[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118083-en":3,"doc-seo-118083-105":30,"detail-sidebar-cat-0-en-105":84},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118083,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","Machine Learning for Function Synthesis - Doctor of Philosophy Thesis","Function synthesis is the automatic construction of functions that satisfy a given specification, where both function space and specification format vary across application domains. This thesis focuses on satisfiability modulo theories, synthesising mathematical expressions that conform to abstract logical formulas used in computer-aided verification. A core difficulty is the combinatorial explosion of candidate expressions as size grows. The thesis tests the hypothesis that machine learning can make synthesis more tractable, by learning search guidance and enabling new synthesis approaches in restricted domains like ranking function synthesis.","Machine Learning for Function Synthesis  \nJulian Parsert St. Catherine’s College  \nUniversity of Oxford  \nA thesis submitted for the degree of Doctor of Philosophy  \nTrinity 2024  \nAcknowledgements  \nFirst, I would like to thank my supervisors Daniel Kröning and Tom Melham for their guidance and support throughout my studies. Their advice on research, writing, and other matters has been invaluable.  \nI want to thank Daniel Kröning in particular, for having impeccable foresight with regard to the COVID-19 pandemic and providing precious advice. In hindsight, I can say without a doubt, that his advice has led to me being able to enjoy a quality of life during the pandemic that would have been inaccessible otherwise. I am forever thankful for that.  \nI am also thankful to my colleagues in Oxford and Edinburgh for the countless insightful discussions and ideas. In particular, I want to thank my collaborators Mirco Giacobbe and Elizabeth Polgreen. I genuinely enjoyed working with you and I believe that I learned a lot from that experience.  \nSimilarly, I want to thank Aart Middeldorp, Vincent van Oostrom, Christian Sternagel, and the Computational Logic group in Innsbruck as a whole for many interesting discussions throughout the years. In particular, I want to point out that the logic course that I attended in 2015 was one of the best courses I have ever attended and is certainly in no small part responsible for my research interests.  \nWhen I started my bachelor’s degree in 2014 I would have never imagined that I would end up pursuing a doctorate degree. I am certain there is nobody that I have to thank more for introducing me to research in computer science than Cezary Kaliszyk. I am thankful for all professional advice that Cezary provided but also the countless and sometimes long (Google Maps tells me our longest discussion took at least 9 hours) discussions about computer science, mathematics, life, the universe, and everything. When attending Cezary’s functional programming course in 2015 I did not expect this to be the beginning of a beautiful friendship. It is safe to say that my life would look very different if I had not been fortunate enough to meet Cezary.  \nFinally, last but not least, I want to thank my friends and family for providing motivation and sometimes necessary distractions. It is thanks to you that I was able to conduct my research while simultaneously pursuing other endeavours in life.  \nAbstract  \nFunction synthesis is the process of automatically constructing functions that satisfy a given specification. The space of functions as well as the format of the specifications vary greatly with each area of application. In this thesis, we consider synthesis in the context of satisfiability modulo theories. Within this domain, the goal is to synthesise mathematical expressions that adhere to abstract logical formulas. These types of synthesis problems find many applications in the field of computer-aided verification. One of the main challenges of function synthesis arises from the combinatorial explosion in the number of potential candidates within a certain size. The hypothesis of this thesis is that machine learning methods can be applied to make function synthesis more tractable.  \nThe first contribution of this thesis is a Monte-Carlo based search method for function synthesis. The search algorithm uses machine learned heuristics to guide the search. This is part of a reinforcement learning loop that trains the machine learning models with data generated from previous search attempts. To increase the set of benchmark problems to train and test synthesis methods, we also present a technique for generating synthesis problems from pre-existing satisfiability modulo theories problems. We implement the Monte-Carlo based synthesis algorithm and evaluate it on standard synthesis benchmarks as well as our newly generated benchmarks. An experimental evaluation shows that the learned heuristics greatly improve on the","cbCaiuaLzPRDb3Qp","https://ap.wps.com/l/cbCaiuaLzPRDb3Qp","pdf",1101791,1,201,"English","en",105,"# Acknowledgements\n# Abstract\n## Monte-Carlo guided function synthesis\n## Learning to rank functions for termination\n# Preface\n## Contributions to co-authored works","[{\"question\":\"What is the second contribution and what is it used for?\",\"answer\":\"The thesis presents a technique for synthesising ranking functions using neural networks, including a framework named Neural Termination Analysis. Neural training replaces direct expression synthesis, and symbolic reasoning is then used to verify that the resulting function is a correct ranking function.\"}]","Machine Learning for Function Synthesis - Doctor of Philosophy Thesis | PDF",1785681434,507,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":79,"head_meta":81,"extra_data":83,"updated_unix":28},"machine-learning-for-function-synthesis-doctor-of-philosophy-thesis","",{"@graph":36,"@context":78},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-for-function-synthesis-doctor-of-philosophy-thesis/118083/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-02",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"What is the second contribution and what is it used for?","Question",{"text":76,"@type":77},"The thesis presents a technique for synthesising ranking functions using neural networks, including a framework named Neural Termination Analysis. 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