Filters








62,159 Hits in 7.1 sec

Complexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations

Georg Moser, Andreas Schnabl, Johannes Waldmann, Marc Herbstritt
2008 Foundations of Software Technology and Theoretical Computer Science  
of context dependent interpretations and restricted triangular matrix interpretations.  ...  In this spirit we investigate two instances of the interpretation method: matrix interpretations and context dependent interpretations.  ...  The parameter changes in the course of evaluating a term, which makes the interpretation dependent on the context.  ... 
doi:10.4230/lipics.fsttcs.2008.1762 dblp:conf/fsttcs/MoserSW08 fatcat:ntpolclienacfphg7qdc2hptya

Automated Complexity Analysis Based on Context-Sensitive Rewriting [chapter]

Nao Hirokawa, Georg Moser
2014 Lecture Notes in Computer Science  
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.  ...  The presented technique is very easy to implement, even in a modular setting, and has been integrated in the Tyrolean Complexity Tool.  ...  Runtime Complexity Analysis Based on Matrix Interpretations We assume familiarity with term rewriting [13, 15] but briefly review basic concepts and notations from term rewriting, context-sensitive rewriting  ... 
doi:10.1007/978-3-319-08918-8_18 fatcat:lucrfr6ie5eetejh3f3gir3qka

Algebraic semantics and complexity of term rewriting systems [chapter]

Tohru Naoi, Yasuyoshi Inagaki
1989 Lecture Notes in Computer Science  
Complexity analysis of term rewriting based on matrix and context dependent interpretations.  ...  Proving and disproving termination of higher-order functions. Tyrolean termination tool: Techniques and features. Automated complexity analysis based on the dependency pair method.  ... 
doi:10.1007/3-540-51081-8_116 fatcat:h6mrdpx6hjem5fld2pridooqdq

Towards the Certification of Complexity Proofs [article]

René Thiemann
2012 arXiv   pre-print
We report on our formalization of matrix-interpretation in Isabelle/HOL. Matrices are required to certify termination proofs and we wish to utilize them for complexity proofs, too.  ...  For the latter aim, only basic methods have already been integrated, and we discuss some upcoming problems which arise when formalizing more complicated results on matrix-interpretations, which are based  ...  To this end, we will shortly recapitulate some theory on term rewriting and matrix interpretations in Sec. 2.  ... 
arXiv:1208.1609v1 fatcat:wvir2f2emrdvbd73ydlnqmblye

Automated Complexity Analysis Based on the Dependency Pair Method [article]

Nao Hirokawa, Georg Moser
2011 arXiv   pre-print
This article is concerned with automated complexity analysis of term rewrite systems.  ...  Among other results, we present a variant of the dependency pair method for analysing runtime complexities of term rewrite systems automatically.  ...  We define runtime complexity and a subclass of matrix interpretations for its analysis in Section 3. In Section 4 we relate context-sensitive rewriting to runtime complexity.  ... 
arXiv:1102.3129v2 fatcat:diqzpia4dzglvmh4f5aakdgllu

The Termination and Complexity Competition [chapter]

Jürgen Giesl, Albert Rubio, Christian Sternagel, Johannes Waldmann, Akihisa Yamada
2019 Msphere  
The termination and complexity competition (termCOMP) focuses on automated termination and complexity analysis for various kinds of programming paradigms, including categories for term rewriting, integer  ...  The goal of the competition is to demonstrate the power and advances of the stateof-the-art tools in each of these areas. A.  ...  The goal of the tool MultumNonMulta [31] is to demonstrate the power of a few selected methods based on matrix interpretations for termination analysis of string rewrite systems.  ... 
doi:10.1007/978-3-030-17502-3_10 fatcat:mixhnq6ylbhgxotdihx3xqz73m

Proof Theory at Work: Complexity Analysis of Term Rewrite Systems [article]

Georg Moser
2009 arXiv   pre-print
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis.  ...  The aim of this introduction is to present the main ideas in an easily accessible fashion to make the result presented accessible to the general public.  ...  In particular my gratitude goes to my co-authors Andreas Schabl, Andreas Weiermann, Martin Avanzini, Nao Hirokawa, and Toshiaysu Arai, who kindly allowed me to include our joint papers into this thesis  ... 
arXiv:0907.5527v2 fatcat:jxonbatpw5hdlabp5z7swfrgdy

Restricting grammatical complexity

Robert Frank
2004 Cognitive Science  
This paper argues that such a characterization is correct, and that fundamental properties of grammar can and should be understood in terms of restrictions on the complexity of possible grammatical computation  ...  , when defined in terms of generative capacity.  ...  Acknowledgments It is a great pleasure to dedicate this paper to Aravind Joshi, whose work and whose humanity have been and continue to be a source of inspiration.  ... 
doi:10.1207/s15516709cog2805_3 fatcat:kwszhtsm4nh43is5uv725selxa

Restricting grammatical complexity

R FRANK
2004 Cognitive Science  
This paper argues that such a characterization is correct, and that fundamental properties of grammar can and should be understood in terms of restrictions on the complexity of possible grammatical computation  ...  , when defined in terms of generative capacity.  ...  Acknowledgments It is a great pleasure to dedicate this paper to Aravind Joshi, whose work and whose humanity have been and continue to be a source of inspiration.  ... 
doi:10.1016/j.cogsci.2004.03.006 fatcat:qttly5tgqrfqlllqhnokaqol4e

Modular Complexity Analysis via Relative Complexity

Harald Zankl, Martin Korp, Marc Herbstritt
2010 International Conference on Rewriting Techniques and Applications  
In this paper we introduce a modular framework which allows to infer (feasible) upper bounds on the (derivational) complexity of term rewrite systems by combining different criteria.  ...  All current investigations to analyze the derivational complexity are based on a single termination proof, possibly preceded by transformations.  ...  As base methods we use the match-bounds technique as well as TMIs and arctic matrix interpretations [16] of dimensions one to three.  ... 
doi:10.4230/lipics.rta.2010.385 dblp:conf/rta/ZanklK10 fatcat:5qbghdmumvbsvjwhn6zw3umdoa

Uncurrying for Innermost Termination and Derivational Complexity

Harald Zankl, Nao Hirokawa, Aart Middeldorp
2011 Electronic Proceedings in Theoretical Computer Science  
First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects.  ...  For the preservation of innermost termination and innermost derivational complexity we give counterexamples.  ...  The implementation of the latter is based on SAT solving (cf. [2] ). For a matrix interpretation of dimension d we used 5 − d bits to represent natural numbers in matrix coefficients.  ... 
doi:10.4204/eptcs.49.4 fatcat:nwpp2h2eljebfhusmmzm6akodu

Modular Complexity Analysis for Term Rewriting

Harald Zankl, Martin Korp, Christopher Lynch
2014 Logical Methods in Computer Science  
Since the fundamental idea is based on relative rewriting, we study how matrix interpretations and match-bounds can be used and extended to measure complexity for relative rewriting, respectively.  ...  All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations.  ...  We thank Johannes Waldmann for directing our attention to Example 4.5 and Martin Avanzini for providing a binary of the 2010 competition version of T C T.  ... 
doi:10.2168/lmcs-10(1:19)2014 fatcat:6je64aycqbfmxc5xb5k342e7xa

Complexity of Acyclic Term Graph Rewriting

Martin Avanzini, Georg Moser, Marc Herbstritt
2016 International Conference on Rewriting Techniques and Applications  
We present adaptions of two prominent complexity techniques from term rewriting, viz, the interpretation method and dependency tuples.  ...  In contrast to term rewriting, term graph rewriting permits sharing of common sub-expressions, and consequently is able to capture more closely reasonable implementations of rule based languages.  ...  Dependency Pairs for Complexity Analysis In the following, we suite dependency tuples [23] , a variant of dependency pairs admissible for the innermost runtime complexity analysis of term rewrite systems  ... 
doi:10.4230/lipics.fscd.2016.10 dblp:conf/rta/AvanziniM16 fatcat:fmrro4nvb5dpzkzeozyrfipalq

Constraint Abstractions [chapter]

Jörgen Gustavsson, Josef Svenningsson
2001 Lecture Notes in Computer Science  
Many type based program analyses with subtyping, such as ow analysis, are based on inequality constraints over a lattice.  ...  As an application, we illustrate how a ow analysis with ow subtyping, ow polymorphism and ow-polymorphic recursion can be implemented in O(n 3 ) time where n is the size of the explicitly typed program  ...  The algorithm is based on a rewrite system which rewrites constraint terms to equivalent but more informative ones.  ... 
doi:10.1007/3-540-44978-7_5 fatcat:jdw23g5my5fuzmtc56id64ojfi

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

FRÉDÉRIC BLANQUI, ADAM KOPROWSKI
2011 Mathematical Structures in Computer Science  
It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools have been developed over the years to address this problem.  ...  In this paper we present a library formalizing important results of the theory of well-founded (rewrite) relations in the proof assistant Coq.  ...  Lianyi Zhang, and those who helped us adapt CoLoR to new versions of Coq: Jean-Marc Notin and Eli Soubiran.  ... 
doi:10.1017/s0960129511000120 fatcat:by6ksdib7nfpdjj54sscojozei
« Previous Showing results 1 — 15 out of 62,159 results