, H.: Measuring the precision of abstract interpretations. In: Lau, K.-K. (ed.) LOPSTR 2000. LNCS, vol. 2042, pp. 147–164. Springer, Heidelberg (2001)
Monniaux, D.: Abstract interpretation of probabilistic semantics. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, Springer, Heidelberg (2000)
Monniaux, D.: Abstract interpretation of probabilistic semantics. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, pp. 322–339. Springer, Heidelberg (2000)
Eaton, J.: Gnu Octave Manual (2002), http://www.octave.org
Cousot, P., Cousot, R.: Systematic Design of Program Analysis Frameworks. In: Symposium on Principles of Programming Languages (POPL), San Antonio, Texas, pp. 269–282 (1979)
Deutsch, F.: Bet Approximation in Inner Product Spaces. CMS Books in Mathematics, vol. 7. Springer, New York (2001)
Ben-Israel, A., Greville, T.: Generalised Inverses — Theory and Applications, 2nd edn. CMS Books in Mathematics, vol. 15. Springer, New York (2003)
Di Pierro, A., Hankin, C., Wiklicky, H.: Probabilistic chemical abstract machine and the expressiveness of linda languages. In: de Boer, F.S., et al. (eds.) FMCO 2005. LNCS, vol. 4111, pp. 388–407. Springer, Heidelberg (2006)
Di Pierro, A., Hankin, C., Wiklicky, H.: Quantitative static analysis of distributed systems. Journal of Functional Programming 15, 1–47 (2005)
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Di Pierro, A., Hankin, C., Wiklicky, H. (2007). Abstract Interpretation for Worst and Average Case Analysis. In: Reps, T., Sagiv, M., Bauer, J. (eds) Program Analysis and Compilation, Theory and Practice. Lecture Notes in Computer Science, vol 4444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71322-7_8
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DOI: https://doi.org/10.1007/978-3-540-71322-7_8
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