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Loop invariants are software properties that hold before and after every iteration of a loop.
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G. Everest, A. van Poorten, I. Shparlinski and T. Ward · 2003
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Enric Rodríguez-Carbonell and Deepak Kapur · 2004
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Bruno Buchberger · 2006
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Manuel Kauers and Burkhard Zimmermann · 2008
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Laura Kovács · 2008
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Deepanjan Kesh and Shashank. Mehta · 2009
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David. Cox, John. Little and Henry. Schenck · 2011
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Manuel Kauers and Peter Paule · 2011
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“Solving non-linear arithmetic”
Dejan Jovanovic and Leonardo de Moura · 2012
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“Positive margins and primary decomposition”
Thomas Kahle, Johannes Rauh and Seth Sullivant · 2014
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“Polynomial Invariants by Linear Algebra”
Steven de Oliveira, Saddek Bensalem and Virgile Prevosto · 2016
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“Binomial ideals” 279
Jürgen Herzog, Takayuki Hibi and Hidefumi Ohsugi · 2018
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“Invariant Generation for Multi-Path Loops with Polynomial Assignments”
Andreas Humenberger, Maximilian Jaroschek and Laura Kovács · 2018
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“Non-Linear Reasoning for Invariant Synthesis”
Zachary Kincaid, John Cyphert, Jason Breck and Thomas. Reps · 2018
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“Efficiently and Effectively Recognizing Toricity of Steady State Varieties”
Dima Grigoriev, Alexandru Iosif, Hamid Rahkooy, Thomas Sturm and Andreas Weber · 2019
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“When is a Polynomial Ideal Binomial After an Ambient Automorphism?”
Lukas Katthän, Mateusz Michalek and Ezra Miller · 2019
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“Ideals, varieties, and algorithms” An introduction to computational algebraic geometry and commutative algebra, Undergraduate Texts in Mathematics
David. Cox, John. Little and Donal O’Shea · 2015
Cited alongside, same era.
“On Linear Recurrence Sequences and Loop Termination”
Joël Ouaknine and James Worrell · 2015
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“Rational Points on Elliptic Curves”
Joseph. Silverman and John. Tate · 2015
Cited alongside, same era.
“On Strongest Algebraic Program Invariants” To appear
E. Hrushovski, J. Ouaknine, A. Pouly and J. Worrell · 2020
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“Toric varieties from cyclic matrix semigroups”
Francesco Galuppi and Mima Stanojkovski · 2021
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“Algebra-Based Reasoning for Loop Synthesis”
Andreas Humenberger, Daneshvar Amrollahi, Nikolaj Bjørner and Laura Kovács · 2022
Later among the works it cites.