Abstract
We present a novel static analysis for inferring precise complexity bounds of imperative and recursive programs. The analysis operates on cost equations. Therefore, it permits uniform treatment of loops and recursive procedures. The analysis is able to provide precise upper bounds for programs with complex execution flow and multi-dimensional ranking functions. In a first phase, a combination of control-flow refinement and invariant generation creates a representation of the possible behaviors of a (possibly inter-procedural) program in the form of a set of execution patterns. In a second phase, a cost upper bound of each pattern is obtained by combining individual costs of code fragments. Our technique is able to detect dependencies between different pieces of code and hence to compute a precise upper bounds for a given program. A prototype has been implemented and evaluated to demonstrate the effectiveness of the approach.
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
Albert, E., Arenas, P., Genaim, S., Puebla, G.: Closed-Form Upper Bounds in Static Cost Analysis. J. of Automated Reasoning 46(2), 161–203 (2011)
Albert, E., Genaim, S., Masud, A.N.: More precise yet widely applicable cost analysis. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 38–53. Springer, Heidelberg (2011)
Alias, C., Darte, A., Feautrier, P., Gonnord, L.: Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 117–133. Springer, Heidelberg (2010)
Alonso-Blas, D.E., Arenas, P., Genaim, S.: Precise cost analysis via local reasoning. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 319–333. Springer, Heidelberg (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)
Bagnara, R., Mesnard, F., Pescetti, A., Zaffanella, E.: A new look at the automatic synthesis of linear ranking functions. Information and Computation 215, 47–67 (2012)
Brockschmidt, M., Cook, B., Fuhs, C.: Better termination proving through cooperation. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 413–429. Springer, Heidelberg (2013)
Brockschmidt, M., Emmes, F., Falke, S., Fuhs, C., Giesl, J.: Alternating runtime and size complexity analysis of integer programs. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 140–155. Springer, Heidelberg (2014)
Chen, H.Y., Mukhopadhyay, S., Lu, Z.: Control flow refinement and symbolic computation of average case bound. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 334–348. Springer, Heidelberg (2013)
Cook, B., See, A., Zuleger, F.: Ramsey vs. Lexicographic termination proving. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 47–61. Springer, Heidelberg (2013)
Flores-Montoya, A., Hähnle, R.: Resource analysis of complex programs with cost equations. Technical report, TU Darmstadt (2014), https://www.se.tu-darmstadt.de/fileadmin/user_upload/Group_SE/Page_Content/Group_Members/Antonio_Flores-Montoya/APLAS14techReport.pdf
Gulavani, B.S., Gulwani, S.: A numerical abstract domain based on expression abstraction and max operator with application in timing analysis. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 370–384. Springer, Heidelberg (2008)
Gulwani, S., Jain, S., Koskinen, E.: Control-flow refinement and progress invariants for bound analysis. In: PLDI (2009)
Gulwani, S., Mehra, K.K., Chilimbi, T.: Speed: Precise and efficient static estimation of program computational complexity. In: POPL, pp. 127–139. ACM, New York (2009)
Gulwani, S., Zuleger, F.: The reachability-bound problem. In: PLDI 2010, pp. 292–304. ACM, New York (2010)
Podelski, A., Rybalchenko, A.: A Complete Method for the Synthesis of Linear Ranking Functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 239–251. Springer, Heidelberg (2004)
Sinn, M., Zuleger, F., Veith, H.: A simple and scalable static analysis for bound analysis and amortized complexity analysis. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 745–761. Springer, Heidelberg (2014)
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
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Flores-Montoya, A., Hähnle, R. (2014). Resource Analysis of Complex Programs with Cost Equations. In: Garrigue, J. (eds) Programming Languages and Systems. APLAS 2014. Lecture Notes in Computer Science, vol 8858. Springer, Cham. https://doi.org/10.1007/978-3-319-12736-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-12736-1_15
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12735-4
Online ISBN: 978-3-319-12736-1
eBook Packages: Computer ScienceComputer Science (R0)