[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-272225-105":59,"doc-detail-272225-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","evaluation-of-ssat-by-reduction-to-decision-diagrams","Evaluation of SSAT by reduction to decision diagrams","","Stochastic satisfiability (SSAT) addresses search and reasoning tasks expressed as quantified Boolean formulas, potentially incorporating randomness and stochasticity. As a PSPACE-complete problem, SSAT generalises NP-complete SAT and plays a central role in computational complexity, computer science, and artificial intelligence. The thesis studies explicit construction and minimisation of decision diagrams to solve SSAT, focusing on binary decision diagrams and sentential decision diagrams.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/evaluation-of-ssat-by-reduction-to-decision-diagrams/272225/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/evaluation-of-ssat-by-reduction-to-decision-diagrams/272225.png","ImageObject",300,407,{"name":92,"@type":93},"Taylor Morgan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does SSAT address?","Question",{"text":113,"@type":114},"SSAT solves search and reasoning problems formulated as quantified Boolean formulas, where randomness and stochasticity may be present.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Why are decision diagrams relevant to this thesis?",{"text":118,"@type":114},"Binary decision diagrams (BDDs) and sentential decision diagrams (SDDs) are canonical representations of Boolean formulas, and the thesis applies explicit construction and minimisation of these structures for SSAT solving.",{"name":120,"@type":111,"acceptedAnswer":121},"How do the proposed algorithms compare in efficiency?",{"text":122,"@type":114},"An SDD-based implementation is generally more efficient than a BDD-based one, but both are often less efficient than leading SSAT solvers erSSAT and ClauSSat; in some test cases, the new algorithms perform better and more reliably.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},272225,1789463834,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Aalto University School of Science  \nMaster’s Programme in Computer, Communication and Information Sciences  \nOskari Ojala  \nEvaluation ofSSAT by reduction to decision diagrams  \nMaster’s Thesis  \nEspoo, July 31, 2022  \nSupervisor: Professor Jussi Rintanen, Aalto University  \nAdvisor: Professor Jussi Rintanen  \nAalto University School of Science  \nMaster’s Programme in Computer, Communication and ABSTRACT OF  \nInformation Sciences MASTER’S THESIS  \n\n| Author: Oskari Ojala\u003Cbr>Title:\u003Cbr>Evaluation of SSAT by reduction to decision diagrams |\n| --- |\n| Date: July 31, 2022 Pages: 63 |\n| Major: Computer Science Code: SCI3042 |\n| Supervisor: Professor Jussi Rintanen\u003Cbr>Advisor: Professor Jussi Rintanen |\n| Stochastic satisfiability (SSAT) is a relatively new concept of solving search and reasoning problems in the form of quantified Boolean formulas, including a possible amount of randomness and stochasticity. SSAT is a complete problem belonging to the computational complexity class PSPACE. It is a generalisation of the NP-complete SAT problem, a fundamental concept in computer science and artificial intelligence. Binary decision diagrams and their generalisations sentential decision diagrams are canonical representations of propositional knowledge bases, also referred to as Boolean formulas. It is known that the evaluation of any typeof satisfiability problem either implicitly or explicitly constructs a binary decision tree-like execution path. Although subproblems of SSAT and decision diagram representations of Boolean logic are widely studied, decision diagrams have not yet been explicitly applied to SSAT solving. The aim of this thesis is to study the potential of this explicit construction and minimisation of decision diagramsand propose new algorithms for SSAT solving.\u003Cbr>We have proven the correctness and rules for universal and complete SSAT evaluation algorithms for BDD and SDD, and implemented corresponding minimisation procedures for both data structures. Our results show that an SDD-based implementation is generally more efficient than a BDD-based one, but both are generally less efficient than the best known SSAT solvers erSSAT and ClauSSat that utilise modern pruning and learning techniques. Yet, in some test cases, our algorithms were more efficient and reliable than erSSAT and ClauSSat. Most of the computational resources were spent on the construction and minimisation of the data structures. Improving the efficiency of construction and minimisation procedures is a key for further computational optimisation. |\n| Keywords: artificial intelligence, SSAT, Binary Decision Diagrams, Sentential Decision Diagrams, automated reasoning, quantified Boolean formulas |\n| Language: English |\n\nAalto-yliopisto  \nPerustieteiden korkeakoulu  \nTieto-, tietoliikenne-ja informaatiotekniikan maisteriohjelma  \nDIPLOMITY¨ON TIIVISTELM¨A  \n\n| Tekija¨: Oskari Ojala\u003Cbr>Tyo¨n nimi:\u003Cbr>SSAT-ongelmien ratkaiseminen pa¨a¨to¨sdiagrammien avulla |\n| --- |\n| Pa¨iva¨ys: 31. heina¨kuuta 2022 Sivuma¨a¨ra¨: 63 |\n| Pa¨a¨aine: Tietotekniikka Koodi: SCI3042 |\n| Valvoja: Professori Jussi Rintanen\u003Cbr>Ohjaaja: Professori Jussi Rintanen |\n| Stokastinen toteutuvuus (SSAT) on suhteellisen uusi tapa ratkaista kvantifioiduiksi Boolen loogisiksi lausekkeiksi muotoiltuja haku-ja pa¨a¨ttelyongelmia, jotka voivat sisa¨lta¨a¨ myo¨s satunnaisuutta ja stokastisuutta. SSAT kuuluu laskennalliselta kompleksisuudeltaan luokkaan PSPACE, ja on PSPACE-ta¨ydellinen, eli silla¨ voidaan esitta¨a¨ kaikki kyseisen kompleksisuusluokan ongelmat. SSAT on yleistys NP-ta¨ydellisesta¨ SAT-toteutuvuusongelmasta, joka kuuluu tietotekniikan ja tekoa¨lytutkimuksen keskeisiin perusteisiin. Bina¨a¨riset pa¨a¨to¨sdiagrammit (BDD) ja niiden yleistykset lausekkeelliset pa¨a¨to¨sdiagrammit (SDD), ovat loogisten lausekkeiden luonnollisia kuvauksia. Tiedeta¨a¨n, etta¨ minka¨ tahansa toteutuvuusongelman ratkaiseminen rakentaa suorituspolun, joka joko implisiittisestitai eksplisiittisesti vastaa bina¨a¨","cbCaiv5SJxEe757r","https://ap.wps.com/l/cbCaiv5SJxEe757r","pdf",586711,63,"English","# Abstract\n## Background and motivation\n## Decision diagrams for SSAT\n## Results and efficiency considerations\n## Computational bottlenecks and future work","[{\"question\":\"What problem does SSAT address?\",\"answer\":\"SSAT solves search and reasoning problems formulated as quantified Boolean formulas, where randomness and stochasticity may be present.\"},{\"question\":\"Why are decision diagrams relevant to this thesis?\",\"answer\":\"Binary decision diagrams (BDDs) and sentential decision diagrams (SDDs) are canonical representations of Boolean formulas, and the thesis applies explicit construction and minimisation of these structures for SSAT solving.\"},{\"question\":\"How do the proposed algorithms compare in efficiency?\",\"answer\":\"An SDD-based implementation is generally more efficient than a BDD-based one, but both are often less efficient than leading SSAT solvers erSSAT and ClauSSat; in some test cases, the new algorithms perform better and more reliably.\"}]","Evaluation of SSAT by reduction to decision diagrams | PDF",159]