Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets

We analyze the computational complexity of motion planning through local "input/output" gadgets with separate entrances and exits, and a subset of allowed traversals from entrances to exits, each of which changes the state of the gadget and thereby the allowed traversals. We study such gadgets in the 0-, 1-, and 2-player settings, in particular extending past motion-planning-through-gadgets work to 0-player games for the first time, by considering "branchless" connections between gadgets that route every gadget's exit to a unique gadget's entrance. Our complexity results include containment in L, NL, P, NP, and PSPACE; as well as hardness for NL, P, NP, and PSPACE. We apply these results to show PSPACE-completeness for certain mechanics in Factorio, [the Sequence], and a restricted version of Trainyard, improving prior results. This work strengthens prior results on switching graphs and reachability switching games.Comment: 37 pages, 36 figure

Traversability, Reconfiguration, and Reachability in the Gadget Framework

Consider an agent traversing a graph of "gadgets", each with local state that changes with each traversal by the agent. We characterize the complexity of universal traversal, where the goal is to traverse every gadget at least once, for DAG gadgets, one-state gadgets, and reversible deterministic gadgets. We also study the complexity of reconfiguration, where the goal is to bring the system of gadgets to a specified state, proving many cases PSPACE-complete, and showing in some cases that reconfiguration can be strictly harder than reachability (where the goal is for the agent to reach a specified location), while in other cases, reachability is strictly harder than reconfiguration.Comment: Full version of article appearing in WALCOM 2022. 23 pages, 14 figure

Pemilihan Supplier Biji Plastik dengan Metode Analitycal Hierarchy Process (AHP) dan Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)

Perusahaan perlu mengevaluasi kinerja supplier untuk mendapatkan supplier masuk sesuai dengan kriteria perusahaan. Permasalahan pada PT. Wonorejo Makmur Abadi adalah belum adanya kriteria dan standar yang tepat untuk ditetapkan dalam pemilihan supplier sehingga perusahaan tidak adanya evaluasi kinerja supplier. Tujuan dari penelitian ini adalah untuk mengetahui bobot nilai dari setiap kriteria yang digunakan dalam pengambilan keputusan pemilihan alternatif supplier terbaik di PT “Wonorejo Makmur Abadi”. Kriteria yang digunakan ada tujuh, antara lain: Harga pembelian, kualitas, waktu tenggang pembayaran, ketepatan pengiriman, kemampuan pemenuhan terhadap jumlah pemesanan, jarak supplier, dan pelayanan. Untuk mendapatkan data yang lengkap, peneliti menggunakan metode berupa wawancara dan pengisian kuesioner. Metode yang digunakan dalam pengolahan data pada penelitian ini yaitu metode AHP dan TOPSIS. Berdasarkan pengolahan data menggunakan metode AHP dihasilkan bobot dengan kriteria tertinggi yaitu pada harga pembelian, dilanjutkan secara berturut-turut yaitu kriteria kualitas, waktu tenggang pembayar, ketepatan pengiriman, kemampuan pemenuhan terhadap jumlah pemesanan, jarak supplier, dan pelayanan. Kemudian untuk pengolahan data menggunakan TOPSIS dapat diketahui bahwa supplier Surabaya merupakan supplier yang paling potensial. Prioritas alternative selanjutnya berdasarkan rangking secara berturut-turut yaitu, Supplier Semarang, Supplier Solo, dan Supplier Bandung

Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets

A door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "open" and "close" tunnel sets the gadget's state to open and closed, respectively, while the "traverse" tunnel can be traversed if and only if the door is in the open state. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar assembly of such door gadgets, removing the traditional need for crossover gadgets and thereby simplifying past PSPACE-hardness proofs of Lemmings and Nintendo games Super Mario Bros., Legend of Zelda, and Donkey Kong Country. Our result holds in all but one of the possible local planar embedding of the open, close, and traverse tunnels within a door gadget; in the one remaining case, we prove NP-hardness. We also introduce and analyze a simpler type of door gadget, called the self-closing door. This gadget has two states and only two tunnels, similar to the "open" and "traverse" tunnels of doors, except that traversing the traverse tunnel also closes the door. In a variant called the symmetric self-closing door, the "open" tunnel can be traversed if and only if the door is closed. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar assembly of either type of self-closing door. Then we apply this framework to prove new PSPACE-hardness results for eight different 3D Mario games and Sokobond.Comment: Accepted to FUN2020, 35 pages, 41 figure

Complexity of Motion Planning of Arbitrarily Many Robots: Gadgets, Petri Nets, and Counter Machines

We extend the motion-planning-through-gadgets framework to several new scenarios involving various numbers of robots/agents, and analyze the complexity of the resulting motion-planning problems. While past work considers just one robot or one robot per player, most of our models allow for one or more locations to spawn new robots in each time step, leading to arbitrarily many robots. In the 0-player context, where all motion is deterministically forced, we prove that deciding whether any robot ever reaches a specified location is undecidable, by representing a counter machine. In the 1-player context, where the player can choose how to move the robots, we prove equivalence to Petri nets, EXPSPACE-completeness for reaching a specified location, PSPACE-completeness for reconfiguration, and ACKERMANN-completeness for reconfiguration when robots can be destroyed in addition to spawned. Finally, we consider a variation on the standard 2-player context where, instead of one robot per player, we have one robot shared by the players, along with a ko rule to prevent immediately undoing the previous move. We prove this impartial 2-player game EXPTIME-complete.Comment: 22 pages, 19 figures. Presented at SAND 202

Complexity of Motion Planning of Arbitrarily Many Robots: Gadgets, Petri Nets, and Counter Machines

We extend the motion-planning-through-gadgets framework to several new scenarios involving various numbers of robots/agents, and analyze the complexity of the resulting motion-planning problems. While past work considers just one robot or one robot per player, most of our models allow for one or more locations to spawn new robots in each time step, leading to arbitrarily many robots. In the 0-player context, where all motion is deterministically forced, we prove that deciding whether any robot ever reaches a specified location is undecidable, by representing a counter machine. In the 1-player context, where the player can choose how to move the robots, we prove equivalence to Petri nets, EXPSPACE-completeness for reaching a specified location, PSPACE-completeness for reconfiguration, and ACKERMANN-completeness for reconfiguration when robots can be destroyed in addition to spawned. Finally, we consider a variation on the standard 2-player context where, instead of one robot per player, we have one robot shared by the players, along with a ko rule to prevent immediately undoing the previous move. We prove this impartial 2-player game EXPTIME-complete

PSPACE-completeness of Pulling Blocks to Reach a Goal

We prove PSPACE-completeness of all but one problem in a large space of pulling-block problems where the goal is for the agent to reach a target destination. The problems are parameterized by whether pulling is optional, the number of blocks which can be pulled simultaneously, whether there are fixed blocks or thin walls, and whether there is gravity. We show NP-hardness for the remaining problem, Pull?-1FG (optional pulling, strength 1, fixed blocks, with gravity).Comment: Full version of JCDCGGG2019 paper, 22 pages, 25 figure

Genetic loci associated with plasma phospholipid N-3 fatty acids: A Meta-Analysis of Genome-Wide association studies from the charge consortium

Long-chain n-3 polyunsaturated fatty acids (PUFAs) can derive from diet or from α-linolenic acid (ALA) by elongation and desaturation. We investigated the association of common genetic variation with plasma phospholipid levels of the four major n-3 PUFAs by performing genome-wide association studies in five population-based cohorts comprising 8,866 subjects of European ancestry. Minor alleles of SNPs in FADS1 and FADS2 (desaturases) were associated with higher levels of ALA (p = 3×10-64) and lower levels of eicosapentaenoic acid (EPA, p = 5×10-58) and docosapentaenoic acid (DPA, p = 4×10-154). Minor alleles of SNPs in ELOVL2 (elongase) were associated with higher EPA (p = 2×10-12) and DPA (p = 1×10-43) and lower docosahexaenoic acid (DHA, p = 1×10-15). In addition to genes in the n-3 pathway, we identified a novel association of DPA with several SNPs in GCKR (glucokinase regulator, p = 1×10-8). We observed a weaker association between ALA and EPA among carriers of the minor allele of a representative SNP in FADS2 (rs1535), suggesting a lower rate of ALA-to-EPA conversion in these subjects. In samples of African, Chinese, and Hispanic ancestry, associations of n-3 PUFAs were similar with a representative SNP in FADS1 but less consistent with a representative SNP in ELOVL2. Our findings show that common variation in n-3 metabolic pathway genes and in GCKR influences plasma phospholipid levels of n-3 PUFAs in populations of European ancestry and, for FADS1, in other ancestries

The genetic determinants of recurrent somatic mutations in 43,693 blood genomes

Nononcogenic somatic mutations are thought to be uncommon and inconsequential. To test this, we analyzed 43,693 National Heart, Lung and Blood Institute Trans-Omics for Precision Medicine blood whole genomes from 37 cohorts and identified 7131 non-missense somatic mutations that are recurrently mutated in at least 50 individuals. These recurrent non-missense somatic mutations (RNMSMs) are not clearly explained by other clonal phenomena such as clonal hematopoiesis. RNMSM prevalence increased with age, with an average 50-year-old having 27 RNMSMs. Inherited germline variation associated with RNMSM acquisition. These variants were found in genes involved in adaptive immune function, proinflammatory cytokine production, and lymphoid lineage commitment. In addition, the presence of eight specific RNMSMs associated with blood cell traits at effect sizes comparable to Mendelian genetic mutations. Overall, we found that somatic mutations in blood are an unexpectedly common phenomenon with ancestry-specific determinants and human health consequences