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s; (3) a definition of linear temporal logic (LTL) modulo $A$ that generalizes Vardi's construction of alternating B\\\"uchi automata from LTL, using (2) to go from LTL modulo $A$ to $NBW_A$ via $ABW_A$. Finally, we present a combination of LTL modulo $A$ with extended regular expressions modulo $A$ that generalizes the Property Specification Language (PSL). Our combination allows regex complement, that is not supported in PSL but can be supported naturally by using symbolic transition terms. ","authors":[{"id":"53f4746adabfaedf4367c985","name":"Margus Veanes"},{"id":"5604111c45cedb33962ea075","name":"Thomas Ball"},{"id":"63734ad2ec88d95668d689f4","name":"Gabriel Ebner"},{"id":"53f4540ddabfaedd74e24c76","name":"Olli Saarikivi"}],"create_time":"2023-10-05T04:47:50.029Z","hashs":{"h1":"saorm","h3":"t"},"id":"651e1c973fda6d7f0688cc08","num_citation":0,"pdf":"https:\u002F\u002Fcz5waila03cyo0tux1owpyofgoryroob.aminer.cn\u002F8F\u002F9C\u002FB8\u002F8F9CB8C1FF14CD4F60B9C23BA97EE5A1.pdf","title":"Symbolic Automata: $\\omega$-Regularity Modulo Theories","urls":["https:\u002F\u002Farxiv.org\u002Fabs\u002F2310.02393"],"venue":{},"versions":[{"id":"651e1c973fda6d7f0688cc08","sid":"2310.02393","src":"arxiv","year":2023},{"id":"6578e58e939a5f408285d372","sid":"W4387389677","src":"openalex","vsid":"S4306400194","year":2023}],"year":2023},{"abstract":" We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline's main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f. Online training on these unproved theorems increases accuracy to 82.6%. With a similar computational budget, we improve the state of the art on the Lean-based miniF2F-curriculum dataset from 31% to 42% proving accuracy. ","authors":[{"id":"5e6f670601caee42d84018b1","name":"Guillaume Lample","org":"Facebook","orgid":"5f71b6ff1c455f439fe5be2b","orgs":["Facebook"]},{"id":"562de57c45ce1e5967b2bfcf","name":"Marie-Anne Lachaux"},{"id":"63791099d49364c9ac9b3982","name":"Thibaut Lavril"},{"id":"650aaa038a47b61c50bbb733","name":"Xavier Martinet"},{"id":"5631c86745cedb3399f1e1ad","name":"Amaury Hayat","org":"ENPC","orgid":"5f71b2891c455f439fe3c8de","orgs":["ENPC"]},{"id":"63734ad2ec88d95668d689f4","name":"Gabriel Ebner"},{"id":"650aaa25768b11dc729d3c31","name":"Aurélien Rodriguez"},{"id":"637235b1ec88d95668cbaef2","name":"Timothée Lacroix"}],"create_time":"2022-05-24T13:48:36.958Z","hashs":{"h1":"hpsnt","h3":"p"},"id":"628c4ce65aee126c0ff59f85","keywords":["theorem proving","automated theorem proving","MCTS","reasoning","AI for math"],"lang":"en","num_citation":45,"pdf":"https:\u002F\u002Fcz5waila03cyo0tux1owpyofgoryroob.aminer.cn\u002F9E\u002FC1\u002FF7\u002F9EC1F77290893EE3E9F0C74DDEB7F809.pdf","pdf_src":["https:\u002F\u002Farxiv.org\u002Fpdf\u002F2205.11491"],"title":"HyperTree Proof Search for Neural Theorem Proving","update_times":{"u_c_t":"2024-01-02T11:41:12.58Z"},"urls":["db\u002Fconf\u002Fnips\u002Fneurips2022.html#LampleLLRHLEM22","http:\u002F\u002Fpapers.nips.cc\u002Fpaper_files\u002Fpaper\u002F2022\u002Fhash\u002Fa8901c5e85fb8e1823bbf0f755053672-Abstract-Conference.html","https:\u002F\u002Fopenreview.net\u002Fforum?id=J4pX8Q8cxHH","https:\u002F\u002Farxiv.org\u002Fabs\u002F2205.11491"],"versions":[{"id":"628c4ce65aee126c0ff59f85","sid":"2205.11491","src":"arxiv","year":2022},{"id":"63a413f690e50fcafd6d1855","sid":"neurips2022#3655","src":"conf_neurips","year":2022},{"id":"6479e3acd68f896efa4e5162","sid":"conf\u002Fnips\u002FLampleLLRHLEM22","src":"dblp","year":2022},{"id":"6578c529939a5f4082552cbd","sid":"W4281489448","src":"openalex","vsid":"journals\u002Fcorr","year":2022},{"id":"63d7ae8290e50fcafdacd5e5","sid":"journals\u002Fcorr\u002Fabs-2205-11491","src":"dblp","vsid":"journals\u002Fcorr","year":2022}],"year":2022},{"abstract":" The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have developed a number of tools for the library which check proof developments for subtle mistakes in the code and generate documentation suited for our varied audience. ","authors":[{"id":"562d0a1f45cedb3398d3728d","name":"van Doorn Floris","org":"University of Pittsburgh,,,Pittsburgh,,USA","orgid":"5f71b2941c455f439fe3cd53","orgs":["University of Pittsburgh,,,Pittsburgh,,USA"]},{"id":"63734ad2ec88d95668d689f4","name":"Ebner Gabriel","org":"Vrije Universiteit Amsterdam,,,Amsterdam,,The Netherlands","orgid":"5f71b29b1c455f439fe3d06e","orgs":["Vrije Universiteit Amsterdam,,,Amsterdam,,The Netherlands"]},{"id":"53f451a4dabfaec09f1f49ee","name":"Lewis Robert Y.","org":"Vrije Universiteit Amsterdam,,,Amsterdam,,The Netherlands","orgid":"5f71b29b1c455f439fe3d06e","orgs":["Vrije Universiteit Amsterdam,,,Amsterdam,,The Netherlands"]}],"create_time":"2020-04-09T13:00:33.055Z","doi":"10.1007\u002F978-3-030-53518-6_16","hashs":{"h1":"mlfm"},"id":"5e8ef2ae91e011679da0f076","issn":"0302-9743","num_citation":8,"pages":{"end":"267","start":"251"},"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F20\u002F2004\u002F2004.03673.pdf","pdf_src":["https:\u002F\u002Farxiv.org\u002Fpdf\u002F2004.03673"],"title":"Maintaining a Library of Formal Mathematics","update_times":{"u_a_t":"2020-07-04T14:06:04.986Z","u_v_t":"2021-01-10T15:06:15.048Z"},"urls":["https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1007\u002F978-3-030-53518-6_16","https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Fmkm\u002FDoornEL20","http:\u002F\u002Fui.adsabs.harvard.edu\u002Fabs\u002F2020arXiv200403673V\u002Fabstract","https:\u002F\u002Fdoi.org\u002F10.1007\u002F978-3-030-53518-6_16","db\u002Fjournals\u002Fcorr\u002Fcorr2004.html#abs-2004-03673","https:\u002F\u002Fwww.narcis.nl\u002Fpublication\u002FRecordID\u002Foai%3Aresearch.vu.nl%3Apublications%2F10b611dd-105b-435b-b267-5da1d0dc5e01","https:\u002F\u002Farxiv-export-lb.library.cornell.edu\u002Fabs\u002F2004.03673","https:\u002F\u002Farxiv.org\u002Fabs\u002F2004.03673","http:\u002F\u002Fdx.doi.org\u002F10.1007\u002F978-3-030-53518-6_16","https:\u002F\u002Fdblp.uni-trier.de\u002Fdb\u002Fjournals\u002Fcorr\u002Fcorr2004.html#abs-2004-03673"],"venue":{"info":{"name":"CICM"},"volume":"abs\u002F2004.03673"},"venue_hhb_id":"5ea1c0e5edb6e7d53c00df86","versions":[{"id":"5e8ef2ae91e011679da0f076","sid":"2004.03673","src":"arxiv","year":2020},{"id":"5f1d5adf91e0119e7bbb7500","sid":"conf\u002Fmkm\u002FDoornEL20","src":"dblp","vsid":"conf\u002Fmkm","year":2020},{"id":"5ff68bc1d4150a363cd041d8","sid":"3100204936","src":"mag","vsid":"0#dblp#journals\u002Fcorr","year":2020},{"id":"62193af25aee126c0fc659c0","sid":"10.1007\u002F978-3-030-53518-6_16","src":"crossref","year":2020},{"id":"6456478ad68f896efae27c53","sid":"journals\u002Fcorr\u002Fabs-2004-03673","src":"dblp","year":2020},{"id":"655f78c3939a5f4082ca5bea","sid":"10.1007\u002F978-3-030-53518-6_16","src":"acm","year":2020},{"id":"65774a1b939a5f40826e6ca1","sid":"W3100204936","src":"openalex","vsid":"conf\u002Fmkm","year":2020},{"id":"621de3265aee126c0faf123b","sid":"10.1007\u002F978-3-030-53518-6_16","src":"springer","vsid":"mkm","year":2020}],"year":2020},{"abstract":"We describe a new method to constructivize proofs based on Herbrand disjunctions by giving a practically effective algorithm that converts (some) classical first-order proofs into intuitionistic proofs. Together with an automated classical first-order theorem prover such a method yields an (incomplete) automated theorem prover for intuitionistic logic. Our implementation of this prover approach, Slakje, performs competitively on the ILTP benchmark suite for intuitionistic provers: it solves 1674 out of 2670 problems (1290 proofs and 384 claims of non-provability) with Vampire as a backend, including 800 previously unsolved problems.","authors":[{"email":"gebner@gebner.org","id":"63734ad2ec88d95668d689f4","name":"Gabriel Ebner","org":"TU WIEN","orgid":"5f71b47e1c455f439fe4a5e1","orgs":["TU Wien, Vienna, Austria"]}],"citations":{"google_citation":0},"create_time":"2019-08-24T13:01:12.234Z","doi":"10.1007\u002F978-3-030-29026-9_20","hashs":{"h1":"hcait","h3":"p"},"id":"5d610c393a55ac9ed9d7ef4a","issn":"0302-9743","num_citation":1,"pages":{"end":"373","start":"355"},"title":"Herbrand Constructivization for Automated Intuitionistic Theorem Proving.","update_times":{"u_a_t":"2020-04-13T08:56:41.767Z","u_c_t":"2020-07-06T08:01:41.537Z","u_v_t":"2019-12-04T04:00:12.172Z"},"urls":["https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1007\u002F978-3-030-29026-9_20","http:\u002F\u002Fwww.webofknowledge.com\u002F","https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Ftableaux\u002FEbner19","https:\u002F\u002Fdoi.org\u002F10.1007\u002F978-3-030-29026-9_20"],"venue":{"info":{"name":"TABLEAUX"},"issue":"","volume":"11714"},"venue_hhb_id":"5ea1b88cedb6e7d53c00ce2f","versions":[{"id":"5d610c393a55ac9ed9d7ef4a","sid":"conf\u002Ftableaux\u002FEbner19","src":"dblp","vsid":"conf\u002Ftableaux","year":2019},{"id":"5db928c947c8f766461e4b10","sid":"2969536091","src":"mag","vsid":"1183852906","year":2019},{"id":"64d4bfd13fda6d7f06f25170","sid":"WOS:000711904000020","src":"wos","year":2019},{"id":"655f45ff939a5f4082a75ca8","sid":"10.1007\u002F978-3-030-29026-9_20","src":"acm","year":2019},{"id":"6218fddb5aee126c0f29c3b6","sid":"10.1007\u002F978-3-030-29026-9_20","src":"crossref","vsid":"conf\u002Ftableaux","year":2019},{"id":"621de45c5aee126c0fb79dd4","sid":"10.1007\u002F978-3-030-29026-9_20","src":"springer","vsid":"tableaux","year":2019}],"year":2019},{"abstract":"We present a new and efficient algorithm to translate proofs generated by resolution-based automated theorem provers into expansion proofs—a formalism for Herbrand disjunctions for non-prenex formulas. In contrast to previous approaches, this algorithm supports definitionintroducing structural clausification and Avatar-style splitting inferences.","authors":[{"id":"63734ad2ec88d95668d689f4","name":"Gabriel Ebner"}],"create_time":"2023-01-14T02:34:31.933Z","hashs":{"h1":"eetrp","h3":"sd"},"id":"5f0e08cc9fced0a24b7a02ab","num_citation":0,"title":"Extracting expansion trees from resolution proofs with splitting and definitions ?","urls":["https:\u002F\u002Fsemanticscholar.org\u002Fpaper\u002F2424f344637259ed9cc382c6036c96c852d9d25f"],"venue":{},"versions":[{"id":"5f0e08cc9fced0a24b7a02ab","sid":"2424f344637259ed9cc382c6036c96c852d9d25f","src":"semanticscholar"}],"year":2018},{"abstract":"Inductive theorem proving based on tree grammars was introduced in [9]. In this approach, proofs with induction on natural numbers are found by generalizing automatically generated proofs of finite instances on the level of Herbrand disjunctions. We extend this method to support general inductive data types, and reasoning modulo a background theory to abstract from irregularities in automatically generated proofs. We present an experimental implementation of the method and show that it automatically produces non-analytic induction formulas for several examples.","authors":[{"id":"63734ad2ec88d95668d689f4","name":"Gabriel Ebner"},{"name":"Stefan Hetzl"}],"create_time":"2023-01-25T07:30:23.634Z","hashs":{"h1":"tgiid","h3":"tmet"},"id":"5f0e94bf9fced0a24b60ee84","num_citation":0,"title":"Tree grammars for induction on inductive data types modulo equational theories ?","urls":["https:\u002F\u002Fsemanticscholar.org\u002Fpaper\u002Fa5c67d99d83642aeb54c34f9494dce2b086b4681"],"venue":{},"versions":[{"id":"5f0e94bf9fced0a24b60ee84","sid":"a5c67d99d83642aeb54c34f9494dce2b086b4681","src":"semanticscholar"}],"year":2018},{"abstract":"Totally rigid acyclic tree grammars (TRATGs) are an emerging grammatical formalism with numerous applications in proof theory and automated reasoning. We determine the computational complexity of several decision problems on TRATGs: membership, containment, disjointness, equivalence, minimization, and the complexity of minimal cover with a fixed number of nonterminals. We relate non-parametric minimal cover to a problem on regular word grammars of unknown complexity.","authors":[{"id":"53f43201dabfaeb2ac024d1d","name":"Sebastian Eberhard","org":"TU Wien, Vienna, Austria","orgid":"5f71b2dd1c455f439fe3ecd2","orgs":["TU Wien, Vienna, Austria"]},{"email":"gebner@gebner.org","id":"63734ad2ec88d95668d689f4","name":"Gabriel Ebner","org":"TU Wien, Vienna, Austria","orgid":"5f71b2dd1c455f439fe3ecd2","orgs":["TU Wien, Vienna, Austria"]},{"email":"stefan.hetzl@tuwien.ac.at","id":"53f479ccdabfaefedbbb912c","name":"Stefan Hetzl","org":"TU Wien, Vienna, Austria","orgid":"5f71b2dd1c455f439fe3ecd2","orgs":["TU Wien, Vienna, Austria"]}],"create_time":"2024-01-17T18:23:27.73Z","doi":"10.1007\u002F978-3-319-98654-8_24","hashs":{"h1":"cdptr","h3":"atg"},"id":"5bbacb4c17c44aecc4eac82d","issn":"0302-9743","num_citation":1,"pages":{"end":"303","start":"291"},"title":"Complexity of Decision Problems on Totally Rigid Acyclic Tree Grammars","urls":["http:\u002F\u002Fwww.webofknowledge.com\u002F","db\u002Fconf\u002Fdlt\u002Fdlt2018.html#EberhardEH18","https:\u002F\u002Fdoi.org\u002F10.1007\u002F978-3-319-98654-8_24","http:\u002F\u002Fdx.doi.org\u002F10.1007\u002F978-3-319-98654-8_24"],"venue":{"info":{"name":"DLT"},"volume":"11088"},"versions":[{"id":"5bbacb4c17c44aecc4eac82d","sid":"conf\u002Fdlt\u002FEberhardEH18","src":"dblp","year":2018},{"id":"6218af8d5aee126c0f6956cf","sid":"10.1007\u002F978-3-319-98654-8_24","src":"crossref"},{"id":"64d4c62a3fda6d7f06f762f4","sid":"WOS:000905585400024","src":"wos"},{"id":"5bbacb4c17c44aecc4eac82d","sid":"10.1007\u002F978-3-319-98654-8_24","src":"springer","vsid":"dlt","year":2018}],"year":2018},{"authors":[{"id":"63734ad2ec88d95668d689f4","name":"Gabriel Ebner"},{"id":"53f448f5dabfaee1c0af762d","name":"Matthias Schlaipfer"}],"citations":{"google_citation":1,"last_citation":1},"create_time":"2018-12-24T10:16:58.41Z","doi":"","hashs":{"h1":"etscp","h3":"ndp"},"id":"5c20b21ada5629702063b31e","isbn":"","issn":"","lang":"en","num_citation":19,"num_wos_citation":0,"pages":{"end":"33","start":"17"},"retrieve_info":{},"title":"Efficient Translation of Sequent Calculus Proofs Into Natural Deduction Proofs.","update_times":{"u_a_t":"2019-09-20T10:32:02.127Z","u_c_t":"2023-03-27T13:07:14.269Z","u_v_t":"2023-03-18T08:39:09.529Z"},"urls":["https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Fcade\u002FEbnerS18","http:\u002F\u002Fceur-ws.org\u002FVol-2162\u002Fpaper-03.pdf"],"venue":{"info":{"name":"PAAR@FLoC"},"issue":"","type":0,"volume":""},"venue_hhb_id":"5ebad2e6edb6e7d53c105668","versions":[{"id":"5c20b21ada5629702063b31e","sid":"conf\u002Fcade\u002FEbnerS18","src":"dblp","vsid":"conf\u002Fcade","year":2018},{"id":"5c757d9ef56def9798b01f02","sid":"2891688494","src":"mag","vsid":"2898186791","year":2018},{"id":"6228aa445aee126c0f525dbb","sid":"W2891688494","src":"openalex","vsid":"conf\u002Fcade","year":2018}],"year":2018}],"profilePubsTotal":16,"profilePatentsPage":0,"profilePatents":null,"profilePatentsTotal":null,"profilePatentsEnd":false,"profileProjectsPage":1,"profileProjects":{"success":true,"msg":"","data":null,"log_id":"2d6xct6ULkGCDQyCFnspVEM2njy"},"profileProjectsTotal":0,"newInfo":null,"checkDelPubs":[]}};