[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84952-en":3,"doc-seo-84952-105":29,"detail-sidebar-cat-0-en-105":91},{"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":13,"seo_description":14,"update_tm":27,"read_time":28},84952,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","A Simple Algorithmic Framework for Disambiguation of Finite Automata","Studies the task of disambiguation of finite state automata, converting a given automaton into an equivalent unambiguous one. Proposes a novel, simple algorithmic framework that generalizes subset construction for determinization while satisfying key properties: it leaves the automaton unchanged if already unambiguous, computes successor states on-the-fly, and constructs each new state in polynomial time, ensuring overall polynomial runtime in the output size. Also introduces partial disambiguation via alternative state-construction criteria, covering finitely and polynomially ambiguous automata, and extends the framework to weighted automata.","arXiv :2607 .06894v2 [ cs .FL] 11 Jul 2026  \nA simple algorithmic framework for disambiguation of finite automata  \nMauricio Cari \\#   \nPontificia Universidad Católica de Chile, Chile  \nMillennium Institute for Foundational Research on Data, Chile Martín Muñoz \\#   \nUniv. Artois, CNRS, UMR 8188, Centre de Recherche en Informatique de Lens (CRIL), F-62300 Lens, France; Pontificia Universidad Católica de Chile & Millennium Institute for Foundational Research on Data (IMFD), Chile  \nCristian Riveros \\#   \nPontificia Universidad Católica de Chile, Chile  \nMillennium Institute for Foundational Research on Data, Chile  \n~~ Abstract ~~  \nWe study the task of disambiguation of finite state automata, namely, converting an automaton into an equivalent, unambiguous one. We do this by developing a novel and simple algorithmic framework that generalizes the subset construction for determinization, and that satisfies some desirable properties: (1) it preserves the original automaton if it was already unambiguous,(2) it computes the successor states on-the-fly and (3) computes each new state in polynomial time—this last point is crucial as it guarantees that the running time is polynomial in the size of the output automaton. Then, we show how to apply this framework for partial disambiguation: by changing the criterion that builds the new states, we develop algorithms for different levels of ambiguity, namely, finitely ambiguous, and polynomially ambiguous automata. These algorithms also satisfy condition (1) for their respective levels, and also (2) and (3) . Finally, we show that the disambiguation framework can easily be extended to other models of automata like weighted automata.  \n2012 ACM Subject Classification Theory of computation → Automata extensions  \nKeywords and phrases Algorithmic automata theory, unambiguous automata models, degree of ambiguity, determinization, disambiguation, weighted automata.  \nFunding The work of Cari and Riveros was supported by ANID Fondecyt Regular project 1230935 and ANID – Millennium Science Initiative Program – Code ICN17  002.  \n 1  Introduction  \nAutomata theory is today one of the main areas of theoretical computer science, studying computational models with restricted resources and having applications in different areas of computer science. For these applications, finding automata models with good algorithmic properties is a crucial task, and determinism is probably the most well-known condition for reaching them. For example, deterministic finite automata are efficiently closed under several operations (i.e., with a polynomial-size output); the evaluation problem can be efficiently computed; equivalence and containment problems are tractable (and intractable in general) [43]; the number of states can be efficiently minimized [22]; and learning can be efficiently performed in an active setting [6], among other results [37] .  \nIn practice, systems employ non-deterministic automata models that are common in user applications. These are, in general, exponentially more succinct than their deterministic counterparts, but unfortunately do not possess such good algorithmic properties. To address this problem, systems typically rely on determinizing non-deterministic models; that is, converting a non-deterministic finite automaton into a deterministic one. The subset construction, introduced by Rabin and Scott [38], is the most used and best-known determinization procedure,  \n2 A simple algorithmic framework for disambiguation of finite automata  \nin which non-determinism is simulated by maintaining subsets of states. Although the output of determinizing the automata could have up to exponential size [33], the subset construction has the advantage that it is simple and easy to implement, and can be computed on-the-fly (i.e., only the necessary part of the determinization is expanded) . Indeed, this is probably the reason why the procedure is used so extensively (see, e.g., [21, 16 , 1 , 39 , 8]) . As a","cbCaicXIvPWSpeLS","https://ap.wps.com/l/cbCaicXIvPWSpeLS","pdf",813443,1,39,"English","en",105,"# Introduction\n# A simple algorithmic framework for disambiguation of finite automata","[{\"question\":\"What is the disambiguation problem for finite automata addressed in the document?\",\"answer\":\"It focuses on transforming an automaton into an equivalent one that is unambiguous, meaning each input has at most one successful run.\"},{\"question\":\"What properties does the proposed disambiguation framework guarantee?\",\"answer\":\"It preserves the original automaton when it is already unambiguous, computes successor states on-the-fly, and constructs each new state in polynomial time so the runtime stays polynomial in the output size.\"},{\"question\":\"How does the framework support partial disambiguation?\",\"answer\":\"By changing the criterion used to build new states, the document derives algorithms for different ambiguity levels, including finitely ambiguous and polynomially ambiguous automata, while maintaining the preservation property for the corresponding 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is the disambiguation problem for finite automata addressed in the document?","Question",{"text":75,"@type":76},"It focuses on transforming an automaton into an equivalent one that is unambiguous, meaning each input has at most one successful run.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What properties does the proposed disambiguation framework guarantee?",{"text":80,"@type":76},"It preserves the original automaton when it is already unambiguous, computes successor states on-the-fly, and constructs each new state in polynomial time so the runtime stays polynomial in the output size.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the framework support partial disambiguation?",{"text":84,"@type":76},"By changing the criterion used to build new states, the document derives algorithms for different ambiguity levels, including finitely ambiguous and polynomially ambiguous automata, while maintaining the preservation property for the corresponding 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