Pub Date : 2026-01-01DOI: 10.1016/j.ic.2026.105404
Jinshan Zhang , Hao Xu , Feng Wang , Meng Xi , Xiaotie Deng , Jianwei Yin
In this work, we investigate truthful mechanisms for the rank-maximal matching problem from an approximation standpoint. Our findings narrow the gap between the upper and lower bounds. We introduce a lexicographically truthful (LT) and nearly Pareto optimal (PO) randomized mechanism with an approximation ratio of , an improvement over the previous best result of 2. Key to our algorithm are preservation lemmas that enable us to leverage techniques from online algorithms to analyze the new approximation ratio. Furthermore, we present several hardness results across different settings to enhance our upper bound. Notably, we improve the lower bound for the approximation ratio of our LT and PO mechanism to . To our knowledge, this is the first instance of a lower bound being established using a linear programming approach in this field.
{"title":"Truthful approximation for rank-maximal matchings","authors":"Jinshan Zhang , Hao Xu , Feng Wang , Meng Xi , Xiaotie Deng , Jianwei Yin","doi":"10.1016/j.ic.2026.105404","DOIUrl":"10.1016/j.ic.2026.105404","url":null,"abstract":"<div><div>In this work, we investigate truthful mechanisms for the rank-maximal matching problem from an approximation standpoint. Our findings narrow the gap between the upper and lower bounds. We introduce a lexicographically truthful (LT) and nearly Pareto optimal (PO) randomized mechanism with an approximation ratio of <span><math><mfrac><mrow><mn>2</mn><msqrt><mrow><mi>e</mi></mrow></msqrt><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn><msqrt><mrow><mi>e</mi></mrow></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac><mo>≈</mo><mn>1.77</mn></math></span>, an improvement over the previous best result of 2. Key to our algorithm are preservation lemmas that enable us to leverage techniques from online algorithms to analyze the new approximation ratio. Furthermore, we present several hardness results across different settings to enhance our upper bound. Notably, we improve the lower bound for the approximation ratio of our LT and PO mechanism to <span><math><mn>18</mn><mo>/</mo><mn>13</mn><mo>≈</mo><mn>1.38</mn></math></span>. To our knowledge, this is the first instance of a lower bound being established using a linear programming approach in this field.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105404"},"PeriodicalIF":1.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976646","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}
Pub Date : 2026-01-01DOI: 10.1016/j.ic.2026.105405
Jingyang Zhao, Mingyu Xiao
The Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In this paper, we consider k-CVRP in general metrics and on general graphs, where k is the vehicle capacity. All three versions are APX-hard for any fixed . Based on an α-approximation algorithm for metric TSP, we propose new approximation algorithms. For , we obtain a -approximation algorithm for the splittable and unit-demand cases, and a -approximation algorithm for the unsplittable case. Our approximation ratio is better than the previous results when k is less than a fairly large value, approximately .
For small values of k, we design independent and elegant algorithms with further improvements. For the splittable and unit-demand cases, we improve the approximation ratio from 1.792 to 1.500 for , and from 1.750 to 1.500 for . For the unsplittable case, we improve the approximation ratio from 1.792 to 1.500 for , from 2.051 to 1.750 for , and from 2.249 to 2.157 for . The approximation ratio for surprisingly achieves the same value as in the splittable case. Our techniques, such as EX-ITP – an extension of the classic ITP method, have the potential to improve algorithms for other routing problems as well.
{"title":"Improved approximations for the capacitated vehicle routing problem with fixed capacity","authors":"Jingyang Zhao, Mingyu Xiao","doi":"10.1016/j.ic.2026.105405","DOIUrl":"10.1016/j.ic.2026.105405","url":null,"abstract":"<div><div>The Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In this paper, we consider <em>k</em>-CVRP in general metrics and on general graphs, where <em>k</em> is the vehicle capacity. All three versions are APX-hard for any fixed <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>. Based on an <em>α</em>-approximation algorithm for metric TSP, we propose new approximation algorithms. For <span><math><mi>α</mi><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, we obtain a <span><math><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mi>Θ</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac><mo>)</mo><mo>)</mo></math></span>-approximation algorithm for the splittable and unit-demand cases, and a <span><math><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>ln</mi><mo></mo><mn>2</mn><mo>−</mo><mi>Θ</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mi>k</mi></mrow></msqrt></mrow></mfrac><mo>)</mo><mo>)</mo></math></span>-approximation algorithm for the unsplittable case. Our approximation ratio is better than the previous results when <em>k</em> is less than a fairly large value, approximately <span><math><mn>1.7</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>7</mn></mrow></msup></math></span>.</div><div>For small values of <em>k</em>, we design independent and elegant algorithms with further improvements. For the splittable and unit-demand cases, we improve the approximation ratio from 1.792 to 1.500 for <span><math><mi>k</mi><mo>=</mo><mn>3</mn></math></span>, and from 1.750 to 1.500 for <span><math><mi>k</mi><mo>=</mo><mn>4</mn></math></span>. For the unsplittable case, we improve the approximation ratio from 1.792 to 1.500 for <span><math><mi>k</mi><mo>=</mo><mn>3</mn></math></span>, from 2.051 to 1.750 for <span><math><mi>k</mi><mo>=</mo><mn>4</mn></math></span>, and from 2.249 to 2.157 for <span><math><mi>k</mi><mo>=</mo><mn>5</mn></math></span>. The approximation ratio for <span><math><mi>k</mi><mo>=</mo><mn>3</mn></math></span> surprisingly achieves the same value as in the splittable case. Our techniques, such as EX-ITP – an extension of the classic ITP method, have the potential to improve algorithms for other routing problems as well.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105405"},"PeriodicalIF":1.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976580","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}
This paper focuses on the embeddability of hypercubes in an important class of Cayley graphs, known as augmented cubes. An n-dimensional augmented cube is constructed by augmenting the n-dimensional hypercube with additional edges, thus making a spanning subgraph of . Dong and Wang (2019) first posed the problem of determining the number of -isomorphic subgraphs in , which still remains open. By exploiting the Cayley properties of , we establish a lower bound for this number. Furthermore, we develop a method for constructing pairs of -isomorphic subgraphs in with the minimum number of common edges. This is accomplished through the use of reciprocal perfect matchings, a technique that also relies on the Cayley property of . As an application, we prove that admits edge-disjoint Hamiltonian cycles when is odd and cycles when n is even, thereby confirming a conjecture by Hung (2015) that admits a Hamiltonian decomposition for odd n with .
本文主要研究一类重要的Cayley图的超立方体的可嵌入性，即增广立方体。通过在n维超立方体Qn上增加额外的边来构造n维增广立方体AQn，从而使Qn成为AQn的生成子图。Dong and Wang（2019）首先提出了确定AQn中qn -同构子图数量的问题，该问题仍然是开放的。通过利用AQn的Cayley性质，我们建立了这个数的下界。在此基础上，提出了一种构造具有最小公共边数的qn -同构子图对的方法。这是通过使用互反完美匹配来实现的，这种技术也依赖于AQn的Cayley性质。作为应用，我们证明了当n≥3为奇数时AQn允许n−1个边不相交的哈密顿循环，当n为偶数时n−2个循环，从而证实了Hung（2015）关于当n≥3时AQn允许奇数n的哈密顿分解的猜想。
{"title":"A perfect matching reciprocity method for embedding multiple hypercubes in an augmented cube: Application to Hamiltonian decomposition","authors":"Da-Wei Yang , Hongyang Zhang , Rong-Xia Hao , Sun-Yuan Hsieh","doi":"10.1016/j.ic.2025.105401","DOIUrl":"10.1016/j.ic.2025.105401","url":null,"abstract":"<div><div>This paper focuses on the embeddability of hypercubes in an important class of Cayley graphs, known as augmented cubes. An <em>n</em>-dimensional augmented cube <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is constructed by augmenting the <em>n</em>-dimensional hypercube <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> with additional edges, thus making <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> a spanning subgraph of <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Dong and Wang (2019) first posed the problem of determining the number of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-isomorphic subgraphs in <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, which still remains open. By exploiting the Cayley properties of <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, we establish a lower bound for this number. Furthermore, we develop a method for constructing pairs of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-isomorphic subgraphs in <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> with the minimum number of common edges. This is accomplished through the use of reciprocal perfect matchings, a technique that also relies on the Cayley property of <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. As an application, we prove that <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> admits <span><math><mi>n</mi><mo>−</mo><mn>1</mn></math></span> edge-disjoint Hamiltonian cycles when <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span> is odd and <span><math><mi>n</mi><mo>−</mo><mn>2</mn></math></span> cycles when <em>n</em> is even, thereby confirming a conjecture by Hung (2015) that <span><math><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> admits a Hamiltonian decomposition for odd <em>n</em> with <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105401"},"PeriodicalIF":1.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884338","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}
Pub Date : 2026-01-01DOI: 10.1016/j.ic.2025.105400
Nikolay Vereshchagin
The fine approach to measure information dependence is based on the total conditional complexity , which is defined as the minimal length of a total program that outputs y on the input x. It is known that the total conditional complexity can be much larger than the plain conditional complexity. Such strings are defined by means of a diagonal argument and are not otherwise interesting. In this paper we investigate whether this happens also for some natural objects having some other interesting properties. More specifically, we consider the following objects: the number of strings of complexity less than n and the lex first string of length n and complexity ⩾n. It is known that they have negligible mutual conditional complexities. In this paper we prove that their mutual total conditional complexities may be large. This is the first example of interesting objects whose plain conditional complexity is much less than the total one.
{"title":"Total conditional complexity of certain objects","authors":"Nikolay Vereshchagin","doi":"10.1016/j.ic.2025.105400","DOIUrl":"10.1016/j.ic.2025.105400","url":null,"abstract":"<div><div>The fine approach to measure information dependence is based on the total conditional complexity <span><math><mtext>CT</mtext><mo>(</mo><mi>y</mi><mo>|</mo><mi>x</mi><mo>)</mo></math></span>, which is defined as the minimal length of a <em>total</em> program that outputs <em>y</em> on the input <em>x</em>. It is known that the total conditional complexity can be much larger than the plain conditional complexity. Such strings <span><math><mi>x</mi><mo>,</mo><mi>y</mi></math></span> are defined by means of a diagonal argument and are not otherwise interesting. In this paper we investigate whether this happens also for some natural objects having some other interesting properties. More specifically, we consider the following objects: the number of strings of complexity less than <em>n</em> and the lex first string of length <em>n</em> and complexity ⩾<em>n</em>. It is known that they have negligible mutual conditional complexities. In this paper we prove that their mutual total conditional complexities may be large. This is the first example of interesting objects whose plain conditional complexity is much less than the total one.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105400"},"PeriodicalIF":1.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884336","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}
Pub Date : 2026-01-01DOI: 10.1016/j.ic.2026.105403
Martin Kutrib , Andreas Malcher , Carlo Mereghetti , Beatrice Palano , Priscilla Raucci , Matthias Wendlandt
The use of translucent input letters represents a way of implementing a discontinuous input processing in automata. In detail, a translucent automaton performs several sweeps from left to right on the input: according to the current state, some symbols are visible and can be processed, whereas some other symbols are invisible and may be processed in another sweep. We also distinguish between the returning and non-returning mode, which differ in the way the automaton behaves after reading a symbol: in the returning mode, a new sweep starts immediately, while in the non-returning mode, the device processes the next visible symbol.
Here, we investigate deterministic pushdown automata with translucent letters both in the returning and non-returning mode. We prove that the non-returning mode strictly outperforms the returning mode, and that the families of the languages accepted by these two types of devices can be ranked strictly between the deterministic context-free languages and the deterministic context-sensitive languages. Moreover, both families are shown to be incomparable to the families of context-free, growing context-sensitive, and Church-Rosser languages. The ability of accepting non-semilinear languages is also emphasized (addressing an open question in the literature). Finally, we study the closure properties of both language families under the Boolean operations, obtaining that they are both closed under complementation but not under union and intersection. Further non-closure results are pointed-out for returning devices.
{"title":"Deterministic pushdown automata with translucent input letters","authors":"Martin Kutrib , Andreas Malcher , Carlo Mereghetti , Beatrice Palano , Priscilla Raucci , Matthias Wendlandt","doi":"10.1016/j.ic.2026.105403","DOIUrl":"10.1016/j.ic.2026.105403","url":null,"abstract":"<div><div>The use of translucent input letters represents a way of implementing a discontinuous input processing in automata. In detail, a translucent automaton performs several sweeps from left to right on the input: according to the current state, some symbols are visible and can be processed, whereas some other symbols are invisible and may be processed in another sweep. We also distinguish between the returning and non-returning mode, which differ in the way the automaton behaves after reading a symbol: in the returning mode, a new sweep starts immediately, while in the non-returning mode, the device processes the next visible symbol.</div><div>Here, we investigate <em>deterministic pushdown automata with translucent letters</em> both in the returning and non-returning mode. We prove that the non-returning mode strictly outperforms the returning mode, and that the families of the languages accepted by these two types of devices can be ranked strictly between the deterministic context-free languages and the deterministic context-sensitive languages. Moreover, both families are shown to be incomparable to the families of context-free, growing context-sensitive, and Church-Rosser languages. The ability of accepting non-semilinear languages is also emphasized (addressing an open question in the literature). Finally, we study the closure properties of both language families under the Boolean operations, obtaining that they are both closed under complementation but not under union and intersection. Further non-closure results are pointed-out for returning devices.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105403"},"PeriodicalIF":1.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976581","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}
Pub Date : 2026-01-01DOI: 10.1016/j.ic.2025.105402
Yusai Wu , Liqing Yu , Yu Yu
{"title":"Corrigendum to “On the equivalence of uniform key agreement and sequential composition insecurity” [Information and Computation 307 (2025) 105365]","authors":"Yusai Wu , Liqing Yu , Yu Yu","doi":"10.1016/j.ic.2025.105402","DOIUrl":"10.1016/j.ic.2025.105402","url":null,"abstract":"","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105402"},"PeriodicalIF":1.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884337","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}
Pub Date : 2025-12-18DOI: 10.1016/j.ic.2025.105399
Yuzhen Zhao , Zhen Yang , Yueguo Luo , Hui Li , Wenke Zang
Spiking neural P systems (SNP systems) are parallel and distributed computational models mimicking the storage, processing, and transmission of spikes in the human brain nervous system. However, they do not consider the non-gated channels in human brain neurons, which would affect the storage and thus further affect the processing and transmission of spikes. To enhance the SNP systems' ability to process complex information and to make SNP systems more biologically plausible, this work constructs the SNP systems with non-gated channels (NGCSNP systems). In NGCSNP systems, when a neuron is not activated, the spikes in it slowly flow out into the environment through non-gated channels until a steady state is reached. That is, the number of spikes in a neuron nonlinearly varies automatically. In terms of computational power, this work proves the Turing universality of NGCSNP systems by simulating register machines. For the ADD/SUB/FIN/INPUT/deterministic ADD modules of the universal register machine, NGCSNP systems utilize only 7, 6, 3, 5, and 4 neurons, with each neuron containing a maximum of 2, 2, 2, 1, and 1 rules for module simulation, respectively. Compared to the other eight variants, NGCSNP systems use fewer computational resources. Also, this work proves the computational efficiency of NGCSNP systems by solving a classical NP-hard problem: Boolean Satisfiability Problems in linear time via a space-for-time strategy. NGCSNP systems introduce nonlinear features at the neuronal level, enhance the computational functionality as well as stability of the systems, save the computational resources, and provide clues for developing computational models that resemble the human brain.
{"title":"Spiking neural P systems with non-gated channels","authors":"Yuzhen Zhao , Zhen Yang , Yueguo Luo , Hui Li , Wenke Zang","doi":"10.1016/j.ic.2025.105399","DOIUrl":"10.1016/j.ic.2025.105399","url":null,"abstract":"<div><div>Spiking neural P systems (SNP systems) are parallel and distributed computational models mimicking the storage, processing, and transmission of spikes in the human brain nervous system. However, they do not consider the non-gated channels in human brain neurons, which would affect the storage and thus further affect the processing and transmission of spikes. To enhance the SNP systems' ability to process complex information and to make SNP systems more biologically plausible, this work constructs the SNP systems with non-gated channels (NGCSNP systems). In NGCSNP systems, when a neuron is not activated, the spikes in it slowly flow out into the environment through non-gated channels until a steady state is reached. That is, the number of spikes in a neuron nonlinearly varies automatically. In terms of computational power, this work proves the Turing universality of NGCSNP systems by simulating register machines. For the ADD/SUB/FIN/INPUT/deterministic ADD modules of the universal register machine, NGCSNP systems utilize only 7, 6, 3, 5, and 4 neurons, with each neuron containing a maximum of 2, 2, 2, 1, and 1 rules for module simulation, respectively. Compared to the other eight variants, NGCSNP systems use fewer computational resources. Also, this work proves the computational efficiency of NGCSNP systems by solving a classical NP-hard problem: Boolean Satisfiability Problems in linear time via a space-for-time strategy. NGCSNP systems introduce nonlinear features at the neuronal level, enhance the computational functionality as well as stability of the systems, save the computational resources, and provide clues for developing computational models that resemble the human brain.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105399"},"PeriodicalIF":1.0,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840783","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}
Pub Date : 2025-12-16DOI: 10.1016/j.ic.2025.105398
Marco Sälzer , Eric Alsmann , Florian Bruse , Martin Lange
Verifying properties and interpreting the behaviour of deep neural networks (DNN) is an important task given their ubiquitous use in applications, including safety-critical ones, and their black-box nature. We propose an automata-theoretic approach to tackling problems arising in DNN analysis. We show that the input-output behaviour of a DNN can be captured precisely by a (special) weak Büchi automaton and we show how these can be used to address common verification and interpretation tasks of DNN like adversarial robustness or minimum sufficient reasons.
{"title":"Verifying and interpreting neural networks using finite automata","authors":"Marco Sälzer , Eric Alsmann , Florian Bruse , Martin Lange","doi":"10.1016/j.ic.2025.105398","DOIUrl":"10.1016/j.ic.2025.105398","url":null,"abstract":"<div><div>Verifying properties and interpreting the behaviour of deep neural networks (DNN) is an important task given their ubiquitous use in applications, including safety-critical ones, and their black-box nature. We propose an automata-theoretic approach to tackling problems arising in DNN analysis. We show that the input-output behaviour of a DNN can be captured precisely by a (special) weak Büchi automaton and we show how these can be used to address common verification and interpretation tasks of DNN like adversarial robustness or minimum sufficient reasons.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105398"},"PeriodicalIF":1.0,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791115","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}
Pub Date : 2025-12-08DOI: 10.1016/j.ic.2025.105397
Mengyuan Hu , An Zhang , Yong Chen , Mingyang Gong , Guohui Lin
For a positive integer , a k-star (-star, -star, respectively) is a connected graph containing a degree-ℓ vertex and ℓ degree-1 vertices, where (, , respectively). The -star packing problem is to cover as many vertices of an input graph G as possible using vertex-disjoint -stars in G; and given , the -star packing problem is to cover as many vertices of G as possible using vertex-disjoint -stars but no t-stars in G. Both problems are NP-hard for any fixed . We present a - and a -approximation algorithms for the -star packing problem when and , respectively, and a -approximation algorithm for the -star packing problem when . They are all local search algorithms and they improve the best known approximation algorithms for the problems, respectively.
{"title":"Approximation algorithms for non-sequential star packing problems","authors":"Mengyuan Hu , An Zhang , Yong Chen , Mingyang Gong , Guohui Lin","doi":"10.1016/j.ic.2025.105397","DOIUrl":"10.1016/j.ic.2025.105397","url":null,"abstract":"<div><div>For a positive integer <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>, a <em>k</em>-star (<span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-star, <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span>-star, respectively) is a connected graph containing a degree-<em>ℓ</em> vertex and <em>ℓ</em> degree-1 vertices, where <span><math><mi>ℓ</mi><mo>=</mo><mi>k</mi></math></span> (<span><math><mi>ℓ</mi><mo>≥</mo><mi>k</mi></math></span>, <span><math><mn>1</mn><mo>≤</mo><mi>ℓ</mi><mo>≤</mo><mi>k</mi></math></span>, respectively). The <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-star packing problem is to cover as many vertices of an input graph <em>G</em> as possible using vertex-disjoint <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-stars in <em>G</em>; and given <span><math><mi>k</mi><mo>></mo><mi>t</mi><mo>≥</mo><mn>1</mn></math></span>, the <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>/</mo><mi>t</mi></math></span>-star packing problem is to cover as many vertices of <em>G</em> as possible using vertex-disjoint <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span>-stars but no <em>t</em>-stars in <em>G</em>. Both problems are NP-hard for any fixed <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>. We present a <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>)</mo></math></span>- and a <span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>-approximation algorithms for the <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-star packing problem when <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, respectively, and a <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>t</mi><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>/</mo><mi>k</mi></mrow></mfrac><mo>)</mo></math></span>-approximation algorithm for the <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>/</mo><mi>t</mi></math></span>-star packing problem when <span><math><mi>k</mi><mo>></mo><mi>t</mi><mo>≥</mo><mn>2</mn></math></span>. They are all local search algorithms and they improve the best known approximation algorithms for the problems, respectively.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105397"},"PeriodicalIF":1.0,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738184","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}
Pub Date : 2025-12-05DOI: 10.1016/j.ic.2025.105396
Andrei Romashchenko
We study the possibility of scaling down algorithmic information quantities in tuples of correlated strings. In particular, we address a question raised by Alexander Shen: whether, for any triple of strings , there exists a string z such that each conditional Kolmogorov complexity is approximately half of the corresponding unconditional Kolmogorov complexity. We give a negative answer to this question by constructing a triple for which no such string z exists. Moreover, we construct a fully explicit example of such a tuple, inspired by Vladimir V'yugin's perspective on the role of structured and natural objects in algorithmic information theory. Our construction is based on combinatorial properties of incidences in finite projective planes and relies on bounds for point-line incidences over prime fields, obtained using tools from additive combinatorics and algebraic methods, notably results by Bourgain–Katz–Tao and Stevens–De Zeeuw. As an application, we show that this impossibility yields lower bounds on the communication complexity of secret key agreement protocols in certain settings. These results reveal algebraic obstructions to efficient information exchange and highlight a separation in information-theoretic behavior between fields with and without proper subfields.
我们研究了在相关字符串元组中缩减算法信息量的可能性。特别地，我们解决了Alexander Shen提出的一个问题：对于任意字符串的三组（a,b,c），是否存在一个字符串z，使得每个条件Kolmogorov复杂度c (a|z), c (b|z), c （c|z）大约是相应的无条件Kolmogorov复杂度的一半。我们通过构造一个不存在这样的字符串z的三元组（a,b,c）来给出这个问题的否定答案。此外，受Vladimir V'yugin关于算法信息论中结构化和自然对象的作用的观点的启发，我们构建了这样一个元组的完全明确的例子。我们的构造是基于有限射影平面上关联的组合性质，并依赖于素域上点线关联的界，这些界是使用加性组合学和代数方法的工具得到的，特别是由Bourgain-Katz-Tao和Stevens-De Zeeuw得到的结果。作为一个应用，我们证明了这种不可能性在某些设置下产生了密钥协议通信复杂性的下界。这些结果揭示了有效信息交换的代数障碍，并突出了有适当子域和没有适当子域的域之间的信息论行为的分离。
{"title":"Algebraic barriers to halving algorithmic information quantities in correlated strings","authors":"Andrei Romashchenko","doi":"10.1016/j.ic.2025.105396","DOIUrl":"10.1016/j.ic.2025.105396","url":null,"abstract":"<div><div>We study the possibility of scaling down algorithmic information quantities in tuples of correlated strings. In particular, we address a question raised by Alexander Shen: whether, for any triple of strings <span><math><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></span>, there exists a string <em>z</em> such that each conditional Kolmogorov complexity <span><math><mi>C</mi><mo>(</mo><mi>a</mi><mo>|</mo><mi>z</mi><mo>)</mo><mo>,</mo><mi>C</mi><mo>(</mo><mi>b</mi><mo>|</mo><mi>z</mi><mo>)</mo><mo>,</mo><mi>C</mi><mo>(</mo><mi>c</mi><mo>|</mo><mi>z</mi><mo>)</mo></math></span> is approximately half of the corresponding unconditional Kolmogorov complexity. We give a negative answer to this question by constructing a triple <span><math><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></span> for which no such string <em>z</em> exists. Moreover, we construct a fully explicit example of such a tuple, inspired by Vladimir V'yugin's perspective on the role of structured and natural objects in algorithmic information theory. Our construction is based on combinatorial properties of incidences in finite projective planes and relies on bounds for point-line incidences over prime fields, obtained using tools from additive combinatorics and algebraic methods, notably results by Bourgain–Katz–Tao and Stevens–De Zeeuw. As an application, we show that this impossibility yields lower bounds on the communication complexity of secret key agreement protocols in certain settings. These results reveal algebraic obstructions to efficient information exchange and highlight a separation in information-theoretic behavior between fields with and without proper subfields.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"308 ","pages":"Article 105396"},"PeriodicalIF":1.0,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738183","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}
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