{"title":"Complexity of the emptiness problem for graph-walking automata and for tilings with star subgraphs","authors":"Olga Martynova","doi":"10.1016/j.ic.2023.105127","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105127","url":null,"abstract":"<div><p>This paper proves the decidability<span> of the emptiness problem for two models which recognize finite graphs: graph-walking automata<span>, and tilings of graphs by star subgraphs (star automata). Furthermore, it is proved that the non-emptiness problem for graph-walking automata (that is, whether a given automaton accepts at least one graph) is NEXP-complete. For star automata, which generalize nondeterministic tree automata to the case of graphs, it is proved that their non-emptiness problem is NP-complete.</span></span></p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"296 ","pages":"Article 105127"},"PeriodicalIF":1.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138490275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Realizability problem for constraint LTL","authors":"Ashwin Bhaskar, M. Praveen","doi":"10.1016/j.ic.2023.105126","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105126","url":null,"abstract":"<div><p>Constraint linear-time temporal logic (CLTL) is an extension of LTL<span> that is interpreted on sequences of valuations of variables over an infinite domain. Atomic formulas can constrain valuations over a range of positions along a sequence, with the range being bounded by a parameter depending on the formula. The satisfiability and model checking problems for CLTL have been studied before. We consider the realizability problem for CLTL. The set of variables is partitioned into two parts, with each part controlled by a player. Players take turns to choose valuations for their variables, generating a sequence of valuations. The winning condition is specified by a CLTL formula — the first player wins if the sequence of valuations satisfies the specified formula. We prove that checking whether the first player has a winning strategy in the realizability game for a given CLTL formula is undecidable in general and identify decidable fragments.</span></p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"296 ","pages":"Article 105126"},"PeriodicalIF":1.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138454326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Choosing the right algorithm with hints from complexity theory","authors":"Shouda Wang , Weijie Zheng , Benjamin Doerr","doi":"10.1016/j.ic.2023.105125","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105125","url":null,"abstract":"<div><p>Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm in a certain broad class of black-box optimizers can give fruitful indications in which direction to search for good established heuristics. We demonstrate this approach on the recently proposed DLB benchmark. Our finding that the unary unbiased black-box complexity is only <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> suggests the Metropolis algorithm as an interesting candidate and we prove that it solves the DLB problem in quadratic time. We also prove that better runtimes cannot be obtained in the class of unary unbiased algorithms. We therefore shift our attention to algorithms that use the information of more parents to generate new solutions and find that the significance-based compact genetic algorithm can solve the DLB problem in time <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"296 ","pages":"Article 105125"},"PeriodicalIF":1.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540123001281/pdfft?md5=8b4268eeef641099a096e9ad52fb7722&pid=1-s2.0-S0890540123001281-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138471961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Succinct data structure for path graphs","authors":"Girish Balakrishnan , Sankardeep Chakraborty , N.S. Narayanaswamy , Kunihiko Sadakane","doi":"10.1016/j.ic.2023.105124","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105124","url":null,"abstract":"<div><p><span>We consider the problem of designing a succinct data structure for </span><em>path graphs</em><span>, that generalizes interval graphs, on </span><em>n</em> vertices while efficiently supporting degree, adjacency, and neighbourhood queries. We provide the following two solutions for this problem:</p><ul><li><span>1.</span><span><p>an <span><math><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>+</mo><mi>o</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>-bit succinct data structure that supports adjacency query in <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> time, neighbourhood query in <span><math><mi>O</mi><mo>(</mo><mi>d</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> time and finally, degree query in <span><math><mi>min</mi><mo></mo><mo>{</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo></mo><mi>n</mi><mo>)</mo><mo>,</mo><mi>O</mi><mo>(</mo><mi>d</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo><mo>}</mo></math></span> time where <em>d</em> is the degree of the queried vertex.</p></span></li><li><span>2.</span><span><p>an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo></mo><mi>n</mi><mo>)</mo></math></span>-bit space-efficient data structure that supports adjacency, neighborhood, and degree queries optimally.</p></span></li></ul> Central to our data structures is the usage of the heavy path decomposition, followed by careful bookkeeping using an orthogonal range search data structure using wavelet trees among others, which may be of independent interest for designing succinct data structures for other graph classes.</div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"296 ","pages":"Article 105124"},"PeriodicalIF":1.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138436395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Special Issue: Selected papers of the 15th International Conference on Language and Automata Theory and Applications, LATA 2021","authors":"Carlos Martín-Vide , Bianca Truthe","doi":"10.1016/j.ic.2023.105101","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105101","url":null,"abstract":"","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105101"},"PeriodicalIF":1.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138396444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Clustering categorical data: Soft rounding k-modes","authors":"Surya Teja Gavva, Karthik C. S., Sharath Punna","doi":"10.1016/j.ic.2023.105115","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105115","url":null,"abstract":"<div><p><span><span>Over the last three decades, researchers have intensively explored various clustering tools for categorical data analysis. Despite the proposal of various </span>clustering algorithms, the classical </span><em>k</em><span>-modes algorithm remains a popular choice for unsupervised learning of categorical data. Surprisingly, our first insight is that in a natural generative block model, the </span><em>k</em><span>-modes algorithm performs poorly for a large range of parameters. We remedy this issue by proposing a soft rounding variant of the </span><em>k</em>-modes algorithm (<span>SoftModes</span>) and theoretically prove that our variant addresses the drawbacks of the <em>k</em><span>-modes algorithm in the generative model. Finally, we empirically verify that </span><span>SoftModes</span> performs well on both synthetic and real-world datasets.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"296 ","pages":"Article 105115"},"PeriodicalIF":1.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138430813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the codewords of generalized Reed-Muller codes reaching the fourth weight","authors":"Somayyeh Golalizadeh, Nasrin Soltankhah","doi":"10.1016/j.ic.2023.105113","DOIUrl":"10.1016/j.ic.2023.105113","url":null,"abstract":"<div><p>Recently, the fourth weight of generalized Reed-Muller codes <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>a</mi><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>b</mi><mo>,</mo><mi>m</mi><mo>)</mo></math></span> have been characterized for <span><math><mn>3</mn><mo>≤</mo><mi>b</mi><mo><</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> and <span><math><mn>0</mn><mo>≤</mo><mi>a</mi><mo>≤</mo><mi>m</mi><mo>−</mo><mn>3</mn></math></span>. In this paper, we study the codewords reaching the fourth weight of generalized Reed-Muller codes. We will determine the fourth weight codewords of generalized Reed-Muller codes of order <span><math><mi>r</mi><mo>=</mo><mi>a</mi><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>b</mi></math></span> with <span><math><mn>3</mn><mo>≤</mo><mi>b</mi><mo><</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> and <span><math><mn>0</mn><mo>≤</mo><mi>a</mi><mo>≤</mo><mi>m</mi><mo>−</mo><mn>3</mn></math></span>. Also, we characterize the number of fourth weight codewords of <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>,</mo><mi>m</mi><mo>)</mo></math></span> for <span><math><mn>3</mn><mo>≤</mo><mi>b</mi><mo><</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"296 ","pages":"Article 105113"},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135714908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Early detection of temporal constraint violations","authors":"Isaac Mackey, Raghubir Chimni, Jianwen Su","doi":"10.1016/j.ic.2023.105114","DOIUrl":"10.1016/j.ic.2023.105114","url":null,"abstract":"<div><p>Software systems rely on events for logging, coordination, handling unusual situations, and more. Monitoring event streams from systems that provide services can ensure the service complies with policies, regulations, and other business rules. Notably, monitoring to detect violations of rules <em>as early as possible</em> is much desired as, for example, the service may reclaim more resources from erring enactments. The primary goal of this paper is to develop techniques for detecting violations of time constraints as early as possible. We formalize a model for events and a language to specify constraints on event timing and data. We develop algorithms to detect violations of individual rules, then use a chase process to detect violations of acyclic sets of rules. We also present optimization techniques to reduce monitoring overhead. Finally, we implement and evaluate our algorithms through experiments to demonstrate our approach is feasible and beneficial.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"296 ","pages":"Article 105114"},"PeriodicalIF":1.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540123001177/pdfft?md5=dc2ca9342303f3541f2eb14baf55a8eb&pid=1-s2.0-S0890540123001177-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exchange of indivisible goods under matroid constraints","authors":"Jinshan Zhang , Bo Tang , Jianwei Yin","doi":"10.1016/j.ic.2023.105110","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105110","url":null,"abstract":"<div><p><span>We study the problem of reallocating indivisible goods among a set of strategic agents by generalizing the original Sharpley-Scarf market to the setting where an object can be allocated to multiple agents but subject to an associated </span><em>matroid</em><span> constraint. We refer to this modified market as the matroid Sharpley-Scarf market. For this general market, we present a Pareto-optimal, individually rational and group strategy-proof mechanism. Our mechanism is simple and natural generalization of the </span><em>Top Trading Cycle</em> mechanism and the <em>Serial Dictator</em> mechanism. In our analysis, we demonstrate that the weak core may be absent in the matroid Sharpley-Scarf market, while a relaxed version called the constrained core does exist. Furthermore, we extend the concept called <em>competitive equilibrium</em> to the matroid Sharpley-Scarf market and show that an allocation is a competitive equilibrium if and only if it can be produced by our mechanism.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105110"},"PeriodicalIF":1.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91987326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Martin Berglund , Henrik Björklund , Johanna Björklund , Adrien Boiret
{"title":"Transduction from trees to graphs through folding","authors":"Martin Berglund , Henrik Björklund , Johanna Björklund , Adrien Boiret","doi":"10.1016/j.ic.2023.105111","DOIUrl":"https://doi.org/10.1016/j.ic.2023.105111","url":null,"abstract":"<div><p>We introduce a fold operation that realises a tree-to-graph transduction by merging selected nodes in the input tree to form a possibly cyclic output graph. The work is motivated by the increasing use of graph-based representations in semantic parsing. We show that a suitable class of graphs languages can be generated by applying the fold operation to regular unranked tree languages. We investigate two versions of the fold operation, one that preserves a depth-first ordering between the edges, and one that does not. Finally, we demonstrate that the time complexity for the associated non-uniform membership problem is solvable in polynomial time for the order-preserving version, and NP-complete for the order-cancelling one.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105111"},"PeriodicalIF":1.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540123001141/pdfft?md5=167ecdf3a6847b5285a2c38d7cd109b1&pid=1-s2.0-S0890540123001141-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92096542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}