Abstract
The COSTA system infers resource consumption bounds from Java bytecode using an internal recurrence solver PUBS. This paper suggests an improvement of the COSTA system, such that it can solve a larger number of recurrences. The idea is to replace one of its static analyses, the ranking function analysis, by another kind of analysis, height analysis, in such a way that polynomial bounds of any degree may be inferred instead of just linear expressions. The work can be seen as an application of some polynomial interpolation techniques used by some of the authors in prior analyses. Finding a way to choose proper test nodes is the key to the solution presented in this paper.
This work was partly funded by the EU Artemis Joint Undertaking in the CHARTER project, grant-nr. 100039, and by Spanish FPU grant AP2006-02154 and projects TIN2008-06622-C03-01 (STAMP), S2009/TIC-1465 (PROMETIDOS).
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References
Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: COSTA: Design and Implementation of a Cost and Termination Analyzer for Java Bytecode. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2007. LNCS, vol. 5382, pp. 113–132. Springer, Heidelberg (2008)
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., Genaim, S., Gómez-Zamalloa, M.: Parametric inference of memory requirements for garbage collected languages. In: Vitek, J., Lea, D. (eds.) ISMM, pp. 121–130. ACM (2010)
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)
Bagnara, R., Zaccagnini, A., Zolo, T.: The automatic solution of recurrence relations. I. Linear recurrences of finite order with constant coefficients. Quaderno 334, Dipartimento di Matematica, Università di Parma, Italy (2003), http://www.cs.unipr.it/Publications/
Bagnara, R., Ricci, E., Zaffanella, E., Hill, P.M.: Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 213–229. Springer, Heidelberg (2002)
Brown, C.W.: QEPCAD: Quantifier Elimination by Partial Cylindrical Algebraic Decomposition (2004), http://www.cs.usna.edu/qepcad/B/QEPCAD.html
Chui, C.K., Lai, M.J.: Vandermonde determinants and lagrange interpolation in R s. In: Nonlinear and Convex Analysis, Proceedings in Honor of Ky Fan, pp. 23–35. Marcel Dekker Inc., N.Y. (1987)
Collins, G.E.: Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)
Cooper, D.C.: Theorem proving in arithmetic without multiplication. Machine Intelligence 7, 91–100 (1972)
Dolzmann, A., Sturm, T.: Redlog user manual. Tech. Rep. MIP-9905, FMI, Universität Passau, edition 2.0 for Version 2.0 (1999)
van Eekelen, M., Shkaravska, O., van Kesteren, R., Jacobs, B., Poll, E., Smetsers, S.: AHA: Amortized Heap space usage Analysis. In: Morazán, M. (ed.) Selected Revised Papers of the 8th International Symposium on Trends in Functional Programming (TFP 2007), pp. 36–53. Intellect, New York (2007)
Hearn, A.C.: REDUCE. User’s Manual. Version 3.8 (2004)
Hoffmann, J., Hofmann, M.: Amortized Resource Analysis with Polynomial Potential. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 287–306. Springer, Heidelberg (2010)
Hoffmann, J., Aehlig, K., Hofmann, M.: Multivariate amortized resource analysis. In: Ball, T., Sagiv, M. (eds.) POPL, pp. 357–370. ACM (2011)
Hofmann, M., Jost, S.: Static prediction of heap space usage for first-order functional programs. In: Proc. 30th ACM Symp. on Principles of Programming Languages, POPL 2003, pp. 185–197. ACM Press (2003)
van Kesteren, R., Shkaravska, O., van Eekelen, M.: Inferring static non-monotonically sized types through testing. In: Proceedings of 16th International Workshop on Functional and (Constraint) Logic Programming (WFLP 2007), Paris, France. ENTCS, vol. 216C, pp. 45–63 (2007)
Lucas, S.: Polynomials over the reals in proofs of termination: from theory to practice. RAIRO Theoretical Informatics and Applications 39(3), 547–586 (2005)
Nipkow, T.: Linear quantifier elimination. J. Autom. Reasoning 45(2), 189–212 (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)
Shkaravska, O., van Eekelen, M., van Kesteren, R.: Polynomial size analysis of first-order shapely functions. Logical Methods in Computer Science 5(2:10), 1–35 (2009); selected Papers from TLCA 2007
Shkaravska, O., van Eekelen, M., Tamalet, A.: Collected Size Semantics for Functional Programs over Lists. In: Scholz, S.-B., Chitil, O. (eds.) IFL 2008. LNCS, vol. 5836, pp. 118–137. Springer, Heidelberg (2011)
Shkaravska, O., van Eekelen, M.C.J.D., van Kesteren, R.: Polynomial size analysis of first-order shapely functions. Logical Methods in Computer Science 5(2) (2009)
Shkaravska, O., Kersten, R., van Eekelen, M.: Test-based inference of polynomial loop-bound functions. In: Proceedings of the 8th International Conference on the Principles and Practice of Programming in Java, PPPJ 2010. ACM (2010)
Tamalet, A., Shkaravska, O., van Eekelen, M.: Size analysis of algebraic data types. In: Achten, P., Koopman, P., Morazán, M.T. (eds.) Selected Revised Papers of the 9th International Symposium on Trends in Functional Programming (TFP 2008), pp. 33–48. Intellect (2009)
Tarski, A.: A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley (1948)
Wegbreit, B.: Mechanical program analysis. Commun. ACM 18(9), 528–539 (1975)
Weispfenning, V.: The complexity of linear problems in fields. J. Symb. Comput. 5(1/2), 3–27 (1988)
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Montenegro, M., Shkaravska, O., van Eekelen, M., Peña, R. (2012). Interpolation-Based Height Analysis for Improving a Recurrence Solver. In: Peña, R., van Eekelen, M., Shkaravska, O. (eds) Foundational and Practical Aspects of Resource Analysis. FOPARA 2011. Lecture Notes in Computer Science, vol 7177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32495-6_3
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DOI: https://doi.org/10.1007/978-3-642-32495-6_3
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