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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.  ...  The system is trained and evaluated on a large suite of related problems coming from the Mizar proof assistant, showing that it is capable to find new and different proofs.  ...  Monte Carlo Tree Search Monte Carlo Tree Search (MCTS) is a procedure to search large spaces by random sampling, biased towards promising parts of the search space.  ... 
doi:10.1007/978-3-319-63046-5_34 fatcat:ryaw5wlcnrhdblcf3hknznbk3q

Reinforcement Learning of Theorem Proving [article]

Cezary Kaliszyk, Josef Urban, Henryk Michalewski, Mirek Olšák
2018 arXiv   pre-print
Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts.  ...  We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search.  ...  Monte-Carlo Guidance To implement Monte-Carlo tree search, we maintain at each search node i the number of its visits n i , the total reward w i , and its prior probability p i .  ... 
arXiv:1805.07563v1 fatcat:c63j46tnmvdh7cposgppuvq4v4

Prolog Technology Reinforcement Learning Prover [chapter]

Zsolt Zombori, Josef Urban, Chad E. Brown
2020 Lecture Notes in Computer Science  
The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP builds on the leanCoP Prolog implementation and adds learning-guided Monte-Carlo Tree Search  ...  Other components include a Python interface to plCoP and machine learners, and an external proof checker that verifies the validity of plCoP proofs.  ...  We provide an external proof checker that certifies the validity of the proofs. 5. The policy model of rlCoP is trained using Monte Carlo search trees of all proof attempts.  ... 
doi:10.1007/978-3-030-51054-1_33 fatcat:e6ilb5wlcne65e2y4qoesydizy

Prolog Technology Reinforcement Learning Prover [article]

Zsolt Zombori, Josef Urban, Chad E. Brown
2020 arXiv   pre-print
The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP builds on the leanCoP Prolog implementation and adds learning-guided Monte-Carlo Tree Search  ...  Other components include a Python interface to plCoP and machine learners, and an external proof checker that verifies the validity of plCoP proofs.  ...  We provide an external proof checker that certifies the validity of the proofs. 5. The policy model of rlCoP is trained using Monte Carlo search trees of all proof attempts.  ... 
arXiv:2004.06997v1 fatcat:mbymzgsnvrczzgpjxt7rgejvua

The Role of Entropy in Guiding a Connection Prover [article]

Zsolt Zombori, Josef Urban, Miroslav Olšák
2021 arXiv   pre-print
Then we use it to observe the system's behaviour in a reinforcement learning setting, i.e., when learning inference guidance from successful Monte-Carlo tree searches on many problems.  ...  This leads us to explore how the entropy of the inference selection implemented via the neural network influences the proof search.  ...  Note that the Monte Carlo tree is thus different from the tableau trees. A branch of this Monte Carlo tree leading to a node with a closed tableau is a valid proof.  ... 
arXiv:2105.14706v2 fatcat:jxm5csv4z5clpc2dejqytaqtbi

Machine Learning Guidance and Proof Certification for Connection Tableaux [article]

Michael Färber, Cezary Kaliszyk, Josef Urban
2018 arXiv   pre-print
Then, we show two guidance methods based on machine learning, namely reordering of proof steps with Naive Bayesian probablities, and expansion of a proof search tree with Monte Carlo Tree Search.  ...  Connection calculi allow for very compact implementations of goal-directed proof search.  ...  Monte Carlo Proof Search In this section, we describe how to expand a proof search tree using Monte Carlo Tree Search (MCTS).  ... 
arXiv:1805.03107v3 fatcat:6aaytx66ujd7djk423fowfwcfe

Machine Learning Guidance for Connection Tableaux

Michael Färber, Cezary Kaliszyk, Josef Urban
2020 Journal of automated reasoning  
Then, we show two guidance methods based on machine learning, namely reordering of proof steps with Naive Bayesian probabilities, and expansion of a proof search tree with Monte Carlo Tree Search.  ...  Connection calculi allow for very compact implementations of goal-directed proof search.  ...  Monte Carlo Tree Search Monte Carlo Tree Search (MCTS) is a method to search potentially infinite trees by sampling random tree paths (called simulations) [17] .  ... 
doi:10.1007/s10817-020-09576-7 pmid:33678931 pmcid:PMC7900060 fatcat:ipgat65s4rfivp4myeuyhqvk4u

Defining and Mining Functional Dependencies in Probabilistic Databases [article]

Sushovan De, Subbarao Kambhampati
2010 arXiv   pre-print
We propose a pruning-based exact algorithm to evaluate the confidence of functional dependencies, a Monte-Carlo based algorithm to evaluate the confidence of approximate functional dependencies and algorithms  ...  Monte Carlo methods have been used in probabilistic databases before, for example, [6] uses Monte Carlo methods to give top-k results for queries on probabilistic databases.  ...  Proof. Suppose the pFD holds on a certain possible world of D. The pattern tableau would then cause certain tuples to be eliminated from consideration.  ... 
arXiv:1005.4714v2 fatcat:l6ssz27exbgwvbtw3yaeu2bgm4

Towards Finding Longer Proofs [article]

Zsolt Zombori, Adrián Csiszárik, Henryk Michalewski, Cezary Kaliszyk, Josef Urban
2021 arXiv   pre-print
We use several simple, structured datasets with very long proofs to show that FLoP can successfully generalise a single training proof to a large class of related problems.  ...  On these benchmarks, FLoP is competitive with strong theorem provers despite using very limited search, due to its ability to solve problems that are prohibitively long for other systems.  ...  A distinctive feature of all these systems is that they rely heavily on an external search procedure, such as Monte Carlo Tree Search [25] , or the search engine of the guided prover.  ... 
arXiv:1905.13100v2 fatcat:ynksh52rrrc2hjuywsnr7pbtam

Clifford recompilation for faster classical simulation of quantum circuits

Hammam Qassim, Joel J. Wallman, Joseph Emerson
2019 Quantum  
In this paper, we describe an improved Monte Carlo algorithm for performing randomized sparsification.  ...  The recompilation routine also facilitates numerical search for Clifford decompositions of products of non-Clifford gates, which can further reduce the runtime in certain cases by reducing the 1-norm of  ...  Set ω ← (a il /|a il |)ω; 8 Output |z = b 1 wU C U H |s . 9 end Monte-Carlo method.  ... 
doi:10.22331/q-2019-08-05-170 fatcat:bkd4vub24bc4bjxljtlmrktycy

Clifford recompilation for faster classical simulation of quantum circuits [article]

Hammam Qassim, Joel J. Wallman, Joseph Emerson
2019 arXiv   pre-print
In this paper, we describe an improved Monte Carlo algorithm for performing randomized sparsification.  ...  The recompilation routine also facilitates numerical search for Clifford decompositions of products of gates, which can further reduce the runtime in certain cases.  ...  Monte-Carlo method.  ... 
arXiv:1902.02359v1 fatcat:ournojwfgba67nefm3ybzrxpia

A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving [article]

Maxwell Crouse, Ibrahim Abdelaziz, Bassem Makni, Spencer Whitehead, Cristina Cornelio, Pavan Kapanipathi, Kavitha Srinivas, Veronika Thost, Michael Witbrock, Achille Fokoue
2020 arXiv   pre-print
Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search.  ...  Closer to TRAIL are the approaches described in (Kaliszyk et al. 2018; Zombori, Urban, and Brown 2020) where RL is combined with Monte-Carlo tree search for theorem proving in FOL.  ...  intelligent proof search.  ... 
arXiv:1911.02065v3 fatcat:zkajly2mnzeaxfn7dr3ma72vpe

Page 386 of None Vol. 34, Issue 1743 [page]

1890 None  
386 MONTE CARLO.  ...  From all of which it will be seen that Monte Carlo is at the very acme of its pros- perity, besides being a synonyme for ease, comfort, and luxury.  ... 

The Winnability of Klondike Solitaire and Many Other Patience Games [article]

Charlie Blake, Ian P. Gent
2019 arXiv   pre-print
Statistics were calculated using R. 22 Experimental Setup Monte Carlo methods using pseudo-random generation were used to create instances of each game.  ...  Because we prioritise giving proofs of unwinnability, we allocate 10% of the original time-limit for a streamlined search and if that fails to prove the game winnable, we allocate the original timelimit  ... 
arXiv:1906.12314v3 fatcat:4cp2plsb6bglbpcc3et6w2oh5q

Construction of weakly CUD sequences for MCMC sampling

Seth D. Tribble, Art B. Owen
2008 Electronic Journal of Statistics  
In Markov chain Monte Carlo (MCMC) sampling considerable thought goes into constructing random transitions. But those transitions are almost always driven by a simulated IID sequence.  ...  Quasi-Monte Carlo In quasi-Monte Carlo sampling, one does not simulate randomness. Instead one picks points that are more uniform than random points would be. Here we sketch QMC sampling.  ...  Then we describe quasi-Monte Carlo sampling (QMC) and use it to define CUD and weakly CUD sequences.  ... 
doi:10.1214/07-ejs162 fatcat:bigx4ij5bbflbkzh6rnd5h7xpq
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