Functional and Logic Programming
DOI: 10.1007/978-3-540-78969-7_11
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Complexity Analysis by Rewriting

Abstract: Abstract. In this paper we introduce a restrictive version of the multiset path order, called polynomial path order. This recursive path order induces polynomial bounds on the maximal number of innermost rewrite steps. This result opens the way to automatically verify for a given program, written in an eager functional programming language, that the maximal number of evaluation steps starting from any function call is polynomial in the input size. To test the feasibility of our approach we have implemented thi… Show more

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Cited by 23 publications
(57 citation statements)
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“…]), so to bound the actual cost of the computation with an ad hoc combination of these two dimensions. In other cases [3,9], results about the derivational complexity of TRS are kept distinct from other results about actual computation time. This body of research has been the main motivation for our work.…”
Section: Consequences For Complexity Analysismentioning
confidence: 70%
“…]), so to bound the actual cost of the computation with an ad hoc combination of these two dimensions. In other cases [3,9], results about the derivational complexity of TRS are kept distinct from other results about actual computation time. This body of research has been the main motivation for our work.…”
Section: Consequences For Complexity Analysismentioning
confidence: 70%
“…The polynomial path order (POP* for short) [4] is defined to be compatible with predicative recursion: f (s(x), y; z) > pop * h(x, y; z, f (x, y; z)). It is worth noting that predicative recursion does not make sense with the usual composition since argument positions can be shifted from left to right.…”
Section: Related Workmentioning
confidence: 99%
“…The definition of PLPO is strongly motivated by path orders based on the normal/safe argument separation [4,5,6]. On one hand, due to allowance of multiset comparison in the polynomial path order POP* [4], PLPO and POP* are incomparable.…”
Section: Comparison To Related Path Orders and Limitations Of Predicamentioning
confidence: 99%
See 1 more Smart Citation
“…No further termination methods that induce at most polynomial derivational complexities for TRSs have previously been known. In particular related work on implicit complexity (for example [17,18,19,20,21]) does not provide methods that induce polynomial derivational complexities, even if sometimes the derivation length can be bounded polynomially, if the set of start terms is suitably restricted. Finally cdi + denotes our standard strategy: First, we search for a strongly linear interpretation.…”
mentioning
confidence: 99%