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Learned Provability Likelihood for Tactical Search

Thibault Gauthier
2021 Electronic Proceedings in Theoretical Computer Science  
We present a method to estimate the provability of a mathematical formula. We adapt the tactical theorem prover TacticToe to factor in these estimations.  ...  Monte Carlo Tree Search with Tactics We integrate the learned provability estimator into the proof search of TacticToe.  ...  In HOList, the prediction effort is concentrated on learning the policy for a few selected tactics and their arguments (theorems) using deep reinforcement learning.  ... 
doi:10.4204/eptcs.342.7 fatcat:xyp7yj4gond3vbw233kaordqoe

Monte Carlo Tableau Proof Search [chapter]

Michael Färber, Cezary Kaliszyk, Josef Urban
2017 Lecture Notes in Computer Science  
We study Monte Carlo Tree Search to guide proof search in tableau calculi. This includes proposing a number of proof-state evaluation heuristics, some of which are learnt from previous proofs.  ...  tactic with MCTS.  ...  Furthermore, all provers below use the same proof format as the leanCoP tactic described in to automatically find proofs for HOL Light, therefore adapting the HOL Light proof tactic to use our Monte Carlo  ... 
doi:10.1007/978-3-319-63046-5_34 fatcat:ryaw5wlcnrhdblcf3hknznbk3q

Learning to Prove with Tactics [article]

Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar, Michael Norrish
2018 arXiv   pre-print
This knowledge is then used in a Monte Carlo tree search algorithm to explore promising tactic-level proof paths.  ...  We implement a automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation.  ...  Acknowledgments We would like to thank Lasse Blaauwbroek and Yutaka Nagashima for their insightful comments which contributed to improve the quality of this paper.  ... 
arXiv:1804.00596v1 fatcat:twmo2yoiwrfaxmj2onudf6sw7a

Counterexample-Driven Genetic Programming: Stochastic Synthesis of Provably Correct Programs

Krzysztof Krawiec, Iwo Błądek, Jerry Swan, John H. Drake
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
We present Counterexample-Driven Genetic Programming (CDGP) that employs evolutionary search to synthesize provably correct programs from formal specifications.  ...  Genetic programming is an effective technique for inductive synthesis of programs from tests, i.e. training examples of desired input-output behavior.  ...  On the other hand, this result is nontrivial, because counterexamples constructed by an SMT solver reflect its sophisticated search tactics, which are reportedly built on years of expert experience, and  ... 
doi:10.24963/ijcai.2018/742 dblp:conf/ijcai/KrawiecBSD18 fatcat:uynbwetkdbadnm4wd2dsphemke

Learning Theorem Proving Components [article]

Karel Chvalovský, Jan Jakubův, Miroslav Olšák, Josef Urban
2021 arXiv   pre-print
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic.  ...  In this work, we describe several algorithms and experiments with ENIGMA, advancing the idea of contextual evaluation based on learning important components of the graph of clauses.  ...  In all these systems, the component procedures or tactics are, however, human-designed and (often painstakingly) human-implemented, with a lot of care both for the components and for the algorithms that  ... 
arXiv:2107.10034v1 fatcat:kh5y3nebt5gbnhkfgvmjquq2dm

Next Generation Resilient Cyber-Physical Systems [article]

Michel Barbeau, Georg Carle, Joaquin Garcia-Alfaro, Vicenç Torra
2019 arXiv   pre-print
Machine Learning -Artificial Intelligence (AI) by means of the subfields of Machine Learning (ML) and search provides a large set of techniques appropriate for resilient cyberphysical systems.  ...  This includes the use of proactive, often short-term, tactical policies to handle failures; and reactive, usually long-term, strategies for attacks [19] , [30] , [32] .  ... 
arXiv:1907.08849v3 fatcat:ncjycpzrnnfz7hjd74g2quwvx4

Extreme SAT-based Constraint solving with R-Solve

James Ezick, Jonathan Springer, Tom Henretty, Chanseok Oh
2014 2014 IEEE High Performance Extreme Computing Conference (HPEC)  
R-S olve brings together a modern, open S AT solver, HPC ideas in ensemble and collaborative parallel solving and a novel set of extensions supporting, for the first time, an efficient system for unrestricted  ...  extending an aggressively optimized competitive solver to support a new class of problem, provide a performance milestone illustrating the potential of R-S olve and S mart Repair and discuss new frontiers for  ...  Solved repetitively for different fitness values, k, Smart Repair can produce provably optimal solutions for NP-hard k-optimization problems using strategic (non-sequential) search over the fitness space  ... 
doi:10.1109/hpec.2014.8466735 dblp:conf/hpec/EzickSHO14 fatcat:fp7x2jo6jbhv7h2q23lwxdyqqy

HOL(y)Hammer: Online ATP Service for HOL Light [article]

Cezary Kaliszyk, Josef Urban
2013 arXiv   pre-print
The system is also available for local installation by interested users, who can customize it for their own proof development.  ...  HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system.  ...  For smaller (proof-local) lemmas such likelihood should be correspondingly higher.  ... 
arXiv:1309.4962v1 fatcat:bionuosmjffodbzothypf4ghpu

Self-Supervised Learning to Prove Equivalence Between Programs via Semantics-Preserving Rewrite Rules [article]

Steve Kommrusch, Martin Monperrus, Louis-Noël Pouchet
2021 arXiv   pre-print
For training the system, we develop an original training technique, which we call self-supervised sample selection.  ...  This incremental training improves the quality, generalizability and extensibility of the learned model.  ...  This work was partially supported by the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program (WASP) funded by Knut and Alice Wallenberg Foundation, and by the Swedish Foundation for  ... 
arXiv:2109.10476v1 fatcat:kp43iyem65gbdksryqyaezfa3q

Network for hypersonic UCAV swarms

Shixun Luo, Zhongshan Zhang, Shuai Wang, Shuo Zhang, Jibo Dai, Xiangyuan Bu, Jianping An
2020 Science China Information Sciences  
In recent years, academia and industry have made many efforts to achieve common tactical data link systems and commercial drone networks.  ...  In addition, a comprehensive survey of potential solutions for the network design is presented.  ...  The rapid development of artificial intelligence has made it possible to establish more effective solutions for collaborative searching.  ... 
doi:10.1007/s11432-019-2765-7 fatcat:73eck6bvangqlopylxjbxlabt4

Premise Selection and External Provers for HOL4

Thibault Gauthier, Cezary Kaliszyk
2015 Proceedings of the 2015 Conference on Certified Programs and Proofs - CPP '15  
In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4.  ...  Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar.  ...  Acknowledgments We would like to thank Josef Urban and Michael Färber for their comments on the previous version of this paper. This work has been supported by the Austrian Science Fund (FWF): P26201.  ... 
doi:10.1145/2676724.2693173 dblp:conf/cpp/GauthierK15 fatcat:p5jxweitsvbvndliq465gsinra

An analysis of errors in interactive proof attempts

S. Aitken, T. Melham
2000 Interacting with computers  
Notable examples include the XIsabelle GUI for the Isabelle theorem prover [8], the CHOL [9] and TkHOL [10] graphical interfaces for the HOL system, the CtCoq interface for the Coq theorem prover [11,  ...  In this paper, however, we do not directly address issues such as the design of graphical displays for proof trees-for example as proposed by Lowe and Duncan [23] or Schubert and Biggs [24]-or the more  ...  This is the backward proof style, in which the search for a proof proceeds by exploring possible strategies for achieving a goal.  ... 
doi:10.1016/s0953-5438(99)00023-5 fatcat:x2kas5faibhxje3iq5l42nfzke

Multi-agent Reinforcement Learning: An Overview [chapter]

Lucian Buşoniu, Robert Babuška, Bart De Schutter
2010 Studies in Computational Intelligence  
This chapter reviews a representative selection of Multi-Agent Reinforcement Learning (MARL) algorithms for fully cooperative, fully competitive, and more general (neither cooperative nor competitive)  ...  The agents must instead discover a solution on their own, using learning. A significant part of the research on multi-agent learning concerns reinforcement learning techniques.  ...  Well-understood, provably convergent algorithms are available for solving the single-agent RL task.  ... 
doi:10.1007/978-3-642-14435-6_7 fatcat:uonoth4kijcjdohhnq73upjnzu

Assurance of System Safety: A Survey of Design and Argument Patterns [article]

Mario Gleirscher, Stefan Kugele
2019 arXiv   pre-print
Furthermore, we comment on how these studies address known challenges and we discuss suggestions for further research.  ...  For each aspect, we provide an overview of relevant studies and synthesize a taxonomy of first principles underlying these patterns.  ...  This issue necessitates search iteration and strengthens the case for snowballing.  ... 
arXiv:1902.05537v1 fatcat:26flno62afhl7kn3g27lryph5y

Machine Learning Methods for Solving Assignment Problems in Multi-Target Tracking [article]

Patrick Emami, Panos M. Pardalos, Lily Elefteriadou, Sanjay Ranka
2018 arXiv   pre-print
We highlight representation learning methods for multi-sensor applications and conclude by providing an overview of current multi-target tracking benchmarks.  ...  We argue that viewing multi-target tracking as an assignment problem conceptually unifies the wide variety of machine learning methods that have been proposed for data association and track-to-track association  ...  the association likelihood for two inputs.  ... 
arXiv:1802.06897v1 fatcat:fsh7cyr2izdcnc23iqnpztowyy
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