Truth table invariant cylindrical algebraic decomposition

Bradford, Russell J.; Davenport, James H.; England, Matthew; McCallum, Scott; Wilson, David J.

doi:10.1016/j.jsc.2015.11.002

Cited by 47 publications

(87 citation statements)

References 59 publications

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“…In particular, we can apply steps 1-4 of Sect. to take the square root of this term, as shown recently in [BDE+14] (14). Indeed, as long as the x i stayed in the same order, we could change the Q i as well.…”

Section: Equational Constraintsmentioning

confidence: 95%

“…A less sensitive property (and one that reflects the cost of using such a decomposition) is the number of cells: for the Collins method this is bounded, by an analysis similar to [BDE+14], by A less sensitive property (and one that reflects the cost of using such a decomposition) is the number of cells: for the Collins method this is bounded, by an analysis similar to [BDE+14], by…”

Section: Cylindrical Algebraic Decomposition By Projection and Liftingmentioning

confidence: 99%

“…This came from an improvement in the lifting phase (discussed in detail in [BDE+14]). First, the CAD of the real line is split into fewer cells (there are not as many cylinders in R 2 ).…”

Section: Equational Constraintsmentioning

confidence: 99%

“…More recently [BDE+14] truth-table invariance has been achieved even when there is no implicit equational constraint, as with an example of the form…”

Section: Equational Constraintsmentioning

confidence: 99%

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Automated Deduction in Geometry

Botana¹,

Recio²

2015

Lecture Notes in Computer Science

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Section: Equational Constraintsmentioning

confidence: 95%

Section: Cylindrical Algebraic Decomposition By Projection and Liftingmentioning

confidence: 99%

“…This came from an improvement in the lifting phase (discussed in detail in [BDE+14]). First, the CAD of the real line is split into fewer cells (there are not as many cylinders in R 2 ).…”

Section: Equational Constraintsmentioning

confidence: 99%

“…More recently [BDE+14] truth-table invariance has been achieved even when there is no implicit equational constraint, as with an example of the form…”

Section: Equational Constraintsmentioning

confidence: 99%

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Automated Deduction in Geometry

Botana¹,

Recio²

2015

Lecture Notes in Computer Science

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“…We organised a Dagstuhl Seminar Symbolic Computation and Satisfiability Checking 15 15-20th November, 2015, which already led to numerous interesting discussions and interactions. At CASC 2016, we will organise a topical session devoted to topics from the cross-community SC 2 area.…”

Section: Standard Languages and Benchmarksmentioning

confidence: 99%

$$\mathsf {SC}^\mathsf{2} $$ : Satisfiability Checking Meets Symbolic Computation

Ábrahám

Abbott

Becker

et al. 2016

Lecture Notes in Computer Science

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Abstract. Symbolic Computation and Satisfiability Checking are two research areas, both having their individual scientific focus but sharing also common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite their commonalities, the two communities are rather weakly connected. The aim of our newly accepted SC 2 project (H2020-FETOPEN-CSA) is to strengthen the connection between these communities by creating common platforms, initiating interaction and exchange, identifying common challenges, and developing a common roadmap from theory along the way to tools and (industrial) applications. In this paper we report on the aims and on the first activities of this project, and formalise some relevant challenges for the unified SC 2 community.

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Comparing Machine Learning Models to Choose the Variable Ordering for Cylindrical Algebraic Decomposition

England

Florescu

2019

Lecture Notes in Computer Science

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There has been recent interest in the use of machine learning (ML) approaches within mathematical software to make choices that impact on the computing performance without affecting the mathematical correctness of the result. We address the problem of selecting the variable ordering for cylindrical algebraic decomposition (CAD), an important algorithm in Symbolic Computation. Prior work to apply ML on this problem implemented a Support Vector Machine (SVM) to select between three existing human-made heuristics, which did better than anyone heuristic alone. Here we extend this result by training ML models to select the variable ordering directly, and by trying out a wider variety of ML techniques. We experimented with the NLSAT dataset and the Regular Chains Library CAD function for Maple 2018. For each problem, the variable ordering leading to the shortest computing time was selected as the target class for ML. Features were generated from the polynomial input and used to train the following ML models: k-nearest neighbours (KNN) classifier, multi-layer perceptron (MLP), decision tree (DT) and SVM, as implemented in the Python scikit-learn package. We also compared these with the two leading human-made heuristics for the problem: the Brown heuristic and sotd. On this dataset all of the ML approaches outperformed the human-made heuristics, some by a large margin.

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Truth table invariant cylindrical algebraic decomposition

Cited by 47 publications

References 59 publications

Automated Deduction in Geometry

Automated Deduction in Geometry

$$\mathsf {SC}^\mathsf{2} $$ : Satisfiability Checking Meets Symbolic Computation

Comparing Machine Learning Models to Choose the Variable Ordering for Cylindrical Algebraic Decomposition

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