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Precise Widening Operators for Proving Termination by Abstract Interpretation [chapter]

Nathanaël Courant, Caterina Urban
<span title="">2017</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;
FuncTion is a static analyzer designed for proving conditional termination of C programs by means of abstract interpretation.  ...  ., the widening operator) of the abstract domain.  ...  Section 2 offers a glimpse into the theory behind proving termination by abstract interpretation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-54577-5_8">doi:10.1007/978-3-662-54577-5_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/as5p5z37inekdhsxf4gxhxbs2a">fatcat:as5p5z37inekdhsxf4gxhxbs2a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190225112022/http://pdfs.semanticscholar.org/5ebe/85f08edbf2c631159308afec238257fc0550.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/5e/be/5ebe85f08edbf2c631159308afec238257fc0550.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-54577-5_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Counterexample Driven Refinement for Abstract Interpretation [chapter]

Bhargav S. Gulavani, Sriram K. Rajamani
<span title="">2006</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;
interpretation techniques prove properties of programs by computing abstract fixpoints. All such analyses suffer from the possibility of false errors.  ...  We sketch how our technique can be used to perform shape analysis by simply defining an appropriate widening operator over shape graphs.  ...  We thank Rustan Leino for providing his example programs from the Boogie project, and Sriram Sankaranarayanan for providing us the invariants generated by StInG.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11691372_34">doi:10.1007/11691372_34</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/so77twiywjbsnikaugufr43v34">fatcat:so77twiywjbsnikaugufr43v34</a> </span>
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Widening Operators for Abstract Interpretation

Agostino Cortesi
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4gnym4oll5fczbcpsn2kvn53em" style="color: black;">2008 Sixth IEEE International Conference on Software Engineering and Formal Methods</a> </i> &nbsp;
In particular, we prove that, for Galois insertions, widening is preserved by abstraction, and we show how widening operators can be combined for the cartesian and reduced product of abstract domains.  ...  Interpretation, one of the most applied techniques for semantics based static analysis of software, is based on two main key-concepts: the correspondence between concrete and abstract semantics through  ...  Many thanks to Xavier Rival, Pietro Ferrara, and Flemming Nielson for their comments on the a first draft of this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sefm.2008.20">doi:10.1109/sefm.2008.20</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sefm/Cortesi08.html">dblp:conf/sefm/Cortesi08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/424qsax5znhjhh6zz6x3poiowi">fatcat:424qsax5znhjhh6zz6x3poiowi</a> </span>
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Widening with thresholds via binary search

Sol Kim, Kihong Heo, Hakjoo Oh, Kwangkeun Yi
<span title="2015-12-04">2015</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/afve5b3tavbfzch46mdtazbqla" style="color: black;">Software, Practice &amp; Experience</a> </i> &nbsp;
We formalize the technique in the abstract interpretation framework and show that, by experiments with a realistic static analyzer for C, our technique considerably improves the efficiency (by 81.5%) of  ...  In this formulation, Theorem 1 corresponds to proving that ∇ satisfies the conditions of widening (i.e., termination of widening).  ...  Static Analysis with Widening We consider a static analysis designed by abstract interpretation [6, 4] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/spe.2381">doi:10.1002/spe.2381</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ywi536qhyrdtrmnongmf5caagi">fatcat:ywi536qhyrdtrmnongmf5caagi</a> </span>
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A minimalistic look at widening operators [article]

David Monniaux
<span title="2009-11-23">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It turns out that many axioms of widening (e.g. widening sequences are ascending) are not useful for proving correctness.  ...  We consider the problem of formalizing the familiar notion of widening in abstract interpretation in higher-order logic.  ...  This work was partially funded by ANR project "ASOPT".  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0902.3722v3">arXiv:0902.3722v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qhyzx66llvb2fngvddjzesr2te">fatcat:qhyzx66llvb2fngvddjzesr2te</a> </span>
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A minimalistic look at widening operators

David Monniaux
<span title="">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t26kxee64ne4xcsmauoqewjwp4" style="color: black;">Higher-Order and Symbolic Computation</a> </i> &nbsp;
It turns out that many axioms of widening (e.g. widening sequences are ascending) are not useful for proving correctness.  ...  We consider the problem of formalizing in higher-order logic the familiar notion of widening from abstract interpretation.  ...  This work was partially funded by ANR project "ASOPT".  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10990-009-9046-8">doi:10.1007/s10990-009-9046-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/53rl62mtpjfvfh5m3sjmk64one">fatcat:53rl62mtpjfvfh5m3sjmk64one</a> </span>
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A Certified Denotational Abstract Interpreter [chapter]

David Cachera, David Pichardie
<span title="">2010</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;
In contrast, abstract interpreters are looking for fixpoints in infinite lattices where widening and narrowing are used for accelerating the convergence.  ...  In this paper, we show how we manage to program and prove correct in Coq an abstract interpreter that uses iteration strategies based on program syntax.  ...  In this paper we focus on the two first classes of potential failures, that is we prove the semantic soundness of an abstract interpreter and addresses the termination problem for a challenging fixpoint  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14052-5_3">doi:10.1007/978-3-642-14052-5_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/spqaffa76bfzzkikywdk5ccu7u">fatcat:spqaffa76bfzzkikywdk5ccu7u</a> </span>
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A combination framework for tracking partition sizes

Sumit Gulwani, Tal Lev-Ami, Mooly Sagiv
<span title="2009-01-21">2009</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xu5bk2lj5rbdxlx6222nw7tsxi" style="color: black;">SIGPLAN notices</a> </i> &nbsp;
We describe an abstract interpretation based framework for proving relationships between sizes of memory partitions.  ...  Technically, we define an abstract domain that is parameterized by an abstract domain for tracking memory partitions (sets of memory locations) and by a numerical abstract domain for tracking relationships  ...  Acknowledgements We would like to thank Nurit Dor, Denis Gopan, and Michal Segalov for reading an earlier draft of this paper. We thank Denis Gopan for his help with the implementation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1594834.1480912">doi:10.1145/1594834.1480912</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rjdjh22tlvexpobhqalb6jx7ly">fatcat:rjdjh22tlvexpobhqalb6jx7ly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090116022919/http://research.microsoft.com/en-us/um/people/sumitg/pubs/popl09_partition.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/aa/ee/aaee0da7ae7a1f4c98b62dc30a237991a7e230e3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1594834.1480912"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

A combination framework for tracking partition sizes

Sumit Gulwani, Tal Lev-Ami, Mooly Sagiv
<span title="">2008</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2qaxtqe2rfgjnfefqcokcnzelq" style="color: black;">Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL &#39;09</a> </i> &nbsp;
We describe an abstract interpretation based framework for proving relationships between sizes of memory partitions.  ...  Technically, we define an abstract domain that is parameterized by an abstract domain for tracking memory partitions (sets of memory locations) and by a numerical abstract domain for tracking relationships  ...  Acknowledgements We would like to thank Nurit Dor, Denis Gopan, and Michal Segalov for reading an earlier draft of this paper. We thank Denis Gopan for his help with the implementation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1480881.1480912">doi:10.1145/1480881.1480912</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/popl/GulwaniLS09.html">dblp:conf/popl/GulwaniLS09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xlbp3ggbq5gm3pstckrbpkzwny">fatcat:xlbp3ggbq5gm3pstckrbpkzwny</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090116022919/http://research.microsoft.com/en-us/um/people/sumitg/pubs/popl09_partition.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/aa/ee/aaee0da7ae7a1f4c98b62dc30a237991a7e230e3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1480881.1480912"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

FuncTion: An Abstract Domain Functor for Termination [chapter]

Caterina Urban
<span title="">2015</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;
The tool automatically infers piecewise-defined ranking functions (and sufficient preconditions for termination) by means of abstract interpretation.  ...  FuncTion is a research prototype static analyzer designed for proving (conditional) termination of C programs.  ...  Moreover, the analyzer fails to prove termination of a significant number of terminating tests cases mainly due to a naïve widening operator [6, 8] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-46681-0_46">doi:10.1007/978-3-662-46681-0_46</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wto5cohbxjdcvpfk3w5v2fwpve">fatcat:wto5cohbxjdcvpfk3w5v2fwpve</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200305065753/https://link.springer.com/content/pdf/10.1007%2F978-3-662-46681-0_46.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/8d/97/8d9784986aae0305bb6d82f6d7a4d513e24f7236.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-46681-0_46"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A Decision Tree Abstract Domain for Proving Conditional Termination [chapter]

Caterina Urban, Antoine Miné
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We have implemented a static analyzer for proving conditional termination of programs written in (a subset of) C and, using experimental evidence, we show that it performs well on a wide variety of benchmarks  ...  abstract domain for the leaf nodes.  ...  We are grateful to the developers of AProVE [19] , T2 [5] , and Ultimate Büchi Automizer [22] for their help with the experiments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-10936-7_19">doi:10.1007/978-3-319-10936-7_19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/thg3xy4jjbag5mxea7b256p4yi">fatcat:thg3xy4jjbag5mxea7b256p4yi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180718230942/https://hal.inria.fr/hal-01105221/file/article-urban-mine-sas14.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/50/0b/500ba7d6566c209e8dac9a85aabdce91f7444a07.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-10936-7_19"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Refining Abstract Interpretation-Based Static Analyses with Hints [chapter]

Vincent Laviron, Francesco Logozzo
<span title="">2009</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 focus our attention on the loss of precision induced by abstract domain operations.  ...  We give some examples of hints, and we provide our experience with hints in Clousot, our abstract interpretation-based static analyzer for .Net.  ...  Saturation hints can provide very precise operations for Cartesian abstract interpretations: They allow the analysis to get additional precision by combining the information present in different abstract  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-10672-9_24">doi:10.1007/978-3-642-10672-9_24</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ilynnfsznbe4fiydpqvty2vsee">fatcat:ilynnfsznbe4fiydpqvty2vsee</a> </span>
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Abstract Interpretation of Annotated Commands [chapter]

Tobias Nipkow
<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;
This paper formalizes a generic abstract interpreter for a while-language, including widening and narrowing.  ...  The collecting semantics and the abstract interpreter operate on annotated commands: the program is represented as a syntax tree with the semantic information directly embedded, without auxiliary labels  ...  Acknowledgement David Pichardie's exemplary review and his many explanations greatly improved my understanding of his work and of abstract interpretation in general.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-32347-8_9">doi:10.1007/978-3-642-32347-8_9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ryuqkqnmlnh2pkcu6chxlkrgpq">fatcat:ryuqkqnmlnh2pkcu6chxlkrgpq</a> </span>
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More Precise Yet Efficient Type Inference for Logic Programs [article]

Claudio Vaucheret, Francisco Bueno
<span title="2002-07-12">2002</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this setting, we discuss the widening operator, arguably a crucial one. We present a new widening which is more precise than those previously proposed.  ...  This covers most classical abstract interpretation-based type analyzers for logic programs, built on either top-down or bottom-up interpretation of the program.  ...  This work has been partially supported by Spanish MCYT project EDIPIA TIC99-1151.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0207049v2">arXiv:cs/0207049v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c6aupeq2jrhetjn5ojmapmubcm">fatcat:c6aupeq2jrhetjn5ojmapmubcm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171008201757/https://core.ac.uk/download/pdf/2418523.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/db/04/db04e4622e6f2e2fb3085cd8c6ef2e14128faeb7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0207049v2" 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>

Bound Analysis for Whiley Programs

Min-Hsien Weng, Mark Utting, Bernhard Pfahringer
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
This paper presents an abstract interpretation-based bound inference approach along with symbolic analysis for Whiley programs.  ...  The bound analyzer combines the bound consistency technique along with a widening operator to give fast time of solving program constraints and of converging to the fixed point.  ...  Acknowledgement Thanks for Dr. David J. Pearce's technical support and to Google for some funding support for this project via a grant to Dr Utting.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2016.01.005">doi:10.1016/j.entcs.2016.01.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qjp7rhd3svcdhj2qurbveq5rpu">fatcat:qjp7rhd3svcdhj2qurbveq5rpu</a> </span>
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