MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers

Kühlwein, Daniel; Urban, Josef

doi:10.1007/s10817-015-9329-1

Cited by 13 publications

(7 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to premise selection and proof guidance, other aspects of theorem proving have also benefited from machine learning. For example, Kühlwein et al [26] applied kernel methods to strategy finding, the problem of searching for good parameter configurations for an automated prover. Similarly, Bridge et al [27] applied SVM and Gaussian Processes to select good heuristics, which are collections of standard settings for parameters and other decisions.…”

Section: Related Workmentioning

confidence: 99%

Premise Selection for Theorem Proving by Deep Graph Embedding

Wang,

Tang,

Wang

et al. 2017

Preprint

View full text Add to dashboard Cite

We propose a deep learning-based approach to the problem of premise selection: selecting mathematical statements relevant for proving a given conjecture. We represent a higher-order logic formula as a graph that is invariant to variable renaming but still fully preserves syntactic and semantic information. We then embed the graph into a vector via a novel embedding method that preserves the information of edge ordering. Our approach achieves state-of-the-art results on the HolStep dataset, improving the classification accuracy from 83% to 90.3%.

show abstract

Section: Related Workmentioning

confidence: 99%

Premise Selection for Theorem Proving by Deep Graph Embedding

Wang,

Tang,

Wang

et al. 2017

Preprint

View full text Add to dashboard Cite

show abstract

“…It seems unlikely that manual ("theorydriven") construction of targeted strategies can scale to large numbers of ATP problems spanning many different areas of mathematics and computer science. Starting with Blind Strategymaker (BliStr) (Urban 2015) that was used to invent E's strategies for MaLARea (Urban et al 2008;Kaliszyk et al 2015b) on the 2012 Mizar@Turing competition prob-lems (Sutcliffe 2013), several systems have been recently developed to invent targeted ATP strategies (Schäfer and Schulz 2015;Kühlwein and Urban 2015). The underlying methods used so far include genetic algorithms and iterated local search, as popularized by the ParamILS (Hutter et al 2009) system.…”

Section: Introduction: Atp Strategy Inventionmentioning

confidence: 99%

BliStrTune: hierarchical invention of theorem proving strategies

Jakubův

Urban

2017

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs

Self Cite

View full text Add to dashboard Cite

Inventing targeted proof search strategies for specific problem sets is a difficult task. State-of-the-art automated theorem provers (ATPs) such as E allow a large number of userspecified proof search strategies described in a rich domain specific language. Several machine learning methods that invent strategies automatically for ATPs were proposed previously. One of them is the Blind Strategymaker (BliStr), a system for automated invention of ATP strategies.In this paper we introduce BliStrTune -a hierarchical extension of BliStr. BliStrTune allows exploring much larger space of E strategies by interleaving search for high-level parameters with their fine-tuning. We use BliStrTune to invent new strategies based also on new clause weight functions targeted at problems from large ITP libraries. We show that the new strategies significantly improve E's performance in solving problems from the Mizar Mathematical Library.

show abstract

“…Their advanced knowledge-based proof finding is an enigma, which is unlikely to be deciphered and programmed completely manually in near future.On large corpora such as Flyspeck, Mizar and Isabelle, the ATP progress has been mainly due to learning how to select the most relevant knowledge, based on many previous proofs [10,12,1,2]. Learning from many proofs has also recently become a very useful method for automated finding of parameters of ATP strategies [22,9,19,16], and for learning of sequences of tactics in interactive theorem provers (ITPs) [7]. Several experiments with the compact leanCoP [18] system have recently shown that directly using trained machine learner for internal clause selection can significantly prune the search space and solve additional problems [24,11,5].…”

mentioning

confidence: 99%

ENIGMA: Efficient Learning-Based Inference Guiding Machine

Jakubův

Urban

2017

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

ENIGMA is a learning-based method for guiding given clause selection in saturationbased theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, using fast feature-based characterization of the clauses . The learned model is then tightly linked with the core prover and used as a basis of a new parameterized evaluation heuristic that provides fast ranking of all generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E's performance. Introduction: Theorem Proving and LearningState-of-the-art resolution/superposition automated theorem provers (ATPs) such as Vampire [15] and E [20] are today's most advanced tools for general reasoning across a variety of mathematical and scientific domains. The stronger the performance of such tools, the more realistic become tasks such as full computer understanding and automated development of complicated mathematical theories, and verification of software, hardware and engineering designs. While performance of ATPs has steadily grown over the past years due to a number of human-designed improvements, it is still on average far behind the performance of trained mathematicians. Their advanced knowledge-based proof finding is an enigma, which is unlikely to be deciphered and programmed completely manually in near future.On large corpora such as Flyspeck, Mizar and Isabelle, the ATP progress has been mainly due to learning how to select the most relevant knowledge, based on many previous proofs [10,12,1,2]. Learning from many proofs has also recently become a very useful method for automated finding of parameters of ATP strategies [22,9,19,16], and for learning of sequences of tactics in interactive theorem provers (ITPs) [7]. Several experiments with the compact leanCoP [18] system have recently shown that directly using trained machine learner for internal clause selection can significantly prune the search space and solve additional problems [24,11,5]. An obvious next step is to implement efficient learning-based clause selection also inside the strongest superposition-based ATPs.In this work, we introduce ENIGMA -Efficient learNing-based Internal Guidance MAchine for state-of-the-art saturation-based ATPs. The method applies fast machine learning algorithms to a large number of proofs, and uses the trained classifier together with simpler heuristics to evaluate the millions of clauses generated during the resolution/superposition proof search. This way, the theorem prover automatically takes into account thousands of previous successes and failures that it has seen in previous problems, similarly to trained humans. Thanks to a carefully chosen efficient learning/evaluation method and its tight integration with the core ATP (in our case the E prover), the penalty for this ubiquitous knowledge-based internal proof guidance is very low. This in turn very significantly improves the per...

show abstract

MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers

Cited by 13 publications

References 23 publications

Premise Selection for Theorem Proving by Deep Graph Embedding

Premise Selection for Theorem Proving by Deep Graph Embedding

BliStrTune: hierarchical invention of theorem proving strategies

ENIGMA: Efficient Learning-Based Inference Guiding Machine

Contact Info

Product

Resources

About