MetiTarski: Past and Future

Paulson, Lawrence C.

doi:10.1007/978-3-642-32347-8_1

Cited by 34 publications

(31 citation statements)

References 29 publications

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“…We use the nlsat dataset 3 produced to evaluate the work in [39]. The main sources of the examples are: MetiTarski [47], an automatic theorem prover for theorems with real-valued special functions (it applies real polynomial bounds and then using QE tools like CAD); problems originating from attempts to prove termination of term-rewrite systems; verification conditions from Keymaera [49]; and parametrized generalizations of geometric problems.…”

Section: Datasetmentioning

confidence: 99%

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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Section: Datasetmentioning

confidence: 99%

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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“…Paulson and co-workers at the University of Cambridge, designed specifically for proving universally quantified first order conjectures featuring transcendental functions (such as sin,cos, ln, exp, etc.) The interested reader may find more details about the MetiTarski system in [2,40].…”

Section: ∂V ∂Xnmentioning

confidence: 99%

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Sogokon

Jackson

Johnson

2017

Lecture Notes in Computer Science

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We propose a method for verifying persistence of nonlinear hybrid systems. Given some system and an initial set of states, the method can guarantee that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flow-pipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study concerning showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flow-pipes or just reasoning about invariants alone can be insufficient. The case study also nicely shows the richness of systems that the method can handle: the case study features a mode with non-polynomial (nonlinear) ODEs and we manage to prove the persistence property with the aid of an automatic prover specifically designed for handling transcendental functions.

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“…Cylindrical algebraic decomposition can be used as tool in program verification, as in the MetiTarski tool [Pau12]. This leads to the question: who will verify the CAD, or at least the inferences we draw from it?…”

Section: How Reliable Is This?mentioning

confidence: 99%