Particle computation: complexity, algorithms, and logic

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). Upon activation of the field, each particle moves maximally in the same direction unt...

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Vydané v:	Natural computing Ročník 18; číslo 1; s. 181 - 201
Hlavní autori:	Becker, Aaron T., Demaine, Erik D., Fekete, Sándor P., Lonsford, Jarrett, Morris-Wright, Rose
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Dordrecht Springer Netherlands 01.03.2019 Springer Nature B.V
Predmet:	Algorithms Artificial Intelligence Complex Systems Complexity Computer Science Computer simulation Configurations Digital electronics Evolutionary Biology Gates Gravitation Inverse problems Logic Logic circuits Permutations Processor Architectures Replicating Stability Theory of Computation Robot swarms Uniform inputs Nano-particles Programmable matter PSPACE-completeness Parallel motion planning NP-completeness Logic gates Array permutations Universal computation Efficient algorithms Complexity
ISSN:	1567-7818, 1572-9796
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Abstract	We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). Upon activation of the field, each particle moves maximally in the same direction until forward progress is blocked by a stationary obstacle or another stationary particle. In an open workspace, this system model is of limited use because it has only two controllable degrees of freedom—all particles receive the same inputs and move uniformly. We show that adding a maze of obstacles to the environment can make the system drastically more complex but also more useful. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and , nand , nor , and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2 × 1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits.
AbstractList	We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). Upon activation of the field, each particle moves maximally in the same direction until forward progress is blocked by a stationary obstacle or another stationary particle. In an open workspace, this system model is of limited use because it has only two controllable degrees of freedom—all particles receive the same inputs and move uniformly. We show that adding a maze of obstacles to the environment can make the system drastically more complex but also more useful. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and, nand, nor, and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2 × 1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits. We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). Upon activation of the field, each particle moves maximally in the same direction until forward progress is blocked by a stationary obstacle or another stationary particle. In an open workspace, this system model is of limited use because it has only two controllable degrees of freedom—all particles receive the same inputs and move uniformly. We show that adding a maze of obstacles to the environment can make the system drastically more complex but also more useful. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and , nand , nor , and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2 × 1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits.
Author	Becker, Aaron T. Demaine, Erik D. Fekete, Sándor P. Morris-Wright, Rose Lonsford, Jarrett
Author_xml	– sequence: 1 givenname: Aaron T. surname: Becker fullname: Becker, Aaron T. organization: Department of Electrical and Computer Engineering, University of Houston – sequence: 2 givenname: Erik D. surname: Demaine fullname: Demaine, Erik D. organization: Computer Science and Artificial Intelligence Laboratory, MIT – sequence: 3 givenname: Sándor P. surname: Fekete fullname: Fekete, Sándor P. email: s.fekete@tu-bs.de organization: Department of Computer Science, TU Braunschweig – sequence: 4 givenname: Jarrett surname: Lonsford fullname: Lonsford, Jarrett organization: Department of Electrical and Computer Engineering, University of Houston – sequence: 5 givenname: Rose surname: Morris-Wright fullname: Morris-Wright, Rose organization: Department of Mathematics, Brandeis University
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Cites_doi	10.1177/0278364911399525 10.1109/ICRA.2014.6907856 10.1039/C2NR32554C 10.1145/1109557.1109668 10.1007/978-3-642-45346-5_5 10.1016/S0925-7721(99)00017-6 10.1177/0278364912467486 10.1109/JCN.2000.6596708 10.1089/cmb.2009.0067 10.1177/0278364912464669 10.1016/0304-3975(85)90047-7 10.1177/02783649922067663 10.1177/0278364909340279 10.1007/BF01530890 10.1109/TRA.2002.802212 10.1109/70.795790 10.1137/1.9781611973730.12 10.1109/IROS.2012.6385723 10.1109/4.597298 10.1007/978-3-540-92910-9_58 10.1007/978-3-540-27820-7_12 10.1109/IROS.2013.6696401 10.1137/1.9781611973402.56 10.1016/j.tcs.2005.05.008 10.1007/BF01857727 10.1177/0278364914543481 10.1109/HPCSim.2011.5999906 10.1109/ROBOT.2008.4543458 10.1145/332833.332842 10.1109/IROS.2013.6696828 10.1007/978-1-4471-0129-1_18 10.1002/mrm.21638 10.1109/IROS.2005.1545576 10.1109/ICRA.2012.6225330 10.1109/56.800 10.1007/BF01891840 10.1145/1137856.1137926 10.1177/027836402320556449 10.1177/0278364904045480 10.1021/nn203969b 10.1109/ICRA.2015.7139951 10.1038/28998 10.1201/9780429487309 10.1007/3-540-45993-6_15 10.1109/ICRA.2013.6631367 10.1016/j.tcs.2002.11.002 10.1109/ICRA.2012.6224638 10.1177/0278364912442430 10.1109/ROBOT.2006.1641956
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Copyright	Springer Science+Business Media B.V., part of Springer Nature 2017 Natural Computing is a copyright of Springer, (2017). All Rights Reserved.
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Keywords	Robot swarms Uniform inputs Nano-particles Programmable matter PSPACE-completeness Parallel motion planning NP-completeness Logic gates Array permutations Universal computation Efficient algorithms Complexity
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SubjectTerms	Algorithms Artificial Intelligence Complex Systems Complexity Computer Science Computer simulation Configurations Digital electronics Evolutionary Biology Gates Gravitation Inverse problems Logic Logic circuits Permutations Processor Architectures Replicating Stability Theory of Computation
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