Theoretical Computer Science最新文献

{"title":"On the difference set of two transductions","authors":"","doi":"10.1016/j.tcs.2024.114780","DOIUrl":"10.1016/j.tcs.2024.114780","url":null,"abstract":"<div><p>The difference set <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> of two (nondeterministic, in general) transducers <span><math><mi>s</mi><mo>,</mo><mi>t</mi></math></span> is the set of all input words for which the output sets of the two transducers are not equal. When the two transducers realize homomorphisms, their difference set is the complement of the well known equality set of the two homomorphisms. However, we show that transducer difference sets result in Chomsky-like classes of languages that are different than the classes resulting from equality sets. We also consider the following word problem: given transducers <span><math><mi>s</mi><mo>,</mo><mi>t</mi></math></span> and input <em>w</em>, tell whether the output sets <span><math><mi>s</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></span> and <span><math><mi>t</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></span> are different. In general the problem is <strong>PSPACE</strong>-complete, but it becomes <strong>NP</strong>-complete when at least one of the given transducers has finite outputs. We also provide a PRAX (polynomial randomized approximation) algorithm for the word problem as well as for the NFA (in)equivalence problem. Our presentation of PRAX algorithms improves the original presentation.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142011471","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":"Intrinsic universality in automata networks II: Glueing and gadgets","authors":"","doi":"10.1016/j.tcs.2024.114779","DOIUrl":"10.1016/j.tcs.2024.114779","url":null,"abstract":"<div><p>An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. This paper is the second of a series about intrinsic universality, i.e. the ability for a family of AN to simulate arbitrary AN. We develop a proof technique to establish intrinsic simulation and universality results which is suitable to deal with families of symmetric networks where connections are non-oriented. It is based on an operation of glueing of networks, which allows to produce complex orbits in large networks from compatible pseudo-orbits in small networks. As an illustration, we give a short proof that the family of networks where each node obeys the rule of the ‘game of life’ cellular automaton is strongly universal. In the third paper of the series, we heavily rely on this proof technique to show intrinsic universality results of various families with particular update schedules.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142011473","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":"Finding the largest separating rectangle among two point sets","authors":"","doi":"10.1016/j.tcs.2024.114778","DOIUrl":"10.1016/j.tcs.2024.114778","url":null,"abstract":"<div><p>Given a set <em>R</em> of <em>n</em> red points and a set <em>B</em> of <em>m</em> blue points, we study the problem of finding a rectangle that contains all the red points, the minimum number of blue points and has the maximum area. We call such a rectangle a <em>maximum-area separating rectangle</em> (MSR). We first address the planar, axis-aligned (2D) version, and present an <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>log</mi><mo>⁡</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> time, <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> space algorithm. The running time reduces to <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> if the points are pre-sorted by one of the coordinates. We also consider the planar arbitrary orientation version, in which the MSR is allowed to have arbitrary orientation. For this arbitrary orientation version, our algorithm takes <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time and <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> space. Finally, we address the 3D axis-aligned version, which asks for the <em>maximum-volume separating box</em> (MSB), i.e., the maximum-volume axis-aligned box containing all the red points and the fewest blue points. For this version, we give an algorithm that runs in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo><mo>)</mo></math></span> time and <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> space.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083665","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":"Playing Guess Who with your kids: Code-word strategy against adversaries","authors":"","doi":"10.1016/j.tcs.2024.114766","DOIUrl":"10.1016/j.tcs.2024.114766","url":null,"abstract":"<div><p>Guess Who is a two-player search game in which each player chooses a character from a deck of 24 cards, and has to infer the other player's character by asking yes-no questions. A simple binary search strategy allows the starting player find the opponent's character by asking 5 questions only, when the opponent is honest.</p><p>Real-life observations show that in more realistic scenarios, the game is played against adversaries that do not strictly follow the rules, e.g., kids. Such players might decide to answer all questions at once, answer only part of the questions as they do not know the answers to all, and even lie occasionally. We devise strategies for such scenarios using techniques from error-correcting and erasure codes. This connects to a recent line of work on search problems on graphs and trees with unreliable auxiliary information, and could be of independent interest.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006346","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":"Subtraction games in more than one dimension","authors":"","doi":"10.1016/j.tcs.2024.114775","DOIUrl":"10.1016/j.tcs.2024.114775","url":null,"abstract":"<div><p>This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966), with finite subtraction sets. In case of two move rulesets we find a complete solution, via a certain <span><math><mi>P</mi></math></span>-to-<span><math><mi>P</mi></math></span> principle (where <span><math><mi>P</mi></math></span> means that the previous player wins). Namely <span><math><mi>x</mi><mo>∈</mo><mi>P</mi></math></span> if and only if <span><math><mi>x</mi><mo>+</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>∈</mo><mi>P</mi></math></span>, where <em>a</em> and <em>b</em> are the two move options. Flammenkamp (1997) observed that, already in one dimension, rulesets with three moves can be hard to analyze, and still today his related conjecture remains open. Here, we solve instances of rulesets with three moves in two dimensions, and conjecture that they all have regular outcomes. Through several computer visualizations of outcomes of multi-move two-dimensional rulesets, we observe that they tend to partition the game board into periodic mosaics on very few regions/segments, which can depend on the number of moves in a ruleset. For example, we have found a five-move ruleset with an outcome segmentation into six semi-infinite slices. In this spirit, we develop a coloring automaton that generalizes the <span><math><mi>P</mi></math></span>-to-<span><math><mi>P</mi></math></span> principle. Given an initial set of colored positions, it quickly paints the <span><math><mi>P</mi></math></span>-positions in segments of the game board. Moreover, we prove that two-dimensional rulesets have row/column eventually periodic outcomes. We pose open problems on the generic hardness of two-dimensional rulesets; several regularity conjectures are provided, but we also conjecture that not all rulesets have regular outcomes.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S030439752400392X/pdfft?md5=3913c36a957868941fdf29ee1800ce1b&pid=1-s2.0-S030439752400392X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006347","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":"Replicated multistage interconnection networks: QoS evaluation for parallel and distributed computing","authors":"","doi":"10.1016/j.tcs.2024.114777","DOIUrl":"10.1016/j.tcs.2024.114777","url":null,"abstract":"<div><p>Introduction to big data becomes very important with dealing in high-performance parallel distributed computing, especially in those systems where communication among a number of processors is required. The current paper takes into consideration different topologies for the Shuffle Exchange Network (SEN) in order to attain optimal data transfer among such scenarios. SEN topologies are a key feature in connecting several processors and implementing the data transfer among them where a single processor fails to handle the load. The study hereby reports in the performance, reliability, and cost analysis of these topologies. These topologies, some of which are advocated to have better performance in many studies, include replicated networks. Our research demystifies claims made in earlier papers that replicated networks have inflated reliability and higher costs due to their additional links. Researchers are therefore guided on accurate performance data that will lead them to make optimum choices of SEN topologies for targeted applications. These findings further highlight that the trade-offs between reliability and cost must be carefully considered during network design so as to arrive at better results for big data communication and computation in parallel and distributed systems. This work provides important insights into the correct evaluation of SEN topologies, helping to correct the misleading facts and to have better network selection for various real-time application realizations.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006348","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":"Computational complexity of counting coincidences","authors":"","doi":"10.1016/j.tcs.2024.114776","DOIUrl":"10.1016/j.tcs.2024.114776","url":null,"abstract":"<div><p>Can you decide if there is a coincidence in the numbers counting two different combinatorial objects? For example, can you decide if two regions in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> have the same number of domino tilings? There are two versions of the problem, with <span><math><mn>2</mn><mo>×</mo><mn>1</mn><mo>×</mo><mn>1</mn></math></span> and <span><math><mn>2</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>1</mn></math></span> boxes. We prove that in both cases the coincidence problem is not in the polynomial hierarchy unless the polynomial hierarchy collapses to a finite level. While the conclusions are the same, the proofs are notably different and generalize in different directions.</p><p>We proceed to explore the coincidence problem for counting independent sets and matchings in graphs, matroid bases, order ideals and linear extensions in posets, permutation patterns, and the Kronecker coefficients. We also make a number of conjectures for counting other combinatorial objects such as plane triangulations, contingency tables, standard Young tableaux, reduced factorizations and the Littlewood–Richardson coefficients.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524003931/pdfft?md5=7678638db921f3cd70363b4dc17d17d4&pid=1-s2.0-S0304397524003931-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141964617","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 priority-proportional payments in financial networks","authors":"","doi":"10.1016/j.tcs.2024.114767","DOIUrl":"10.1016/j.tcs.2024.114767","url":null,"abstract":"<div><p>We study financial systems from a game-theoretic standpoint. A financial system is represented by a network, where nodes correspond to banks, and directed labeled edges correspond to debt contracts between them. The existence of cycles in the network indicates that a payment of a bank to one of its lenders might affect the bank's incoming payments. So, if a bank cannot fully repay its debt, then the exact payments it makes to each of its lenders can affect the cash inflow back to itself. We naturally assume that the banks are interested in their financial well-being (utility) which is aligned with the amount of incoming payments they receive from the network. This defines a game among the banks, that can be seen as utility-maximizing agents who strategize over their payments.</p><p>We introduce a class of financial network games that arise under some natural payment strategies called priority-proportional payments. We compute valid payment profiles for fixed payment strategies and we investigate existence and (in)efficiency of equilibrium strategies, under different variations of the game that capture several financial aspects that commonly arise in practice. We conclude with examining the computational complexity of a variety of related problems.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933734","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":"Linear time online algorithms for constructing linear-size suffix trie","authors":"","doi":"10.1016/j.tcs.2024.114765","DOIUrl":"10.1016/j.tcs.2024.114765","url":null,"abstract":"<div><p>The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a text string <em>T</em> of length <em>n</em> has <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> nodes and edges, and the string label of each edge is encoded by a pair of positions in <em>T</em>. Thus, even after the tree is built, the input string <em>T</em> needs to be kept stored and random access to <em>T</em> is still needed. The <em>linear-size suffix tries</em> (<em>LSTs</em>), proposed by Crochemore et al. [Linear-size suffix tries, TCS 638:171-178, 2016], are a “stand-alone” alternative to the suffix trees. Namely, the LST of an input text string <em>T</em> of length <em>n</em> occupies <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> total space, and supports pattern matching and other tasks with the same efficiency as the suffix tree without the need to store the input text string <em>T</em>. Crochemore et al. proposed an <em>offline</em> algorithm which transforms the suffix tree of <em>T</em> into the LST of <em>T</em> in <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>σ</mi><mo>)</mo></math></span> time and <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> space, where <em>σ</em> is the alphabet size. In this paper, we present two types of <em>online</em> algorithms which “directly” construct the LST, from right to left, and from left to right, without constructing the suffix tree as an intermediate structure. Both algorithms construct the LST incrementally when a new symbol is read, and do not access the previously read symbols. Both of the right-to-left construction algorithm and the left-to-right construction algorithm work in <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>σ</mi><mo>)</mo></math></span> time and <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> space. The main feature of our algorithms is that the input text string does not need to be stored.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141964616","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":"Diagnosability of labeled Dp-automata","authors":"","doi":"10.1016/j.tcs.2024.114743","DOIUrl":"10.1016/j.tcs.2024.114743","url":null,"abstract":"<div><p>In this paper, we formulate a notion of diagnosability for labeled weighted automata over a class of dioids which admit both positive and negative numbers as well as vectors. The weights can represent diverse physical meanings such as time elapsing and position deviations. We also develop an original tool called concurrent composition to verify diagnosability for such automata. These results are fundamentally new compared with the existing ones in the literature.</p><p>In a little more detail, <em>diagnosability</em> is characterized for a labeled weighted automaton <span><math><msup><mrow><mi>A</mi></mrow><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></msup></math></span> over a special dioid <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> called <em>progressive</em>, which can represent diverse physical meanings such as time elapsing and position deviations. In a progressive dioid, the canonical order is total, there is at least one <em>eventually dominant</em> element, there is no zero divisor, and the cancellative law is satisfied, where the functionality of an eventually dominant element <em>t</em> is to make every nonzero element <em>a</em> arbitrarily large by multiplying <em>a</em> by <em>t</em> for sufficiently many times. A notion of diagnosability is formulated for <span><math><msup><mrow><mi>A</mi></mrow><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></msup></math></span>. By developing a notion of <em>concurrent composition</em>, a necessary and sufficient condition is given for diagnosability of automaton <span><math><msup><mrow><mi>A</mi></mrow><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></msup></math></span>. It is proven that the problem of computing the concurrent composition for an automaton <span><math><msup><mrow><mi>A</mi></mrow><mrow><munder><mrow><mi>Q</mi></mrow><mo>_</mo></munder></mrow></msup></math></span> is <span><math><mi>NP</mi></math></span>-complete, then the problem of verifying diagnosability of <span><math><msup><mrow><mi>A</mi></mrow><mrow><munder><mrow><mi>Q</mi></mrow><mo>_</mo></munder></mrow></msup></math></span> is proven to be <span><math><mi>coNP</mi></math></span>-complete, where the <span><math><mi>NP</mi></math></span>-hardness and <span><math><mi>coNP</mi></math></span>-hardness results even hold for deterministic, deadlock-free, and divergence-free automaton <span><math><msup><mrow><mi>A</mi></mrow><mrow><munder><mrow><mi>N</mi></mrow><mo>_</mo></munder></mrow></msup></math></span>, where <span><math><munder><mrow><mi>Q</mi></mrow><mo>_</mo></munder></math></span> and <span><math><munder><mrow><mi>N</mi></mrow><mo>_</mo></munder></math></span> are the max-plus dioids having elements in <span><math><mi>Q</mi><mo>∪</mo><mo>{</mo><mo>−</mo><mo>∞</mo><mo>}</mo></math></span> and <span><math><mi>N</mi><mo>∪</mo><mo>{</mo><mo>−</mo><mo>∞</mo><mo>}</mo></math></span>, respectively.","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933726","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}