Yiming Li, Shengli Liu, Shuai Han, Dawu Gu, J. Weng
{"title":"Simulatable verifiable random function from the LWE assumption","authors":"Yiming Li, Shengli Liu, Shuai Han, Dawu Gu, J. Weng","doi":"10.2139/ssrn.4197049","DOIUrl":"https://doi.org/10.2139/ssrn.4197049","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"42 1","pages":"113826"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85209429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.48550/arXiv.2303.00110
A. Alhazov, Vincent Ferrari-Dominguez, R. Freund, N. Glade, Sergiu Ivanov
A Boolean network is a discrete dynamical system operating on vectors of Boolean variables. The action of a Boolean network can be conveniently expressed as a system of Boolean update functions, computing the new values for each component of the Boolean vector as a function of the other components. Boolean networks are widely used in modelling biological systems that can be seen as consisting of entities which can be activated or deactivated, expressed or inhibited, on or off. P systems on the other hand are classically introduced as a model of hierarchical multiset rewriting. However, over the years the community has proposed a wide range of P system variants including diverse ingredients suited for various needs. In this work, we propose a new variant -- Boolean P systems -- specifically designed for reasoning about sequential controllability of Boolean networks, and use it to first establish a crisp formalization of the problem, and then to prove that the problem of sequential controllability is PSPACE-complete. We further claim that Boolean P systems are a demonstration of how P systems can be used to construct ad hoc formalisms, custom-tailored for reasoning about specific problems, and providing new advantageous points of view.
{"title":"A P Systems Variant for Reasoning about Sequential Controllability of Boolean Networks","authors":"A. Alhazov, Vincent Ferrari-Dominguez, R. Freund, N. Glade, Sergiu Ivanov","doi":"10.48550/arXiv.2303.00110","DOIUrl":"https://doi.org/10.48550/arXiv.2303.00110","url":null,"abstract":"A Boolean network is a discrete dynamical system operating on vectors of Boolean variables. The action of a Boolean network can be conveniently expressed as a system of Boolean update functions, computing the new values for each component of the Boolean vector as a function of the other components. Boolean networks are widely used in modelling biological systems that can be seen as consisting of entities which can be activated or deactivated, expressed or inhibited, on or off. P systems on the other hand are classically introduced as a model of hierarchical multiset rewriting. However, over the years the community has proposed a wide range of P system variants including diverse ingredients suited for various needs. In this work, we propose a new variant -- Boolean P systems -- specifically designed for reasoning about sequential controllability of Boolean networks, and use it to first establish a crisp formalization of the problem, and then to prove that the problem of sequential controllability is PSPACE-complete. We further claim that Boolean P systems are a demonstration of how P systems can be used to construct ad hoc formalisms, custom-tailored for reasoning about specific problems, and providing new advantageous points of view.","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"26 1","pages":"114056"},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73232547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-01DOI: 10.1007/978-3-030-91081-5_15
Yotam Ashkenazi, S. Dolev, S. Kamei, Y. Katayama, Fukuhito Ooshita, K. Wada
{"title":"Location Functions for Self-stabilizing Byzantine Tolerant Swarms","authors":"Yotam Ashkenazi, S. Dolev, S. Kamei, Y. Katayama, Fukuhito Ooshita, K. Wada","doi":"10.1007/978-3-030-91081-5_15","DOIUrl":"https://doi.org/10.1007/978-3-030-91081-5_15","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"48 1","pages":"113755"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75374751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-01DOI: 10.1007/978-3-030-61792-9_26
Siddhesh Chaubal, A. Gál
{"title":"Tight Bounds on Sensitivity and Block Sensitivity of Some Classes of Transitive Functions","authors":"Siddhesh Chaubal, A. Gál","doi":"10.1007/978-3-030-61792-9_26","DOIUrl":"https://doi.org/10.1007/978-3-030-61792-9_26","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"103 1","pages":"113687"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85846162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Improved NP-hardness results for the minimum t-spanner problem on bounded-degree graphs","authors":"Renzo Gómez, F. Miyazawa, Yoshiko Wakabayashi","doi":"10.2139/ssrn.4025071","DOIUrl":"https://doi.org/10.2139/ssrn.4025071","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"19 1","pages":"113691"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74304851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-13DOI: 10.48550/arXiv.2212.06646
Shuyang Gu, Chuangen Gao, Jun Huang, Weili Wu
In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions. DR-submodular is a further extended submodular concept for functions over the integer lattice, which captures the diminishing return property. Such functions find many applications in machine learning, social networks, wireless networks, etc. The techniques for submodular set function maximization can be applied to DR-submodular function maximization, e.g., the double greedy algorithm has a $1/2$-approximation ratio, whose running time is $O(nB)$, where $n$ is the size of the ground set, $B$ is the integer bound of a coordinate. In our study, we design a $1/2$-approximate binary search double greedy algorithm, and we prove that its time complexity is $O(nlog B)$, which significantly improves the running time. Specifically, we consider its application to the profit maximization problem in social networks with a bipartite model, the goal of this problem is to maximize the net profit gained from a product promoting activity, which is the difference of the influence gain and the promoting cost. We prove that the objective function is DR-submodular over integer lattice. We apply binary search double greedy algorithm to this problem and verify the effectiveness.
{"title":"Profit Maximization in Social Networks and Non-monotone DR-submodular Maximization","authors":"Shuyang Gu, Chuangen Gao, Jun Huang, Weili Wu","doi":"10.48550/arXiv.2212.06646","DOIUrl":"https://doi.org/10.48550/arXiv.2212.06646","url":null,"abstract":"In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions. DR-submodular is a further extended submodular concept for functions over the integer lattice, which captures the diminishing return property. Such functions find many applications in machine learning, social networks, wireless networks, etc. The techniques for submodular set function maximization can be applied to DR-submodular function maximization, e.g., the double greedy algorithm has a $1/2$-approximation ratio, whose running time is $O(nB)$, where $n$ is the size of the ground set, $B$ is the integer bound of a coordinate. In our study, we design a $1/2$-approximate binary search double greedy algorithm, and we prove that its time complexity is $O(nlog B)$, which significantly improves the running time. Specifically, we consider its application to the profit maximization problem in social networks with a bipartite model, the goal of this problem is to maximize the net profit gained from a product promoting activity, which is the difference of the influence gain and the promoting cost. We prove that the objective function is DR-submodular over integer lattice. We apply binary search double greedy algorithm to this problem and verify the effectiveness.","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"1 1","pages":"113847"},"PeriodicalIF":0.0,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79794104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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