Acta Informatica最新文献

{"title":"Simple linear time algorithm for sorting strings in omega-order with applications","authors":"Ruixi Luo,&nbsp;Taikun Zhu,&nbsp;Kai Jin","doi":"10.1007/s00236-026-00530-5","DOIUrl":"10.1007/s00236-026-00530-5","url":null,"abstract":"<div><p>We present a simple linear time algorithm for the following sorting problem: Given <i>n</i> words <span>(A_1,ldots ,A_n)</span>, find a permutation <span>({pi _1,ldots ,pi _n})</span> of <span>(1,ldots ,n)</span> so that <span>((A_{pi _1})^omega le ldots le (A_{pi _n})^omega)</span>, where <span>((A)^omega)</span> denotes the infinitely repeating string <span>(AAAldots)</span>. Let <i>L</i> denote the total length of the given strings. We note that the running time of our algorithm is <i>O</i>(<i>L</i>) even if the size of alphabet is beyond <i>O</i>(1). We also present an <span>(O(L+n log n))</span> time algorithm for the restricted model where we are only allowed to compare symbols. In other words, the main result of this paper is that the time complexity of sorting <span>(A_1,ldots, A_n)</span> in omega-order is the same as that of sorting them in lexicographic order under all common models (bounded alphabet, unbounded alphabet, compare-based model). Our main results find applications in related problems such as rearranging and concatenating given words so that the result is lexicographically smallest or largest.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-026-00530-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737774","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":"A lazy and modular approach to int-blasting","authors":"Max Barth,&nbsp;Matthias Heizmann,&nbsp;Jochen Hoenicke","doi":"10.1007/s00236-026-00529-y","DOIUrl":"10.1007/s00236-026-00529-y","url":null,"abstract":"<div><p>Bit-vector operations are ubiquitous in programming languages and formal verification, but their complex semantics pose challenges for SMT solvers. Although bit-blasting—translating bit-vectors to Boolean variables—is widely used, it struggles with arithmetic bit-vector operations on large bit-widths (e.g., 64-bit or 256-bit variables) due to exponential blowup. Int-blasting, which maps bit-vectors to integer arithmetic, offers a scalable alternative for arithmetic bit-vector operations, but introduces many modulo operations of which some are redundant. This article presents a modular three-step translation from bit-vector formulas to integer formulas, designed to keep the amount of modulo operations low, while preserving correctness. In the first step, we translate bit-vector operations to integer operations. Thereby, we introduce the two functions <span>(texttt {bv2nat})</span> and <span>(texttt {nat2bv}_k)</span> as explicit operators in the SMT-LIB theory of bit-vectors. Each integer operation is wrapped by <span>(texttt {bv2nat})</span> and <span>(texttt {nat2bv}_k)</span>. Hence, the sort of all bit-vector terms is preserved. Therefore, the first translation step is an equivalence transformation. In the second step, we simplify the formula by replacing the composition <span>(texttt {bv2nat} circ texttt {nat2bv}_k)</span> with a modulo operation. These modulo operations are added lazily, i.e., if the modulo does not change the result of the operation, it is omitted. In our experiments this reduced the average amount of modulo operations by 51%. In the third step, we introduce lemmas to precisely capture the meaning of <span>(texttt {bv2nat})</span> and <span>(texttt {nat2bv}_k)</span>. We prove that these lemmas suffice to solve bit-vector formulas. Furthermore, we illustrate that these lemmas are also sufficient for bit-vector formulas with quantifiers, arrays and uninterpreted functions. We implement our translation in <span>SMTInterpol</span> and evaluate it on 19570 SMT-LIB benchmarks. Results show that our lazy int-blasting solves 15% more tasks than an eager int-blasting, with 35% faster average runtime and 12% lower memory usage.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-026-00529-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147643135","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":"Graphs of order n with exactly (n+1) complementarity eigenvalues","authors":"S. Pirzada,&nbsp;Pawan Kumar,&nbsp; Merajuddin","doi":"10.1007/s00236-026-00527-0","DOIUrl":"10.1007/s00236-026-00527-0","url":null,"abstract":"<div><p>This work explores the complementarity spectrum <span>(Pi (G))</span> of a graph <i>G</i>. Previous studies have established that for a graph of order <i>n</i>, the complementarity spectrum satisfies <span>(|Pi (G)| ge n)</span>, with equality holding only for elementary graphs. This implies that any non-elementary graph of order <i>n</i> has at least <span>(n+1)</span> distinct complementarity eigenvalues. In this article, we focus on connected graphs of order <i>n</i> that admit exactly <span>(n+1)</span> complementarity eigenvalues. We characterize this class by examining the structural features responsible for such spectral behavior. For instance, we show that any graph of sufficiently large order in this family induces exactly one subgraph of order <span>(n-1)</span> that also belongs to the same family. Furthermore, we demonstrate that graphs in this class are uniquely determined by their complementarity spectra, emphasizing the potential of complementarity eigenvalues in graph identification where traditional spectral methods may fall short.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642652","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":"New orientable sequences","authors":"Chris J. Mitchell,&nbsp;Peter R. Wild","doi":"10.1007/s00236-026-00528-z","DOIUrl":"10.1007/s00236-026-00528-z","url":null,"abstract":"<div><p>Orientable sequences of order <i>n</i> are infinite periodic sequences with symbols drawn from a finite alphabet of size <i>k</i> with the property that any tuple of <i>n</i> elements or its reverse occurs at most once as a contiguous subsequence (i.e. a substring or factor) in a period. They were introduced in the early 1990s in the context of possible applications in position sensing. Bounds on the period of such sequences and a range of methods of construction have been devised, although apart from very small cases a significant gap remains between the largest known period for such a sequence and the best known upper bound. In this paper we first give improved upper bounds on the period of such sequences. We then give a new general method of construction for orientable sequences involving subgraphs of the de Bruijn graph with special properties, and describe two different approaches for generating such subgraphs. This enables us to construct orientable sequences with periods meeting the improved upper bounds when <i>n</i> is 2 or 3, as well as <span>(n=4)</span> and <i>k</i> odd. For <span>(4le nle 8)</span>, in some cases the sequences produced by the methods described have periods larger than for any previously known sequences.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-026-00528-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560552","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":"On the change of Seidel energy of the tripartite Turán graph T(n, 3) by an edge embedding","authors":"Masood Ur Rehman,&nbsp;Muhammad Ajmal,&nbsp;Gaixiang Cai","doi":"10.1007/s00236-026-00526-1","DOIUrl":"10.1007/s00236-026-00526-1","url":null,"abstract":"<div><p>The Seidel energy of a simple and undirected graph <span>(Gamma)</span>, denoted by <span>(SE(Gamma ))</span>, is the sum of the absolute values of the eigenvalues of the Seidel matrix <span>(S(Gamma ))</span> of <span>(Gamma)</span>. The Seidel energy is a valuable tool for analyzing the structural properties of networks. This paper investigates how this energy changes when the topology of a graph is locally perturbed by embedding a new edge. We focus on the tripartite Turán graph <i>T</i>(<i>n</i>, 3), a model of extremal network connectivity. When an edge <span>(e=u_1u_2)</span> is embedded in the tripartite Turán graph <span>(T(8,3)cong K_{{u_1,u_2},{v_1,v_2,v_3},{w_1,w_2,w_3}})</span>, then <span>(SE(T(8,3)+e)approx 16.9282 &lt; SE(T(8,3))approx 17.2111)</span>. It is proved that except for <i>T</i>(8, 3), the Seidel energy of the tripartite Turán graph <i>T</i>(<i>n</i>, 3) with order at least 8 is always increased when an edge is embedded. This result has implications for dynamically understanding the sensitivity and stability of network descriptors.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559307","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":"Space separating special geffert normal form for succinct representation of star-controlled insertion-deletion systems","authors":"Henning Fernau,&nbsp;Lakshmanan Kuppusamy,&nbsp;Indhumathi Raman","doi":"10.1007/s00236-026-00524-3","DOIUrl":"10.1007/s00236-026-00524-3","url":null,"abstract":"<div><p>Graph-controlled insertion-deletion (GCID) systems are regulated extensions of insertion-deletion systems. At AFL 2023, <i>star-controlled</i> GCID system was introduced as a restriction of GCID systems. Such a system has several components and each component contains some insertion-deletion rules. The components are the vertices of a directed control graph, whose arcs describe how strings can move between components. A rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule. The language of the system is the set of all terminal strings collected in the final component. In this paper, we impose the restriction in the structure of the underlying graph to be a star structure where there is a central, control component which acts like a master and transmits a string (after applying one of its rules) to one of the components specified in the applied rule. A component which receives the string can process the obtained string with any applicable rule available in it and sends back the resultant string only to the center component. In this restricted GCID, where there is a special component, namely, a <i>central</i> component that will process the string and then send it to any other component that processes another step and then send the string back to the central component. With this restriction, here we obtain three new, different computational completeness results for some typical descriptional complexity measures, hence sharpening the Pareto frontier of this type of grammar. These results are crucially based on a variant of Special Geffert normal form (SGNF) of type-0 grammars, that we called space separating SGNF in a paper that appeared in <i>Natural Computing</i> in 2019.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336815","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":"Structure of finite maximal prefix codes with constant average length 4","authors":"Haiyan Liu,&nbsp;Rongdong Cui,&nbsp;Shunyong Yu,&nbsp;Xin Wang","doi":"10.1007/s00236-026-00525-2","DOIUrl":"10.1007/s00236-026-00525-2","url":null,"abstract":"<div><p>In this paper, we give the structure of finite maximal prefix codes over binary alphabet with constant average length 4, and prove that the families of finite maximal prefix codes are divided into 217 classes. In addition, some finite maximal prefix codes with constant average length greater than or equal to 5 are found, conduct a preliminary exploration of the case.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342683","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":"Fast algorithms for window accumulated subsequence matching problem","authors":"Zdenek Tronicek","doi":"10.1007/s00236-026-00523-4","DOIUrl":"10.1007/s00236-026-00523-4","url":null,"abstract":"<div><p>A subsequence of a string <i>T</i> is any string that can be obtained by removing zero or more symbols from <i>T</i>. The paper deals with the Window Accumulated Subsequence matching Problem (WASP), which is defined as follows: Given two strings, the text <i>T</i> and the pattern <i>P</i>, and a positive integer <i>w</i>, the window size, find the number of size <i>w</i> substrings of <i>T</i> that contain <i>P</i> as a subsequence. Three algorithms for this problem are introduced: a bit-parallel approach, an algorithm preprocessing the pattern, and an algorithm preprocessing the text. The bit-parallel approach outperforms the state-of-the-art algorithm, and the other two algorithms outperform the bit-parallel approach for small alphabets, short patterns, and windows that are not much larger than the pattern. Furthermore, a preprocessing of the text that solves WASP for a fixed window size and each possible pattern of a given size is described. This is beneficial when we are to solve WASP for a single text and multiple patterns, because when the text is preprocessed, a solution is provided promptly.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342230","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":"Deterministic tree-walking-storage automata","authors":"Martin Kutrib,&nbsp;Uwe Meyer","doi":"10.1007/s00236-026-00522-5","DOIUrl":"10.1007/s00236-026-00522-5","url":null,"abstract":"<div><p>We introduce and investigate tree-walking-storage automata, which are finite-state devices equipped with a tree-like storage. The automata are generalized stack automata, where the linear stack storage is replaced by a non-linear tree-like stack. Therefore, tree-walking-storage automata have the ability to explore the interior of the tree storage without altering the contents, where the possible moves of the tree pointer correspond to those of tree-walking automata. In addition, a tree-walking-storage automaton can append (push) non-existent descendants to a tree node and remove (pop) leaves from the tree. As for classical stack automata, we also consider non-erasing and checking variants. As a first step to investigate these models we consider the computational capacities of deterministic one-way variants. In particular, a primary focus lies on comparing the different variants of tree-walking-storage automata as well as with classical stack automata, enabling us to draw a complete picture. Basic closure properties of the induced families of languages are shown. In particular, we consider Boolean operations and several AFL operations.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-026-00522-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341742","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":"Reconstruction of SMT proofs with Lambdapi","authors":"Alessio Coltellacci,&nbsp;Bruno Andreotti,&nbsp;Haniel Barbosa,&nbsp;Gilles Dowek,&nbsp;Stephan Merz","doi":"10.1007/s00236-025-00515-w","DOIUrl":"10.1007/s00236-025-00515-w","url":null,"abstract":"<div><p>The Alethe format has been adopted by several SMT solvers for explaining why a set of constraints is unsatisfiable. We describe how to interpret Alethe proof traces and generate corresponding proofs that are accepted by the Lambdapi proof checker, a foundational proof assistant based on dependent type theory and rewriting that is intended to serve as a pivot for exchanging proofs between interactive proof assistants. We give an overview of the encoding of SMT logic and of Alethe proof traces in Lambdapi and present results of the evaluation of the checker on benchmark examples.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341099","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}