Abstract
The classical approach to static cost analysis is based on first transforming a given program into a set of cost relations, and then solving them into closed-form upper-bounds. The quality of the upper-bounds and the scalability of such cost analysis highly depend on the precision and efficiency of the solving phase. Several techniques for solving cost relations exist, some are efficient but not precise enough, and some are very precise but do not scale to large cost relations. In this paper we explore the gap between these techniques, seeking for ones that are both precise and efficient. In particular, we propose a novel technique that first splits the cost relation into several atomic ones, and then uses precise local reasoning for some and less precise but efficient reasoning for others. For the precise local reasoning, we propose several methods that define the cost as a solution of a universally quantified formula. Preliminary experiments demonstrate the effectiveness of our approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Companion Web-Page, http://costa.ls.fi.upm.es/amor/
Albert, E., Alonso, D., Arenas, P., Genaim, S., Puebla, G.: Asymptotic Resource Usage Bounds. In: Hu, Z. (ed.) APLAS 2009. LNCS, vol. 5904, pp. 294–310. Springer, Heidelberg (2009)
Albert, E., Arenas, P., Genaim, S., Puebla, G.: Closed-Form Upper Bounds in Static Cost Analysis. J. Autom. Reasoning 46(2), 161–203 (2011)
Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost Analysis of Object-Oriented Bytecode Programs. Theor. Comput. Sci. 413(1), 142–159 (2012)
Albert, E., Genaim, S., Masud, A.N.: On the Inference of Resource Usage Upper and Lower Bounds. ACM Trans. Comput. Log. (to appear, 2013)
Alonso-Blas, D.E., Genaim, S.: On the Limits of the Classical Approach to Cost Analysis. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 405–421. Springer, Heidelberg (2012)
Anderson, H., Khoo, S.-C., Andrei, Ş., Luca, B.: Calculating Polynomial Runtime Properties. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 230–246. Springer, Heidelberg (2005)
Bagnara, R., Mesnard, F., Pescetti, A., Zaffanella, E.: A new look at the automatic synthesis of linear ranking functions. Inf. Comput. 215, 47–67 (2012)
Benzinger, R.: Automated higher-order complexity analysis. Theor. Comput. Sci. 318(1-2), 79–103 (2004)
Danner, N., Paykin, J., Royer, J.S.: A Static Cost Analysis for a Higher-Order Language. In: PLPV, pp. 25–34. ACM (2013)
Debray, S.K., Lin, N.: Cost Analysis of Logic Programs. ACM Trans. Program. Lang. Syst. 15(5), 826–875 (1993)
Grobauer, B.: Cost Recurrences for DML Programs. In: ICFP, pp. 253–264. ACM (2001)
Gulwani, S., Mehra, J.K., Chilimbi, T.M.: SPEED: Precise and Efficient Static Estimation of Program Computational Complexity. In: POPL, pp. 127–139. ACM (2009)
Gulwani, S., Zuleger, F.: The Reachability-Bound Problem. In: PLDI, pp. 292–304. ACM (2010)
Hoffmann, J., Aehlig, a.K., Hofmannn, M.: Multivariate Amortized Resource Analysis. ACM Trans. Program. Lang. Syst. 34(3), 14:1–14:62 (2012)
Simões, H.R., Vasconcelos, P.B., Florido, M., Jost, S., Hammond, K.: Automatic Amortised Analysis of Dynamic Memory Allocation for Lazy Functional Programs. In: ICFP, pp. 165–176. ACM (2012)
Vasconcelos, P.B., Hammond, K.: Inferring Cost Equations for Recursive, Polymorphic and Higher-Order Functional Programs. In: Trinder, P., Michaelson, G.J., Peña, R. (eds.) IFL 2003. LNCS, vol. 3145, pp. 86–101. Springer, Heidelberg (2004)
Wegbreit, B.: Mechanical Program Analysis. Commun. ACM 18(9), 528–539 (1975)
Zuleger, F., Gulwani, S., Sinn, M., Veith, H.: Bound Analysis of Imperative Programs with the Size-Change Abstraction. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 280–297. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Alonso-Blas, D.E., Arenas, P., Genaim, S. (2013). Precise Cost Analysis via Local Reasoning. In: Van Hung, D., Ogawa, M. (eds) Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, vol 8172. Springer, Cham. https://doi.org/10.1007/978-3-319-02444-8_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-02444-8_23
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02443-1
Online ISBN: 978-3-319-02444-8
eBook Packages: Computer ScienceComputer Science (R0)