Pub Date : 2022-09-15DOI: 10.48550/arXiv.2209.07090
Kenji Hashimoto, S. Maneth
It is well known that attributed tree transducers can be equipped with"regular look-around"in order to obtain a more robust class of translations. We present two characterizations of this class in terms of macro tree transducers (MTTs): the first one is a static restriction on the rules of the MTTs, where the MTTs need to be equipped with regular look-around. The second characterization is a dynamic one, where the MTTs only need regular look-ahead.
{"title":"Characterizing Attributed Tree Translations in Terms of Macro Tree Transducers","authors":"Kenji Hashimoto, S. Maneth","doi":"10.48550/arXiv.2209.07090","DOIUrl":"https://doi.org/10.48550/arXiv.2209.07090","url":null,"abstract":"It is well known that attributed tree transducers can be equipped with\"regular look-around\"in order to obtain a more robust class of translations. We present two characterizations of this class in terms of macro tree transducers (MTTs): the first one is a static restriction on the rules of the MTTs, where the MTTs need to be equipped with regular look-around. The second characterization is a dynamic one, where the MTTs only need regular look-ahead.","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"38 2 1","pages":"113943"},"PeriodicalIF":0.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87441368","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 : 2022-09-03DOI: 10.48550/arXiv.2209.01366
R. Feng, Jesse T. Geneson, Andrew Lee, Espen Slettnes
We determine sharp bounds on the price of bandit feedback for several variants of the mistake-bound model. The first part of the paper presents bounds on the $r$-input weak reinforcement model and the $r$-input delayed, ambiguous reinforcement model. In both models, the adversary gives $r$ inputs in each round and only indicates a correct answer if all $r$ guesses are correct. The only difference between the two models is that in the delayed, ambiguous model, the learner must answer each input before receiving the next input of the round, while the learner receives all $r$ inputs at once in the weak reinforcement model. In the second part of the paper, we introduce models for online learning with permutation patterns, in which a learner attempts to learn a permutation from a set of permutations by guessing statistics related to sub-permutations. For these permutation models, we prove sharp bounds on the price of bandit feedback.
{"title":"Sharp bounds on the price of bandit feedback for several models of mistake-bounded online learning","authors":"R. Feng, Jesse T. Geneson, Andrew Lee, Espen Slettnes","doi":"10.48550/arXiv.2209.01366","DOIUrl":"https://doi.org/10.48550/arXiv.2209.01366","url":null,"abstract":"We determine sharp bounds on the price of bandit feedback for several variants of the mistake-bound model. The first part of the paper presents bounds on the $r$-input weak reinforcement model and the $r$-input delayed, ambiguous reinforcement model. In both models, the adversary gives $r$ inputs in each round and only indicates a correct answer if all $r$ guesses are correct. The only difference between the two models is that in the delayed, ambiguous model, the learner must answer each input before receiving the next input of the round, while the learner receives all $r$ inputs at once in the weak reinforcement model. In the second part of the paper, we introduce models for online learning with permutation patterns, in which a learner attempts to learn a permutation from a set of permutations by guessing statistics related to sub-permutations. For these permutation models, we prove sharp bounds on the price of bandit feedback.","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"1 1","pages":"113980"},"PeriodicalIF":0.0,"publicationDate":"2022-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89453720","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 : 2022-09-01DOI: 10.1016/j.tcs.2022.09.018
R. Scheffler
{"title":"On the recognition of search trees generated by BFS and DFS","authors":"R. Scheffler","doi":"10.1016/j.tcs.2022.09.018","DOIUrl":"https://doi.org/10.1016/j.tcs.2022.09.018","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"71 1","pages":"116-128"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76606565","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 : 2022-09-01DOI: 10.4230/LIPIcs.FSTTCS.2020.30
Nils Morawietz, Niels Grüttemeier, Christian Komusiewicz, Frank Sommer
In a graph G = (V,E) with an edge coloring ` : E → C and two distinguished vertices s and t, a colored (s, t)-cut is a set C̃ ⊆ C such that deleting all edges with some color c ∈ C̃ from G disconnects s and t. Motivated by applications in the design of robust networks, we introduce a family of problems called colored cut games. In these games, an attacker and a defender choose colors to delete and to protect, respectively, in an alternating fashion. It is the goal of the attacker to achieve a colored (s, t)-cut and the goal of the defender to prevent this. First, we show that for an unbounded number of alternations, colored cut games are PSPACE-complete. We then show that, even on subcubic graphs, colored cut games with a constant number i of alternations are complete for classes in the polynomial hierarchy whose level depends on i. To complete the dichotomy, we show that all colored cut games are polynomial-time solvable on graphs with degree at most two. Finally, we show that all colored cut games admit a polynomial kernel for the parameter k + κr where k denotes the total attacker budget and, for any constant r, κr is the number of vertex deletions that are necessary to transform G into a graph where the longest path has length at most r. In the case of r = 1, κ1 is the vertex cover number vc of the input graph and we obtain a kernel with O(vc2k2) edges. Moreover, we introduce an algorithm solving the most basic colored cut game, Colored (s, t)-Cut, in 2vc+knO(1) time. 2012 ACM Subject Classification Theory of computation → Parameterized complexity and exact algorithms; Theory of computation → Graph algorithms analysis; Theory of computation → Problems, reductions and completeness
{"title":"Colored Cut Games","authors":"Nils Morawietz, Niels Grüttemeier, Christian Komusiewicz, Frank Sommer","doi":"10.4230/LIPIcs.FSTTCS.2020.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2020.30","url":null,"abstract":"In a graph G = (V,E) with an edge coloring ` : E → C and two distinguished vertices s and t, a colored (s, t)-cut is a set C̃ ⊆ C such that deleting all edges with some color c ∈ C̃ from G disconnects s and t. Motivated by applications in the design of robust networks, we introduce a family of problems called colored cut games. In these games, an attacker and a defender choose colors to delete and to protect, respectively, in an alternating fashion. It is the goal of the attacker to achieve a colored (s, t)-cut and the goal of the defender to prevent this. First, we show that for an unbounded number of alternations, colored cut games are PSPACE-complete. We then show that, even on subcubic graphs, colored cut games with a constant number i of alternations are complete for classes in the polynomial hierarchy whose level depends on i. To complete the dichotomy, we show that all colored cut games are polynomial-time solvable on graphs with degree at most two. Finally, we show that all colored cut games admit a polynomial kernel for the parameter k + κr where k denotes the total attacker budget and, for any constant r, κr is the number of vertex deletions that are necessary to transform G into a graph where the longest path has length at most r. In the case of r = 1, κ1 is the vertex cover number vc of the input graph and we obtain a kernel with O(vc2k2) edges. Moreover, we introduce an algorithm solving the most basic colored cut game, Colored (s, t)-Cut, in 2vc+knO(1) time. 2012 ACM Subject Classification Theory of computation → Parameterized complexity and exact algorithms; Theory of computation → Graph algorithms analysis; Theory of computation → Problems, reductions and completeness","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"1 1","pages":"13-32"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83082284","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 : 2022-09-01DOI: 10.1016/j.tcs.2022.09.026
Marcel Turkensteen, G. Jäger
{"title":"Efficient computation of tolerances in the sensitivity analysis of combinatorial bottleneck problems","authors":"Marcel Turkensteen, G. Jäger","doi":"10.1016/j.tcs.2022.09.026","DOIUrl":"https://doi.org/10.1016/j.tcs.2022.09.026","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"44 1","pages":"1-21"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89895673","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 : 2022-09-01DOI: 10.1016/j.tcs.2022.09.025
Xiaotao Lü, Jin Chen, Zhi-Xiong Wen
{"title":"On the 2-abelian complexity of generalized Cantor sequences","authors":"Xiaotao Lü, Jin Chen, Zhi-Xiong Wen","doi":"10.1016/j.tcs.2022.09.025","DOIUrl":"https://doi.org/10.1016/j.tcs.2022.09.025","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"124 1","pages":"172-183"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79494652","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 : 2022-09-01DOI: 10.1016/j.tcs.2022.09.028
Jing-jing Tan, Fengmin Wang, Weina Ye, Xiaoqing Zhang, Yang Zhou
{"title":"Streaming algorithms for monotone non-submodular function maximization under a knapsack constraint on the integer lattice","authors":"Jing-jing Tan, Fengmin Wang, Weina Ye, Xiaoqing Zhang, Yang Zhou","doi":"10.1016/j.tcs.2022.09.028","DOIUrl":"https://doi.org/10.1016/j.tcs.2022.09.028","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"1 1","pages":"39-49"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83723110","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 : 2022-09-01DOI: 10.1016/j.tcs.2022.09.027
Mathieu Gascon, R. Dondi, N. El-Mabrouk
{"title":"MUL-tree pruning for consistency and optimal reconciliation - complexity and algorithms","authors":"Mathieu Gascon, R. Dondi, N. El-Mabrouk","doi":"10.1016/j.tcs.2022.09.027","DOIUrl":"https://doi.org/10.1016/j.tcs.2022.09.027","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"33 1","pages":"22-38"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73899375","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 : 2022-09-01DOI: 10.1007/978-3-030-91081-5_22
Rongcheng Dong, Y. Sudo, Taisuke Izumi, T. Masuzawa
{"title":"Loosely-Stabilizing Maximal Independent Set Algorithms with Unreliable Communications","authors":"Rongcheng Dong, Y. Sudo, Taisuke Izumi, T. Masuzawa","doi":"10.1007/978-3-030-91081-5_22","DOIUrl":"https://doi.org/10.1007/978-3-030-91081-5_22","url":null,"abstract":"","PeriodicalId":23063,"journal":{"name":"Theor. Comput. Sci.","volume":"81 1","pages":"69-84"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78931120","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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