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Author Bitar, N.; Goles, E.; Montealegre, P.
Title COMPUTATIONAL COMPLEXITY OF BIASED DIFFUSION-LIMITED AGGREGATION Type
Year 2022 Publication Siam Journal On Discrete Mathematics Abbreviated Journal SIAM Discret. Math.
Volume 36 Issue 1 Pages 823-866
Keywords diffusion-limited aggregation; computational complexity; space complexity; NL-completeness; P-completeness
Abstract Diffusion-Limited Aggregation (DLA) is a cluster-growth model that consists in a set of particles that are sequentially aggregated over a two-dimensional grid. In this paper, we introduce a biased version of the DLA model, in which particles are limited to move in a subset of possible directions. We denote by k-DLA the model where the particles move only in k possible directions. We study the biased DLA model from the perspective of Computational Complexity, defining two decision problems The first problem is Prediction, whose input is a site of the grid c and a sequence S of walks, representing the trajectories of a set of particles. The question is whether a particle stops at site c when sequence S is realized. The second problem is Realization, where the input is a set of positions of the grid, P. The question is whether there exists a sequence S that realizes P, i.e. all particles of S exactly occupy the positions in P. Our aim is to classify the Prediciton and Realization problems for the different versions of DLA. We first show that Prediction is P-Complete for 2-DLA (thus for 3-DLA). Later, we show that Prediction can be solved much more efficiently for 1-DLA. In fact, we show that in that case the problem is NL-Complete. With respect to Realization, we show that restricted to 2-DLA the problem is in P, while in the 1-DLA case, the problem is in L.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0895-4801 ISBN Medium
Area Expedition Conference
Notes WOS:000778502000037 Approved
Call Number UAI @ alexi.delcanto @ Serial 1558
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Author Goles, E.; Montealegre, P.
Title Computational complexity of threshold automata networks under different updating schemes Type
Year 2014 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.
Volume 559 Issue Pages 3-19
Keywords Automata networks; Threshold functions; Computational complexity; Updating scheme; P-completeness; NC; NP-Hard
Abstract Given a threshold automata network, as well as an updating scheme over its vertices, we study the computational complexity associated with the prediction of the future state of a vertex. More precisely, we analyze two classes of local functions: the majority and the AND-OR rule (vertices take the AND or the OR logic functions over the state of its neighborhoods). Depending on the updating scheme, we determine the complexity class (NC, P, NP, PSPACE) where the prediction problem belongs. (C) 2014 Elsevier B.V. All rights reserved.
Address [Goles, Eric] Univ Adolfo Ibanez, Fac Ciencias & Tecnol, Santiago, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0304-3975 ISBN Medium
Area Expedition Conference
Notes WOS:000347025300002 Approved
Call Number UAI @ eduardo.moreno @ Serial 434
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Author Goles, E.; Montealegre, P.
Title The complexity of the majority rule on planar graphs Type
Year 2015 Publication Advances In Applied Mathematics Abbreviated Journal Adv. Appl. Math.
Volume 64 Issue Pages 111-123
Keywords Automata networks; Computational complexity; Majority; P-Completeness; NC; Planar graph
Abstract We study the complexity of the majority rule on planar automata networks. We reduce a special case of the Monotone Circuit Value Problem to the prediction problem of determining if a vertex of a planar graph will change its state when the network is updated with the majority rule. (C) 2014 Elsevier Inc. All rights reserved.
Address [Goles, Eric] Univ Adolfo Ibanez, Fac Ciencias & Tecnol, Santiago, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Academic Press Inc Elsevier Science Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0196-8858 ISBN Medium
Area Expedition Conference
Notes WOS:000348883400007 Approved
Call Number UAI @ eduardo.moreno @ Serial 445
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Author Goles, E.; Montealegre, P.
Title The complexity of the asynchronous prediction of the majority automata Type
Year 2020 Publication Information and Computation Abbreviated Journal Inf. Comput.
Volume 274 Issue SI Pages
Keywords Majority automata; Cellular automata; Prediction problem; Asynchronous updating; Computational complexity; Parallel algorithms; Bootstrap percolation; NP-Completeness
Abstract We consider the asynchronous prediction problem for some automaton as the one consisting in determining, given an initial configuration, if there exists a non-zero probability that some selected site changes its state, when the network is updated picking one site at a time uniformly at random. We show that for the majority automaton, the asynchronous prediction problem is in NC in the two-dimensional lattice with von Neumann neighborhood. Later, we show that in three or more dimensions the problem is NP-Complete.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0890-5401 ISBN Medium
Area Expedition Conference
Notes Approved
Call Number UAI @ eduardo.moreno @ Serial 1124
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