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Page 3680 of Mathematical Reviews Vol. , Issue 89G [page]

<span title="">1989</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;
From the introduction: “This bibliography seeks to provide a basic collection of literature on algorithmic quantifier elimination for real-closed fields.  ...  Jean-Jacques Risler (F-POLY) 89g:12003 12D15 O0AI5 03C10 03C60 12L12 Arnon, Dennis S. (1-XEROX) A bibliography of quantifier elimination for real closed fields. J.  ... 
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Thirty Years of Virtual Substitution

Thomas Sturm
<span title="">2018</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC &#39;18</a> </i> &nbsp;
In 1988, Weispfenning published a seminal paper introducing a substitution technique for quantifier elimination in the linear theories of ordered and valued fields.  ...  The original focus was on complexity bounds including the important result that the decision problem for Tarski Algebra is bounded from below by a double exponential function.  ...  ACKNOWLEDGMENTS This work has been partly supported by the European Union's Horizon 2020 research and innovation programme under grant agreement No H2020-FETOPEN-2015-CSA 712689 SC-SQUARE.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3208976.3209030">doi:10.1145/3208976.3209030</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/Sturm18.html">dblp:conf/issac/Sturm18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nwl25qgjrzh6tpqeouxgzv2ety">fatcat:nwl25qgjrzh6tpqeouxgzv2ety</a> </span>
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Page 7535 of Mathematical Reviews Vol. , Issue 98M [page]

<span title="">1998</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;
(D-PASS-LM; Passau Quantifier elimination for real algebrathe quadratic case and beyond. (English summary) Appl. Algebra Engrg. Comm. Comput. 8 (1997), no. 2, 85-101.  ...  The author presents some new efficient algorithms for quantifier elimination in a special class of first-order formulas in the theory of real closed fields.  ... 
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QEPCAD B

Christopher W. Brown
<span title="2003-12-01">2003</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hab6y3yvcbd2hpuybkxo2pp34a" style="color: black;">ACM SIGSAM Bulletin</a> </i> &nbsp;
This paper briefly discusses some of the improvements in the implementation of CAD and quantifier elimination via CAD, and provides somewhat more detail on extensions to the system that go beyond quantifier  ...  Qepcad b both extends and improves upon the Qepcad system for quantifier elimination by partial cylindrical algebraic decomposition written by Hoon Hong in the early 1990s.  ...  an extension of the language of Tarski formulas, and quantifier elimination for an extended class of quantifiers. 1 2 CAD, semi-algebraic sets, and the quantifier elimination problem CADs provide an  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/968708.968710">doi:10.1145/968708.968710</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/455ys43turhlljrmuslucmbnny">fatcat:455ys43turhlljrmuslucmbnny</a> </span>
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Verification of model predictive control laws using weispfenning's quantifier elimination by virtual substitution algorithm

K. Siaulys, J. M. Maciejowski
<span title="">2016</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2016 IEEE 55th Conference on Decision and Control (CDC)</a> </i> &nbsp;
A method based on a quantifier elimination algorithm is suggested for obtaining explicit model predictive control (MPC) laws for linear time invariant systems with quadratic objective and polytopic constraints  ...  Extension to cases beyond linear MPC using Weispfenning's algorithm is part of future work.  ...  Tarski discovered the first quantifier elimination algorithm [1] for the first order theory of real numbers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2016.7798471">doi:10.1109/cdc.2016.7798471</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/SiaulysM16.html">dblp:conf/cdc/SiaulysM16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bzn26ia3yfgkpk7vk4el7mhd7q">fatcat:bzn26ia3yfgkpk7vk4el7mhd7q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200310220955/https://www.repository.cam.ac.uk/bitstream/handle/1810/287166/quantifier_elimination_CDC16_final.pdf;jsessionid=56E549C527EF1122ED9DFCAC5A1778A7?sequence=1" 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/6d/bd/6dbddabc4c1b77ec1cf1fca42016ea8e8815e0a4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2016.7798471"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Development of SyNRAC [chapter]

Hitoshi Yanami, Hirokazu Anai
<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;
The current version of SyNRAC has added quantifier elimination (QE) by cylindrical algebraic decomposition (CAD) as well as QE by virtual substitution for weakly parametric linear formulas.  ...  We present newly implemented procedures in SyNRAC, which is a Maple package for solving real algebraic constraints derived from various engineering problems.  ...  In general case, all the quantifiers in the formula can be eliminated inside out by changing the innermost one to ∃x i and then removing it.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11428862_82">doi:10.1007/11428862_82</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/665d323lrvd5xp5macj3d2xxie">fatcat:665d323lrvd5xp5macj3d2xxie</a> </span>
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Real algebraic geometry

<span title="2014-01-21">2014</span> <i title="American Library Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pjjljho22jhnrmpk3k2jxhxzv4" style="color: black;">ChoiceReviews</a> </i> &nbsp;
the pool of the Real Algebraic Geometry of tomorrow.  ...  We also wish to thank the numerous sponsors who allowed us to welcome so many participants under proper conditions, in particular a large number of PhD students and post-PhD students called to constitute  ...  We also discuss the known lower bounds for real quantifier elimination.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5860/choice.51-3296">doi:10.5860/choice.51-3296</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xm5l6ieafzewtfpuegkxsbtzhy">fatcat:xm5l6ieafzewtfpuegkxsbtzhy</a> </span>
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Virtual Substitution for SMT-Solving [chapter]

Florian Corzilius, Erika Ábrahám
<span title="">2011</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;
Currently available decision procedures for real algebra -the first-order theory of the reals with addition and multiplication -do not exhibit these features.  ...  For efficiency, the theory solver should be able to work incrementally and generate infeasible subsets.  ...  Preliminaries In this paper we focus on satisfiability checking for a subset of the existential fragment of real algebra (quadratic and beyond).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-22953-4_31">doi:10.1007/978-3-642-22953-4_31</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/66peapiggrfwbesvb53uekibl4">fatcat:66peapiggrfwbesvb53uekibl4</a> </span>
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Page 5262 of Mathematical Reviews Vol. , Issue 98H [page]

<span title="">1998</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;
and optimization by quantifier elimination.  ...  (D-HUMB,; Berlin) Polar varieties, real equation solving, and data structures: the hypersurface case. (English summary) J. Complexity 13 (1997), no. 1, 5-27.  ... 
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Verification and synthesis using real quantifier elimination

Thomas Sturm, Ashish Tiwari
<span title="">2011</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC &#39;11</a> </i> &nbsp;
We present the application of real quantifier elimination to formal verification and synthesis of continuous and switched dynamical systems.  ...  Existing off-the-shelf quantifier elimination procedures are not successful in eliminating quantifiers from many of our benchmarks.  ...  Acknowledgments We would like to thank Andreas Weber for encouraging and supporting the first author in visiting SRI.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1993886.1993935">doi:10.1145/1993886.1993935</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/SturmT11.html">dblp:conf/issac/SturmT11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jeyfoaeqcncznflip2fzymnzl4">fatcat:jeyfoaeqcncznflip2fzymnzl4</a> </span>
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The Tarski Problems and Their Solutions

Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, Dennis Spellman
<span title="">2015</span> <i title="Scientific Research Publishing, Inc,"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j2aqr755kjfl3grimwbah5xj4m" style="color: black;">Advances in Pure Mathematics</a> </i> &nbsp;
Around 1945, Alfred Tarski proposed several questions concerning the elementary theory of nonabelian free groups. These remained open for 60 years until they were proved by O. Kharlampovich and A.  ...  We then provide the basic strategy for the proof. We finish this paper with a brief discussion of elementary free groups.  ...  In the Kharlampovich-Myasnikov approach the quantifier elimination is handled by an implicit function theorem for quadratic systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/apm.2015.54023">doi:10.4236/apm.2015.54023</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/35xxoyikn5hxhgepie5ptryryi">fatcat:35xxoyikn5hxhgepie5ptryryi</a> </span>
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A Proof-Producing Decision Procedure for Real Arithmetic [chapter]

Sean McLaughlin, John Harrison
<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;
For example, the well-known criterion for a quadratic equation to have a (real) root can be considered as an example of quantifier elimination in a suitable theory T of reals: T |= (∃x. ax 2 + bx + c =  ...  We present a fully proof-producing implementation of a quantifier elimination procedure for real closed fields.  ...  Acknowledgments The first author would like to thank Frank Pfenning and for the Logosphere grant that helped to support this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11532231_22">doi:10.1007/11532231_22</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lpghikfpo5bpbjk2slhaxi7paa">fatcat:lpghikfpo5bpbjk2slhaxi7paa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070221093007/http://www.cl.cam.ac.uk:80/~jrh13/papers/cade05.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/90/f0/90f0ffd512e33e08563252e219246ec4578e3105.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11532231_22"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Testing Stability by Quantifier Elimination

HOON HONG, RICHARD LISKA, STANLY STEINBERG
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
The newer Quantifier Elimination by Partial Algebraic Decomposition (QEPCAD) algorithm is far more practical, allowing the solution of some non-trivial problems.  ...  In this paper, we show how to write all common stability problems as quantifier-elimination problems, and develop a set of computer-algebra tools that allows us to find analytic solutions to simple stability  ...  We also wish to thank the reviewers for many helpful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jsco.1997.0121">doi:10.1006/jsco.1997.0121</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ndp2st5jhfeunkev4lc7cdxmr4">fatcat:ndp2st5jhfeunkev4lc7cdxmr4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170929073556/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/764/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDc0NzcxNzE5NzkwMTIxOA%3D%3D.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/74/1a/741a813372f4cf2a9b5d15a1d5496217770c5448.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jsco.1997.0121"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Symbolic Computation and Complexity Theory Transcript of My Talk [chapter]

Erich L. Kaltofen
<span title="">2014</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/n2id5rhzcvgsddxce5wh2evxmi" style="color: black;">Computer Mathematics</a> </i> &nbsp;
Collins's 1974 cylindrical algebraic decomposition algorithm performs Tarski's quantifier elimination.  ...  Shaoshi Chen has told me while he was at NCSU that some of the algorithms for symbolic summation have worst case performance beyond quadratic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-43799-5_1">doi:10.1007/978-3-662-43799-5_1</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ascm/Kaltofen12.html">dblp:conf/ascm/Kaltofen12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ryld7hmxpjfe3ck625lwctsjhi">fatcat:ryld7hmxpjfe3ck625lwctsjhi</a> </span>
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Generating Non-Linear Interpolants by Semidefinite Programming [article]

Liyun Dai and Bican Xia and Naijun Zhan
<span title="2013-03-03">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed.  ...  In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.  ...  for quantifier elimination.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1302.4739v2">arXiv:1302.4739v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vwlrc3v6rjaxdau7gljpejcnwa">fatcat:vwlrc3v6rjaxdau7gljpejcnwa</a> </span>
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