[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83266-en":3,"doc-seo-83266-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83266,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","On Computing Minimum Wheeler DFA From Their Language","Wheeler automata generalize the Burrows–Wheeler Transform and support optimal linear-time pattern matching on compressed labeled graphs, making the computation of a minimum equivalent Wheeler DFA a valuable indexing strategy. While Problem 1 is known PSPACE-hard for nondeterministic inputs, existing DFA-focused methods either handle only acyclic topologies or are prohibitively slow for general graphs. This work introduces the first near-optimal, linearithmic output-sensitive algorithm for general DFAs, preserving acyclic-level efficiency while ensuring full generality.","arXiv :2607 .07563v 1 [ cs .DS] 8 Jul 2026  \nOn Computing Minimum Wheeler DFA From Their Language  \nRuben Becker \\#  Ca’ Foscari University of Venice, Italy Davide Cenzato \\#  Ca’ Foscari University of Venice, Italy Nicola Prezza \\#  Ca’ Foscari University of Venice, Italy Daniel Puttini \\#  Ca’ Foscari University of Venice, Italy  \n~~ Abstract ~~  \nWheeler automata have recently emerged as a powerful generalization of the Burrows-Wheeler Transform, enabling optimal linear-time pattern matching on compressed labeled graphs—a task that is otherwise computationally hard. Consequently, when an automaton recognizes a Wheeler language (i.e., it is equivalent to some Wheeler automaton), computing its minimum equivalent Wheeler DFA is a powerful indexing strategy. This problem is particularly relevant in computational pangenomics, where pangenome graphs frequently recognize Wheeler languages.  \nHowever, constructing the minimum Wheeler DFA for a Wheeler language has remained a computational bottleneck. The problem is known to be PSPACE-hard for nondeterministic inputs. When the input is a DFA, state-of-the-art solutions forced a compromise: they were either fast but limited to acyclic DFAs (Alanko et al., SODA 2020) or capable of handling general topologies but prohibitively slow (D’Agostino et al., TCS 2023) . In this work, we bridge this gap with the first algorithm solving the problem for general DFAs in near-optimal, linearithmic output-sensitive time. By matching the efficiency of acyclic-only solutions while retaining full generality, our approach improves upon the previous general solution by at least a quadratic factor. We demonstrate the practical impact of our algorithm on real-world pangenome graphs; our tool achieves a processing throughput of over 105 transitions per second on a standard workstation, enabling the construction of a provably optimal pattern matching data structure in such applications.  \n2012 ACM Subject Classification Theory of computation → Design and analysis of algorithms; Information systems → Data compression  \nKeywords and phrases Wheeler Automata, Minimum DFA, Pangenomics, Pattern Matching  \nFunding Funded by the European Union (ERC, REGINDEX, 101039208) . Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.  \nR. Becker, D. Cenzato, N. Prezza, and D. Puttini 1  \n 1  Introduction  \nPattern matching lies at the heart of computer science, but while we have mastered it on strings, much work remains to be done on labeled graphs. As Equi et al. [9] proved, pattern matching on general labeled graphs can likely not be solved in strongly subquadratic time; asa result, even basic pattern-matching-related tasks can quickly become prohibitively expensive depending on graph topology and size. This algorithmic bottleneck has long slowed down progress in data-intensive fields like bioinformatics, where pangenomics requires aligning millions of sequencing reads against complex graph-structured collections of genomes.  \nWheeler automata, introduced by Gagie et al. [11], side-step the lower bound of Equiet al. [9] by imposing a specific structural constraint: informally speaking, their states can be totally sorted according to the co-lexicographic order of the strings labeling the paths reaching them. In the (simpler) case of Wheeler DFA, this means that u \u003C v in Wheeler order for any two states u, v if and only if all (possibly, left-infinite) strings labeling paths entering in u are co-lexicographically smaller than those labeling paths entering in v. This seemingly simple ordering property unlocks a “best-of-both-worlds” scenario: it generalizes the celebrated Burrows-Wheeler Transform (BWT) [4] from linear strings to complex graphs, enabling pattern matching in optimal constant time per character—just ","cbCaipZZ4PNm9Q1U","https://ap.wps.com/l/cbCaipZZ4PNm9Q1U","pdf",775573,4,1,26,"English","en",105,"# Introduction\n## State of the Art","[{\"question\":\"What does the document aim to solve regarding Wheeler automata?\",\"answer\":\"It targets Problem 1: given the minimum DFA D that accepts a Wheeler language L, compute the minimum equivalent Wheeler DFA Dw that also accepts L.\"},{\"question\":\"Why is computing a minimum Wheeler DFA considered challenging?\",\"answer\":\"The paper notes PSPACE-hardness for nondeterministic inputs and that previous DFA methods either restrict to acyclic DFAs or become prohibitively slow on general topologies, creating a computational bottleneck.\"},{\"question\":\"What improvement does the proposed algorithm provide over prior work?\",\"answer\":\"The algorithm solves the problem for general DFAs in near-optimal, linearithmic output-sensitive time, matching the efficiency of acyclic-only approaches while retaining full generality and improving prior general solutions by at least a quadratic 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does the document aim to solve regarding Wheeler automata?","Question",{"text":75,"@type":76},"It targets Problem 1: given the minimum DFA D that accepts a Wheeler language L, compute the minimum equivalent Wheeler DFA Dw that also accepts L.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is computing a minimum Wheeler DFA considered challenging?",{"text":80,"@type":76},"The paper notes PSPACE-hardness for nondeterministic inputs and that previous DFA methods either restrict to acyclic DFAs or become prohibitively slow on general topologies, creating a computational bottleneck.",{"name":82,"@type":73,"acceptedAnswer":83},"What improvement does the proposed algorithm provide over prior work?",{"text":84,"@type":76},"The algorithm solves the problem for general DFAs in near-optimal, linearithmic output-sensitive time, matching the efficiency of acyclic-only approaches while retaining full generality and improving prior general solutions by at least a quadratic 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