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A New Order-theoretic Characterisation of the Polytime Computable Functions [article]

Martin Avanzini and Naohi Eguchi and Georg Moser
<span title="2012-01-16">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We propose a new order, the small polynomial path order (sPOP* for short). The order sPOP* provides a characterisation of the class of polynomial time computable function via term rewrite systems.  ...  On the other hand any function defined by a rewrite system compatible with sPOP* is polynomial time computable. Technically sPOP* is a tamed recursive path order with product status.  ...  In [7] a recursion-theoretic characterisation B of the class of polytime computable functions is proposed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1201.2553v2">arXiv:1201.2553v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c2d56n55t5coldxyo7owlou36a">fatcat:c2d56n55t5coldxyo7owlou36a</a> </span>
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A New Order-Theoretic Characterisation of the Polytime Computable Functions [chapter]

Martin Avanzini, Naohi Eguchi, Georg Moser
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order (sPOP * for short).  ...  This termination order entails a new syntactic method to analyse the innermost runtime complexity of term rewrite systems fully automatically: for any rewrite system compatible with sPOP * that employs  ...  Acknowledgements We would like to thank the anonymous reviewers for their valuable comments that greatly helped in improving the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-35182-2_20">doi:10.1007/978-3-642-35182-2_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/52ifrnf5lnhdzptmjocd4eozsa">fatcat:52ifrnf5lnhdzptmjocd4eozsa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809151349/http://www.math.s.chiba-u.ac.jp/~neguchi/papers/AEM_ICC_final.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/34/64/3464c6bd633bd94778c958a4f88a183a0a8037b4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-35182-2_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A new order-theoretic characterisation of the polytime computable functions

Martin Avanzini, Naohi Eguchi, Georg Moser
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
We propose a new order-theoretic characterisation of the class of polytime computable functions. To this avail we define the small polynomial path order (sPOP * for short).  ...  This termination order entails a new syntactic method to analyse the innermost runtime complexity of term rewrite systems fully automatically: for any rewrite system compatible with sPOP * that employs  ...  Acknowledgements We would like to thank the anonymous reviewers for their valuable comments that greatly helped in improving the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2015.03.003">doi:10.1016/j.tcs.2015.03.003</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26412933">pmid:26412933</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4567075/">pmcid:PMC4567075</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c2yo4ebnhnfotoyl75f76dhdhe">fatcat:c2yo4ebnhnfotoyl75f76dhdhe</a> </span>
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Parametrised second-order complexity theory with applications to the study of interval computation [article]

Eike Neumann, Florian Steinberg
<span title="2019-06-12">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The complexity of an algorithm is measured in terms of its running time as a second-order function in the parameter, as well as in terms of how much it increases the complexity of a given name, as measured  ...  polytime computable.  ...  to a well-known characterisation of the polytime computable functions on the natural numbers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1711.10530v2">arXiv:1711.10530v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h4ajdetiobhp3kgvxcverntkna">fatcat:h4ajdetiobhp3kgvxcverntkna</a> </span>
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Proofs of Termination of Rewrite Systems for Polytime Functions [chapter]

Toshiyasu Arai, Georg Moser
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We dene a new path order ≺pop so that for a nite rewrite system R compatible with ≺pop, the complexity or derivation length function Dl f R for each function symbol f is guaranteed to be bounded by a polynomial  ...  in the length of the inputs.  ...  We would like to thank Arnold Beckmann who uncovered an embarrassing error in an earlier version of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11590156_43">doi:10.1007/11590156_43</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/miels4wejzcnhmhvqug3m626pi">fatcat:miels4wejzcnhmhvqug3m626pi</a> </span>
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Representations and evaluation strategies for feasibly approximable functions [article]

Michal Konečný, Eike Neumann
<span title="2019-10-21">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense.  ...  The theoretical framework for this is the second-order complexity theory for operators in analysis which was introduced by Kawamura and Cook (2012).  ...  The composition of polytime computable functions is again a polytime computable function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.03702v3">arXiv:1710.03702v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2cvzdnli7vaodi3jd7424xqv4q">fatcat:2cvzdnli7vaodi3jd7424xqv4q</a> </span>
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A Semantic Proof of Polytime Soundness of Light Affine Logic

Ugo Dal Lago, Martin Hofmann
<span title="2009-04-07">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qj6jzeossfhihfshwf7nb7lbcq" style="color: black;">Theory of Computing Systems</a> </i> &nbsp;
We define a denotational semantics for Light Affine Logic (LAL) which has the property that denotations of functions are polynomial time computable by construction of the model.  ...  This gives a new proof of polytime-soundness of LAL which is considerably simpler than the standard proof based on proof nets and also is entirely semantical in nature.  ...  One can thus view LAL as the first resource-free and purely proof-theoretic characterisation of polynomial time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-009-9210-x">doi:10.1007/s00224-009-9210-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g24fgs5acjhulpdzoolesuf5py">fatcat:g24fgs5acjhulpdzoolesuf5py</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200709235220/https://www.tcs.ifi.lmu.de/mitarbeiter/martin-hofmann/publikationen-pdfs/c44-semanticproofpolytimesoundness.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6a/f3/6af3c1829b7c3cccecf668d612bae5d02a40e16d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-009-9210-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A New Term Rewriting Characterisation of ETIME functions [article]

Martin Avanzini, Naohi Eguchi
<span title="2013-12-30">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Adopting former term rewriting characterisations of polytime and exponential-time computable functions, we introduce a new reduction order, the Path Order for ETIME (POE* for short), that is sound and  ...  complete for ETIME computable functions.  ...  Moser the authors introduced the (small) polynomial path order (sPOP * ) [3] that constitutes an order-theoretic characterisation of the polytime functions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1312.7284v2">arXiv:1312.7284v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/btgnkp6xenfb3ndhrx27w3tfeq">fatcat:btgnkp6xenfb3ndhrx27w3tfeq</a> </span>
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Polynomial Path Orders

Martin Avanzini, Georg Moser, Franz Baader
<span title="2013-11-01">2013</span> <i title="Logical Methods in Computer Science e.V."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c67srop7pbe3nciquoxzy3d6pm" style="color: black;">Logical Methods in Computer Science</a> </i> &nbsp;
On the other hand POP* provides an order-theoretic characterisation of the polytime computable functions: the polytime computable functions are exactly the functions computable by an orthogonal constructor  ...  We introduce a path order with multiset status, the polynomial path order POP*, that is applicable in two related, but distinct contexts.  ...  Furthermore the second author would like to thank Toshiyasu Arai for having introduced him to the topic of predicative recursion.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2168/lmcs-9(4:9)2013">doi:10.2168/lmcs-9(4:9)2013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dwikxzghx5dojfhakj7qkz24xq">fatcat:dwikxzghx5dojfhakj7qkz24xq</a> </span>
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On Higher-Order Cryptography

Boaz Barak, Raphaëlle Crubillé, Ugo Dal Lago, Emanuela Merelli, Anuj Dawar, Artur Czumaj
<span title="2020-06-29">2020</span> <i title="Schloss Dagstuhl - Leibniz-Zentrum für Informatik"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pf6v2q6ji5h7birkbrtpdc2uhy" style="color: black;">International Colloquium on Automata, Languages and Programming</a> </i> &nbsp;
can be generalized so as to encompass algorithms of order strictly higher than two, and finally proving some positive and negative results about the existence of higher-order cryptographic primitives,  ...  This paper gives an answer to this question, by first describing why higher-order cryptography is interesting as an object of study, then showing how the concept of probabilistic polynomial time algorithm  ...  In order to do it, we build a third-order randomized algorithm, which will be shown to fit into our game-theoretic framework.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2020.108">doi:10.4230/lipics.icalp.2020.108</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icalp/BarakCL20.html">dblp:conf/icalp/BarakCL20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2cpfbuuqerhhrb3f6imvydqp7e">fatcat:2cpfbuuqerhhrb3f6imvydqp7e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201211113639/https://drops.dagstuhl.de/opus/volltexte/2020/12515/pdf/LIPIcs-ICALP-2020-108.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ff/c0/ffc0209c43fb002dd88b753172dbfe8a3e5c2f58.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2020.108"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

On exact counting and quasi-quantum complexity [article]

Niel de Beaudrap
<span title="2015-09-25">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation.  ...  Our work considers similar modifications of the quantum computational model, but in the setting of exact algorithms, and algorithms with zero error and constant success probability.  ...  is equal to a given polytime-computable function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1509.07789v1">arXiv:1509.07789v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/we6kmumf2nbhtknpojcrxknrtm">fatcat:we6kmumf2nbhtknpojcrxknrtm</a> </span>
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Polynomial Path Orders: A Maximal Model [article]

Martin Avanzini, Georg Moser
<span title="2012-09-17">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
As an application in the context of ICC we provide an order-theoretic characterisation of the polytime computable functions.  ...  To be precise, the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*.  ...  Resource free characterisation of FP: The class of predicative recursive rewrite systems entail new order-theoretic characterisation of FP, the polytime computable functions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1209.3793v1">arXiv:1209.3793v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lvm5673ln5drxms3z4eap5omju">fatcat:lvm5673ln5drxms3z4eap5omju</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1209.3793/1209.3793.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1209.3793v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 4643 of Mathematical Reviews Vol. , Issue 2002G [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
She constructs a new free ordered algebra on one generator which is a conservative extension of the algebra of her previous paper. Therefore the same cardinality result holds here as well.  ...  Summary: “We give a proof, valid in any elementary topos, of the theorem of Zermelo that any set possessing a choice function for its set of inhabited subsets can be well-ordered.  ... 
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A feasible theory of truth over combinatory algebra

Sebastian Eberhard
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
We define an applicative theory of truth T PT which proves totality exactly for the polynomial time computable functions.  ...  For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.  ...  Results of this kind are of interest because they might suggest new implicit characterisations of well-known complexity classes using different computation principles.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2013.12.002">doi:10.1016/j.apal.2013.12.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/movkb2tooreotidpz62ihnsqzm">fatcat:movkb2tooreotidpz62ihnsqzm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190310063658/https://core.ac.uk/download/pdf/33081504.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/38/0a/380a978c969e4bfd93f002a828df1e58f69845ea.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2013.12.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

On sharing, memoization, and polynomial time

Martin Avanzini, Ugo Dal Lago
<span title="">2018</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
By our invariance theorem, the function algebra is sound for polynomial time, and consequently GRSR characterizes the class of polytime computable functions.  ...  Our invariance theorem (see Theorem 17) relates, within a polynomial overhead, the memoized runtime complexity of programs to the cost of implementing the defined functions on a classical model of computation  ...  This form of ramification of functions effectively tames primitive recursion, resulting in a characterisation of the class of polytime computable functions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2018.05.003">doi:10.1016/j.ic.2018.05.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jqh5pmhx5neergx7qholahw76e">fatcat:jqh5pmhx5neergx7qholahw76e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180512210437/http://drops.dagstuhl.de/opus/volltexte/2015/4904/pdf/4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cd/70/cd70bb6639f78fd1a08a6a93cd6a3dfc7b9a6846.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2018.05.003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>
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