Abstract
In this paper we present a simple technique for analysing the runtime complexity of rewrite systems. In complexity analysis many techniques are based on reduction orders. We show how the monotonicity condition for orders can be weakened by using the notion of context-sensitive rewriting. The presented technique is very easy to implement, even in a modular setting, and has been integrated in the Tyrolean Complexity Tool. We provide ample experimental data for assessing the viability of our method.
This research is partly supported by JSPS KAKENHI Grant Number 25730004 and FWF (Austrian Science Fund) project I 963-N15.
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
Bonfante, G., Cichon, A., Marion, J.Y., Touzet, H.: Algorithms with polynomial interpretation termination proof. JFP 11(1), 33–53 (2001)
Middeldorp, A., Moser, G., Neurauter, F., Waldmann, J., Zankl, H.: Joint spectral radius theory for automated complexity analysis of rewrite systems. In: Winkler, F. (ed.) CAI 2011. LNCS, vol. 6742, pp. 1–20. Springer, Heidelberg (2011)
Avanzini, M., Moser, G.: Polynomial path orders. LMCS 9(4) (2013)
Hirokawa, N., Moser, G.: Automated complexity analysis based on the dependency pair method. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 364–379. Springer, Heidelberg (2008)
Noschinski, L., Emmes, F., Giesl, J.: Analyzing innermost runtime complexity of term rewriting by dependency pairs. JAR 51(1), 27–56 (2013)
Zankl, H., Korp, M.: Modular complexity analysis via relative complexity. LMCS 10(1:19), 1–33 (2014)
Avanzini, M., Moser, G.: A combination framework for complexity. In: Proc. 24th RTA. LIPIcs, vol. 21, pp. 55–70 (2013)
Moser, G.: Proof Theory at Work: Complexity Analysis of Term Rewrite Systems. CoRR abs/0907.5527 (2009) Habilitation Thesis.
Baillot, P., Marion, J.Y., Rocca, S.R.D.: Guest editorial: Special issue on implicit computational complexity. TOCL 10(4) (2009)
Avanzini, M., Moser, G.: Closing the gap between runtime complexity and polytime computability. In: Proc. 21st RTA. LIPIcs, vol. 6, pp. 33–48 (2010)
Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical Report AIB-2001-09, RWTH Aachen (2001)
Hofbauer, D., Lautemann, C.: Termination proofs and the length of derivations. In: Dershowitz, N. (ed.) RTA 1989. LNCS, vol. 355, pp. 167–177. Springer, Heidelberg (1989)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)
Choppy, C., Kaplan, S., Soria, M.: Complexity analysis of term-rewriting systems. TCS 67(2-3), 261–282 (1989)
TeReSe: Term Rewriting Systems. Cambridge Tracks in Theoretical Computer Science, vol. 55. Cambridge University Press (2003)
Lucas, S.: Context-sensitive rewriting strategies. IC 178(1), 294–343 (2002)
Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. JAR 40(3), 195–220 (2008)
Hofbauer, D., Waldmann, J.: Termination of string rewriting with matrix interpretations. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 328–342. Springer, Heidelberg (2006)
Neurauter, F., Zankl, H., Middeldorp, A.: Revisiting matrix interpretations for polynomial derivational complexity of term rewriting. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 550–564. Springer, Heidelberg (2010)
Waldmann, J.: Polynomially bounded matrix interpretations. In: Proc. 21st RTA. LIPIcs, vol. 6, pp. 357–372 (2010)
Steinbach, J., Kühler, U.: Check your ordering – termination proofs and open problems. Technical Report SR-90-25, Universität Kaiserslautern (1990)
Fernández, M.L.: Relaxing monotonicity for innermost termination. Information Processing Letters 93(1), 117–123 (2005)
Avanzini, M.: Verifying Polytime Computability Automatically. PhD thesis, University of Innsbruck (2013)
Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 216–231. Springer, Heidelberg (2005)
Avanzini, M., Moser, G.: Tyrolean Complexity Tool: Features and usage. In: Proc. 24th RTA. LIPIcs, vol. 21, pp. 71–80 (2013)
Moser, G., Schnabl, A., Waldmann, J.: Complexity analysis of term rewriting based on matrix and context dependent interpretations. In: Proc. 28th FSTTCS. LIPIcs, vol. 2, pp. 304–315 (2008)
Alarcón, B., Gutiérrez, R., Lucas, S.: Context-sensitive dependency pairs. IC 208(8), 922–968 (2010)
Hoffmann, J., Aehlig, K., Hofmann, M.: Resource aware ML. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 781–786. Springer, Heidelberg (2012)
Hofmann, M., Moser, G.: Amortised resource analysis and typed polynomial interpretations. In: Dowek, G. (ed.) RTA-TLCA 2014. LNCS, vol. 8560, pp. 272–287. Springer, Heidelberg (2014)
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
Hirokawa, N., Moser, G. (2014). Automated Complexity Analysis Based on Context-Sensitive Rewriting. In: Dowek, G. (eds) Rewriting and Typed Lambda Calculi. RTA TLCA 2014 2014. Lecture Notes in Computer Science, vol 8560. Springer, Cham. https://doi.org/10.1007/978-3-319-08918-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-08918-8_18
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08917-1
Online ISBN: 978-3-319-08918-8
eBook Packages: Computer ScienceComputer Science (R0)