Particle computation: Device fan-out and binary memory

Shad, Hamed Mohtasham; Morris-Wright, Rose; Demaine, Erik D.; Fekete, Sándor P.; Becker, Aaron T.

doi:10.1109/icra.2015.7139951

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…Preliminary versions of Section 4 and Section 5 are main topics of our paper [7] with an extra result proving the system to give rise to pspacecompleteness in Section 5.3 from paper [8]. The particle logic in Sections 6 and 7 was introduced in [8] and completed in paper [58]. This work has been partially supported by the National Science Foundation (Grant No.…”

Section: Resultsmentioning

confidence: 99%

Particle computation: complexity, algorithms, and logic

Becker

Demaine²,

Fekete

et al. 2017

Nat Comput

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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.

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Section: Resultsmentioning

confidence: 99%

Particle computation: complexity, algorithms, and logic

Becker

Demaine²,

Fekete

et al. 2017

Nat Comput

Self Cite

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“…Becker et al [6] show that particles can be used for computation by implementing not, nand, nor, xor and xnor gates within a particularly designed obstacle environment. If the model is generalized by adding 2 × 1 particles (dominoes), it is also possible to construct fan-out gates [9,47].…”

Section: Tilt Problemsmentioning

confidence: 99%

Particle-Based Assembly Using Precise Global Control

et al. 2022

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In micro- and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. In the presence of adhesive particles that can attach to each other, the challenge is to decide whether a shape is constructible. Previous work provides a class of shapes for which constructibility can be decided efficiently when particles move maximally into the same direction induced by a global signal. In this paper we consider the single step model, i.e., a model in which each particle moves one unit step into the given direction. We restrict the assembly process such that at each single time step actually one particle is added to and moved within the workspace. We prove that deciding constructibility is NP-complete for three-dimensional shapes, and that a maximum constructible shape can be approximated. The same approximation algorithm applies for 2D. We further present linear-time algorithms to decide whether or not a tree-shape in 2D or 3D is constructible. Scaling a shape yields constructibility; in particular we show that the 2-scaled copy of every non-degenerate polyomino is constructible. In the three-dimensional setting we show that the 3-scaled copy of every non-degenerate polycube is constructible.

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“…If an obstacle environment can be designed, Becker et al [6] show that particles can be used for computation by implementing not, nand, nor, xor and xnor gates. If the model is generalized by adding 2 × 1 particles (dominoes), it is also possible to construct fan-out gates [5,41].…”

Section: Self-assemblymentioning

confidence: 99%

Particle-Based Assembly Using Precise Global Control

Keller¹,

Rieck²,

Scheffer³

et al. 2021

Preprint

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In micro-and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. In the presence of adhesive particles that can attach to each other, the challenge is to decide whether a shape is constructible. Previous work provides a class of shapes for which constructibility can be decided efficiently, when particles move maximally into the same direction on actuation.In this paper, we consider a stronger model. On actuation, each particle moves one unit step into the given direction. We prove that deciding constructibility is NP-hard for three-dimensional shapes, and that a maximum constructible shape can be approximated. The same approximation algorithm applies for 2D. We further present linear-time algorithms to decide whether a tree-shape in 2D or 3D is constructible. If scaling is allowed, we show that the c-scaled copy of every non-degenerate polyomino is constructible, for every c ≥ 2.

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Particle computation: Device fan-out and binary memory

Cited by 8 publications

References 18 publications

Particle computation: complexity, algorithms, and logic

Particle computation: complexity, algorithms, and logic

Particle-Based Assembly Using Precise Global Control

Particle-Based Assembly Using Precise Global Control

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