In this paper, we study two variants of Coloring - Dominator Coloring and Class Domination Coloring. In both problems, we are given a graph G and a and the goal is to properly color the vertices with at most ℓ colors. In Dominator Coloring, we require for each , a color c such that v dominates all vertices colored c. In Class Domination Coloring, we require for each color c, a which dominates all vertices colored c. We prove that Dominator Coloring is FPT when parameterized by the size of a graph's CVD set and that Class Domination Coloring is FPT parameterized by CVD set size plus the number of remaining cliques. En route, we design simpler algorithms when the problems are parameterized by the size of a graph's twin cover. When the parameter is the size of a graph's clique modulator, we design a randomized single-exponential time algorithm.
{"title":"Dominator coloring and CD coloring in almost cluster graphs","authors":"Aritra Banik , Prahlad Narasimhan Kasthurirangan , Venkatesh Raman","doi":"10.1016/j.jcss.2025.103633","DOIUrl":"10.1016/j.jcss.2025.103633","url":null,"abstract":"<div><div>In this paper, we study two variants of Coloring - <span>Dominator Coloring</span> and <span>Class Domination Coloring</span>. In both problems, we are given a graph <em>G</em> and a <span><math><mi>ℓ</mi><mo>∈</mo><mi>N</mi></math></span> and the goal is to properly color the vertices with at most <em>ℓ</em> colors. In <span>Dominator Coloring</span>, we require for each <span><math><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, a color <em>c</em> such that <em>v</em> dominates all vertices colored <em>c</em>. In <span>Class Domination Coloring</span>, we require for each color <em>c</em>, a <span><math><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> which dominates all vertices colored <em>c</em>. We prove that <span>Dominator Coloring</span> is <span>FPT</span> when parameterized by the size of a graph's CVD set and that <span>Class Domination Coloring</span> is <span>FPT</span> parameterized by CVD set size plus the number of remaining cliques. En route, we design simpler algorithms when the problems are parameterized by the size of a graph's twin cover. When the parameter is the size of a graph's clique modulator, we design a randomized single-exponential time algorithm.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"150 ","pages":"Article 103633"},"PeriodicalIF":1.1,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider structural parameterizations of several variants of Dominating Set in the parameter ecology program. We give improved FPT algorithms and lower bounds under well-known conjectures for Dominating Set and its variants in graphs that are k vertices away from a cluster graph or a split graph. These are graphs in which there is a set of k vertices (called the modulator) whose deletion results in a cluster graph or a split graph. We also call k as the deletion distance (to the appropriate class of graphs). For example, we show that when parameterized by the deletion distance k to cluster graphs: Dominating Set, Independent Dominating Set, Dominating Clique, Efficient Dominating Set and Total Dominating Set can be solved in -time. Additionally, when parameterized by the deletion distance k to split graphs, we prove that Efficient Dominating Set can be solved in -time breaking the barrier.
{"title":"Parameterized complexity of dominating set variants in almost cluster and split graphs","authors":"Dishant Goyal , Ashwin Jacob , Kaushtubh Kumar , Diptapriyo Majumdar , Venkatesh Raman","doi":"10.1016/j.jcss.2025.103631","DOIUrl":"10.1016/j.jcss.2025.103631","url":null,"abstract":"<div><div>We consider structural parameterizations of several variants of <span>Dominating Set</span> in the parameter ecology program. We give improved FPT algorithms and lower bounds under well-known conjectures for <span>Dominating Set</span> and its variants in graphs that are <em>k</em> vertices away from a cluster graph or a split graph. These are graphs in which there is a set of <em>k</em> vertices (called the modulator) whose deletion results in a cluster graph or a split graph. We also call <em>k</em> as the deletion distance (to the appropriate class of graphs). For example, we show that when parameterized by the deletion distance <em>k</em> to cluster graphs: <span>Dominating Set</span>, <span>Independent Dominating Set</span>, <span>Dominating Clique</span>, <span>Efficient Dominating Set</span> and <span>Total Dominating Set</span> can be solved in <span><math><msup><mrow><mn>3</mn></mrow><mrow><mi>k</mi></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>-time. Additionally, when parameterized by the deletion distance <em>k</em> to split graphs, we prove that <span>Efficient Dominating Set</span> can be solved in <span><math><msup><mrow><mn>3</mn></mrow><mrow><mi>k</mi><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>-time breaking the <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></math></span> barrier.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"150 ","pages":"Article 103631"},"PeriodicalIF":1.1,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143386924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-03DOI: 10.1016/j.jcss.2025.103632
Piotr Faliszewski , Piotr Skowron , Arkadii Slinko , Krzysztof Sornat , Stanisław Szufa , Nimrod Talmon
We introduce and study isomorphic distances between ordinal elections (with the same numbers of candidates and voters). The main feature of these distances is that they are invariant to renaming the candidates and voters, and two elections are at distance zero if and only if they are isomorphic. Specifically, we consider isomorphic extensions of distances between preference orders: Given such a distance d, we extend it to distance between elections by unifying candidate names and finding a matching between the votes, so that the sum of the d-distances between the matched votes is as small as possible. We show that testing isomorphism of two elections can be done in polynomial time so, in principle, such distances can be tractable. Yet, we show that two very natural isomorphic distances are NP-complete and hard to approximate. We attempt to rectify the situation by showing FPT algorithms for several natural parameterizations.
{"title":"How similar are two elections?","authors":"Piotr Faliszewski , Piotr Skowron , Arkadii Slinko , Krzysztof Sornat , Stanisław Szufa , Nimrod Talmon","doi":"10.1016/j.jcss.2025.103632","DOIUrl":"10.1016/j.jcss.2025.103632","url":null,"abstract":"<div><div>We introduce and study isomorphic distances between ordinal elections (with the same numbers of candidates and voters). The main feature of these distances is that they are invariant to renaming the candidates and voters, and two elections are at distance zero if and only if they are isomorphic. Specifically, we consider isomorphic extensions of distances between preference orders: Given such a distance <em>d</em>, we extend it to distance <span><math><mi>d</mi><mtext>-</mtext><mrow><mi>ID</mi></mrow></math></span> between elections by unifying candidate names and finding a matching between the votes, so that the sum of the <em>d</em>-distances between the matched votes is as small as possible. We show that testing isomorphism of two elections can be done in polynomial time so, in principle, such distances can be tractable. Yet, we show that two very natural isomorphic distances are NP-complete and hard to approximate. We attempt to rectify the situation by showing FPT algorithms for several natural parameterizations.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"150 ","pages":"Article 103632"},"PeriodicalIF":1.1,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
Pub Date : 2025-02-03DOI: 10.1016/j.jcss.2025.103630
George B. Mertzios , Hendrik Molter , Malte Renken , Paul G. Spirakis , Philipp Zschoche
In a temporal network with discrete time-labels on its edges, information can only “flow” along sequences of edges with non-decreasing (resp. increasing) time-labels. In this paper we make a first attempt to understand how the direction of information flow on one edge can impact the direction of information flow on other edges. By naturally extending the classical notion of a transitive orientation in static graphs, we introduce the fundamental notion of a temporal transitive orientation, and we systematically investigate its algorithmic behavior. Our main result is a conceptually simple, yet technically quite involved, polynomial-time algorithm for recognizing whether a temporal graph is transitively orientable. In wide contrast we prove that, surprisingly, it is NP-hard to recognize whether is strictly transitively orientable. Additionally we introduce further related problems to temporal transitivity, notably among them the temporal transitive completion problem, for which we prove both algorithmic and hardness results.
{"title":"The complexity of transitively orienting temporal graphs","authors":"George B. Mertzios , Hendrik Molter , Malte Renken , Paul G. Spirakis , Philipp Zschoche","doi":"10.1016/j.jcss.2025.103630","DOIUrl":"10.1016/j.jcss.2025.103630","url":null,"abstract":"<div><div>In a temporal network with discrete time-labels on its edges, information can only “flow” along sequences of edges with non-decreasing (resp. increasing) time-labels. In this paper we make a first attempt to understand how the direction of information flow on one edge can impact the direction of information flow on other edges. By naturally extending the classical notion of a transitive orientation in static graphs, we introduce the fundamental notion of a temporal transitive orientation, and we systematically investigate its algorithmic behavior. Our main result is a conceptually simple, yet technically quite involved, polynomial-time algorithm for recognizing whether a temporal graph <span><math><mi>G</mi></math></span> is transitively orientable. In wide contrast we prove that, surprisingly, it is NP-hard to recognize whether <span><math><mi>G</mi></math></span> is strictly transitively orientable. Additionally we introduce further related problems to temporal transitivity, notably among them the temporal transitive completion problem, for which we prove both algorithmic and hardness results.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"150 ","pages":"Article 103630"},"PeriodicalIF":1.1,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
Pub Date : 2025-01-21DOI: 10.1016/j.jcss.2025.103619
Cristina Bazgan , Katrin Casel , Pierre Cazals
We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is half its average degree, that is, the ratio of its number of edges and its number of vertices. This problem, called Dense Graph Partition, is known to be NP-hard on general graphs and polynomial-time solvable on trees, and polynomial-time 2-approximable. In this paper we study the restriction of Dense Graph Partition to particular sparse and dense graph classes. In particular, we prove that it is NP-hard on dense bipartite graphs as well as on cubic graphs. On dense graphs on n vertices, it is polynomial-time solvable on graphs with minimum degree and NP-hard on -regular graphs. Some polynomial-time approximation results are also established.
{"title":"Dense graph partitioning on sparse and dense graphs","authors":"Cristina Bazgan , Katrin Casel , Pierre Cazals","doi":"10.1016/j.jcss.2025.103619","DOIUrl":"10.1016/j.jcss.2025.103619","url":null,"abstract":"<div><div>We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is half its average degree, that is, the ratio of its number of edges and its number of vertices. This problem, called Dense Graph Partition, is known to be NP-hard on general graphs and polynomial-time solvable on trees, and polynomial-time 2-approximable. In this paper we study the restriction of Dense Graph Partition to particular sparse and dense graph classes. In particular, we prove that it is NP-hard on dense bipartite graphs as well as on cubic graphs. On dense graphs on <em>n</em> vertices, it is polynomial-time solvable on graphs with minimum degree <span><math><mi>n</mi><mo>−</mo><mn>3</mn></math></span> and NP-hard on <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>4</mn><mo>)</mo></math></span>-regular graphs. Some polynomial-time approximation results are also established.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"150 ","pages":"Article 103619"},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
In this paper, we study temporal graphs arising from 1 dimensional mobility models, where vertices correspond to agents moving on a line and edges appear each time two agents meet. If each pair of agents meets exactly once, we get a simple temporal clique. In order to characterize such temporal cliques, we introduce the notion of forbidden patterns in temporal graphs. We extend the forbidden pattern characterization to simple mobility graphs (where each edge appears at most once) and to the analogous circular problem, where agents are moving along a circle. We also study the problem where pairs of agents are allowed to cross each other several times, using an approach from automata theory. We observe that in this case, there is no finite set of forbidden patterns that characterize such temporal graphs, nevertheless provide a linear time algorithm to recognize them.
{"title":"Forbidden patterns in temporal graphs resulting from encounters in a corridor","authors":"Mónika Csikós , Michel Habib , Minh-Hang Nguyen , Mikaël Rabie , Laurent Viennot","doi":"10.1016/j.jcss.2025.103620","DOIUrl":"10.1016/j.jcss.2025.103620","url":null,"abstract":"<div><div>In this paper, we study temporal graphs arising from 1 dimensional mobility models, where vertices correspond to agents moving on a line and edges appear each time two agents meet. If each pair of agents meets exactly once, we get a simple temporal clique. In order to characterize such temporal cliques, we introduce the notion of forbidden patterns in temporal graphs. We extend the forbidden pattern characterization to simple mobility graphs (where each edge appears at most once) and to the analogous circular problem, where agents are moving along a circle. We also study the problem where pairs of agents are allowed to cross each other several times, using an approach from automata theory. We observe that in this case, there is no finite set of forbidden patterns that characterize such temporal graphs, nevertheless provide a linear time algorithm to recognize them.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"150 ","pages":"Article 103620"},"PeriodicalIF":1.1,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
Pub Date : 2025-01-08DOI: 10.1016/j.jcss.2024.103618
Matthew Connor, Othon Michail
We study programmable matter systems consisting of modules that perform the minimal mechanical operation of rotating by 90° around each other. We represent the modules as nodes lying on the cells of a two-dimensional square grid. We are interested in characterising families whose shapes can be transformed into each other by a sequence of rotation moves that maintains global connectivity. Shapes can only be transformed into each other by rotation if they are colour-consistent, meaning that their nodes have identical colour cardinalities on a checkered colouring of the grid. We develop a generic centralised transformation and prove that, for any pair A, B of connected, colour-consistent, orthogonally convex shapes, it can transform A into B, using a seed of 3 or 4 nodes to trigger the transformation. The running time of our transformation is an optimal sequential moves, where .
{"title":"Transformation of modular robots by rotation: 3 + 1 musketeers for all orthogonally convex shapes","authors":"Matthew Connor, Othon Michail","doi":"10.1016/j.jcss.2024.103618","DOIUrl":"10.1016/j.jcss.2024.103618","url":null,"abstract":"<div><div>We study programmable matter systems consisting of modules that perform the minimal mechanical operation of rotating by 90° around each other. We represent the modules as nodes lying on the cells of a two-dimensional square grid. We are interested in characterising families whose shapes can be transformed into each other by a sequence of rotation moves that maintains global connectivity. Shapes can only be transformed into each other by rotation if they are <em>colour-consistent</em>, meaning that their nodes have identical colour cardinalities on a checkered colouring of the grid. We develop a generic centralised transformation and prove that, for any pair <em>A</em>, <em>B</em> of connected, colour-consistent, orthogonally convex shapes, it can transform <em>A</em> into <em>B</em>, using a <em>seed</em> of 3 or 4 nodes to trigger the transformation. The running time of our transformation is an optimal <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> sequential moves, where <span><math><mi>n</mi><mo>=</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>=</mo><mo>|</mo><mi>B</mi><mo>|</mo></math></span>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"150 ","pages":"Article 103618"},"PeriodicalIF":1.1,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
Pub Date : 2025-01-07DOI: 10.1016/j.jcss.2024.103617
Eun Jung Kim , Euiwoong Lee , Dimitrios M. Thilikos
The Weighted -Vertex Deletion for a class of graphs asks, weighted graph G, for a minimum weight vertex set S such that . The case when is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for Weighted -Vertex Deletion. Only three cases of minor-closed are known to admit constant-factor approximations, namely Vertex Cover, Feedback Vertex Set and Diamond Hitting Set. We study the problem for the class of -minor-free graphs, under the equivalent setting of the Weightedc-Bond Cover problem, and present a constant-factor approximation algorithm using the primal-dual method. Besides making an important step in the quest of (dis)proving a constant-factor approximation for Weighted -Vertex Deletion, our result may be useful as a template for algorithms for other minor-closed families.
{"title":"A constant-factor approximation for weighted bond cover","authors":"Eun Jung Kim , Euiwoong Lee , Dimitrios M. Thilikos","doi":"10.1016/j.jcss.2024.103617","DOIUrl":"10.1016/j.jcss.2024.103617","url":null,"abstract":"<div><div>The <span>Weighted</span> <span><math><mi>F</mi></math></span>-<span>Vertex Deletion</span> for a class <span><math><mi>F</mi></math></span> of graphs asks, weighted graph <em>G</em>, for a minimum weight vertex set <em>S</em> such that <span><math><mi>G</mi><mo>−</mo><mi>S</mi><mo>∈</mo><mi>F</mi></math></span>. The case when <span><math><mi>F</mi></math></span> is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for <span>Weighted</span> <span><math><mi>F</mi></math></span>-<span>Vertex Deletion</span>. Only three cases of minor-closed <span><math><mi>F</mi></math></span> are known to admit constant-factor approximations, namely <span>Vertex Cover</span>, <span>Feedback Vertex Set</span> and <span>Diamond Hitting Set</span>. We study the problem for the class <span><math><mi>F</mi></math></span> of <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>-minor-free graphs, under the equivalent setting of the <span>Weighted</span> <em>c</em><span>-Bond Cover</span> problem, and present a constant-factor approximation algorithm using the primal-dual method. Besides making an important step in the quest of (dis)proving a constant-factor approximation for <span>Weighted</span> <span><math><mi>F</mi></math></span>-<span>Vertex Deletion</span>, our result may be useful as a template for algorithms for other minor-closed families.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"149 ","pages":"Article 103617"},"PeriodicalIF":1.1,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-12-11DOI: 10.1016/j.jcss.2024.103615
Reijo Jaakkola , Antti Kuusisto , Miikka Vilander
We demonstrate novel links between entropy and description complexity, a notion referring to the minimal formula length for specifying given properties. Let PLC denote propositional logic with the ability to count assignments, and let be the fragment that counts only to one, essentially quantifying assignments. In the finite, is expressively complete for specifying sets of variable assignments, while PLC is expressively complete for multisets. We show that for both logics, the model classes with maximal Boltzmann entropy are the ones with maximal description complexity. Concerning PLC, we show that expected Boltzmann entropy is asymptotically equivalent to expected description complexity multiplied by the number of proposition symbols considered. For contrast, we prove this link breaks for first-order logic over vocabularies with higher-arity relations. Our results relate to links between Kolmogorov complexity and entropy, providing analogous results in the logic-based scenario with relational structures classified by formulas of different sizes.
{"title":"Relating description complexity to entropy","authors":"Reijo Jaakkola , Antti Kuusisto , Miikka Vilander","doi":"10.1016/j.jcss.2024.103615","DOIUrl":"10.1016/j.jcss.2024.103615","url":null,"abstract":"<div><div>We demonstrate novel links between entropy and description complexity, a notion referring to the minimal formula length for specifying given properties. Let PLC denote propositional logic with the ability to count assignments, and let <span><math><msup><mrow><mi>PLC</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> be the fragment that counts only to one, essentially quantifying assignments. In the finite, <span><math><msup><mrow><mi>PLC</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> is expressively complete for specifying sets of variable assignments, while PLC is expressively complete for multisets. We show that for both logics, the model classes with maximal Boltzmann entropy are the ones with maximal description complexity. Concerning PLC, we show that expected Boltzmann entropy is asymptotically equivalent to expected description complexity multiplied by the number of proposition symbols considered. For contrast, we prove this link breaks for first-order logic over vocabularies with higher-arity relations. Our results relate to links between Kolmogorov complexity and entropy, providing analogous results in the logic-based scenario with relational structures classified by formulas of different sizes.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"149 ","pages":"Article 103615"},"PeriodicalIF":1.1,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
Pub Date : 2024-12-11DOI: 10.1016/j.jcss.2024.103616
Andreea-Teodora Nász
The HOM-problem, which asks whether the image of a regular tree language under a tree homomorphism is again regular, is known to be decidable. In this paper, we prove the weighted HOM-problem for all fields decidable, provided that the tree homomorphism is tetris-free (a condition that generalizes injectivity). To this end, we reduce the problem to a property of the device representing the homomorphic image in question; to prove this property decidable, we then derive a pumping lemma for such devices from the well-known pumping lemma for regular tree series over fields, proved by Berstel and Reutenauer in 1982.
{"title":"The weighted HOM-problem over fields","authors":"Andreea-Teodora Nász","doi":"10.1016/j.jcss.2024.103616","DOIUrl":"10.1016/j.jcss.2024.103616","url":null,"abstract":"<div><div>The <em>HOM-problem</em>, which asks whether the image of a regular tree language under a tree homomorphism is again regular, is known to be decidable. In this paper, we prove the <em>weighted</em> HOM-problem for all fields decidable, provided that the tree homomorphism is <em>tetris-free</em> (a condition that generalizes injectivity). To this end, we reduce the problem to a property of the device representing the homomorphic image in question; to prove this property decidable, we then derive a pumping lemma for such devices from the well-known pumping lemma for regular tree series over fields, proved by Berstel and Reutenauer in 1982.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"149 ","pages":"Article 103616"},"PeriodicalIF":1.1,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
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