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We investigate computational issues in the distributed model Amoebots of programmable matter. In this model, the computational entities, called particles, are anonymous finite-state machines that operate and move on an hexagonal tasselation…

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…

Motivated by targeted drug delivery, we investigate the gathering of particles in the full tilt model of externally controlled motion planning: A set of particles is located at the tiles of a polyomino with all particles reacting uniformly…

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research…

Consider the problem of planning collision-free motion of $n$ objects in the plane movable through contact with a robot that can autonomously translate in the plane and that can move a maximum of $m \leq n$ objects simultaneously. This…

We implement and evaluate different methods for the reconfiguration of a connected arrangement of tiles into a desired target shape, using a single active robot that can move along the tile structure. This robot can pick up, carry, or drop…

Many robots are not equipped with a manipulator and many objects are not suitable for prehensile manipulation (such as large boxes and cylinders). In these cases, pushing is a simple yet effective non-prehensile skill for robots to interact…

Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…

The idea behind universal coating is to have a thin layer of a specific substance covering an object of any shape so that one can measure a certain condition (like temperature or cracks) at any spot on the surface of the object without…

Many order fulfillment applications in logistics, such as packing, involve picking objects from unstructured piles before tightly arranging them in bins or shipping containers. Desirable robotic solutions in this space need to be low-cost,…

This paper considers the problem of rearrangement planning, i.e finding a sequence of manipulation actions that displace multiple objects from an initial configuration to a given goal configuration. Rearrangement is a critical skill for…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…

Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA)…

A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…

We consider programmable matter consisting of simple computational elements, called particles, that can establish and release bonds and can actively move in a self-organized way, and we investigate the feasibility of solving fundamental…

Robot manipulation in cluttered environments often requires complex and sequential rearrangement of multiple objects in order to achieve the desired reconfiguration of the target objects. Due to the sophisticated physical interactions…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…