Proceedings of the 13 ESSLLI Student Session - Multiple Choices ...

POP ∗ . Our automation works by a reduction to SAT and employing a state-of-the-art
SAT-solver. To our best knowledge, this is the first SAT encoding of recursive path orders
with finite semantic labeling. The experimental results confirm the feasibility of our approach.
Moreover, they demonstrate that by semantic labeling we significantly increase
the power of POP ∗ .
Our research seems also comparable to (Bonfante, Marion and Pchoux, 2007), where
recursive path orders together with strongly linear polynomial quasi-interpretations are
employed in the complexity analysis. However, this method relies on caching techniques
to achieve polytime computability. Opposite to this, we only demand an eager evaluation
strategy.
In future work we will strengthen the applicability of our methods. Currently we investigate
in the integration of POP ∗ into the dependency pair framework for an automatic
complexity analysis as proposed in (Hirokawa and Moser, 2008). As this framework allows
the use of argument filterings (Kusakari, Nakamura and Toyama, 1999) and usable
rules (Arts and Giesl, 2000), we expect a significant increase in the ability to automatically
verify polynomial runtime complexities.
Finally we want to mention another exciting field of application. There is a long interest
in the functional programming community to automatically verify complexity properties
of programs. For brevity we just mention (Rosendahl, 1989; Anderson, Khoo,
Andrei and Luca, 2005; Bonfante et al., 2007). Rewriting naturally models the evaluation
of functional programs, and termination behavior of functional programs via transformations
to rewrite systems has been extensively studied. For instance, one recent approach is
described in (Giesl, Swiderski, Schneider-Kamp and Thiemann, 2006) where Haskell programs
are covered. In joint work with Hirokawa, Middeldorp and Moser (Avanzini, Hirokawa,
Middeldorp and Moser, 2007) we propose a translation from (a subset of higherorder)
Scheme programs to term rewrite systems. The transformation is designed to be
complexity preserving and thus allows the study of the complexity of a Scheme program
P by the analysis of the transformed rewrite system R. Hence from compatibility of R
with POP ∗ we can directly conclude that the number of evaluation steps of the Scheme
program P is polynomially bounded with respect to the input sizes. All necessary steps
can be performed mechanically and thus we arrive at a completely automatic complexity
analysis for Scheme, and eagerly evaluated functional programs in general.
References
Proceedings of the 13 th ESSLLI Student Session
Anderson, H., Khoo, S.-C., Andrei, S. and Luca, B. (2005). Calculating polynomial
runtime properties, Proc. 3th APLAS, pp. 230–246.
Arts, T. and Giesl, J. (2000). Termination of term rewriting using dependency pairs, TCS
236(1-2): 133–178.
Avanzini, M., Hirokawa, N., Middeldorp, A. and Moser, G. (2007). Proving termination
of scheme programs by rewriting. Draft 6 .
Avanzini, M. and Moser, G. (2008). Complexity analysis by rewriting, Proc. 9th FLOPS,
Vol. 4989 of LICS, pp. 130–146.
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