Shape recognition by a finite automaton robot

Robert Gmyr, Kristian Hinnenthal, I. Kostitsyna, Fabian Kuhn, Dorian Rudolph, Christian Scheideler

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Motivated by the problem of shape recognition by nanoscale computing agents, we investigate the problem of detecting the geometric shape of a structure composed of hexagonal tiles by a finite-state automaton robot. In particular, in this paper we consider the question of recognizing whether the tiles are assembled into a parallelogram whose longer side has length l = f(h), for a given function f(*), where h is the length of the shorter side. To determine the computational power of the finite-state automaton robot, we identify functions that can or cannot be decided when the robot is given a certain number of pebbles. We show that the robot can decide whether l = ah+b for constant integers a and b without any pebbles, but cannot detect whether l = f(h) for any function f(x) = omega(x). For a robot with a single pebble, we present an algorithm to decide whether l = p(h) for a given polynomial p(*) of constant degree. We contrast this result by showing that, for any constant k, any function f(x) = omega(x^(6k + 2)) cannot be decided by a robot with k states and a single pebble. We further present exponential functions that can be decided using two pebbles. Finally, we present a family of functions f_n(*) such that the robot needs more than n pebbles to decide whether l = f_n(h).
Original languageEnglish
Number of pages6
Publication statusPublished - 2018
Event34th European Workshop on Computational Geometry (EuroCG2018) - Berlin, Germany
Duration: 21 Mar 201823 Mar 2018


Conference34th European Workshop on Computational Geometry (EuroCG2018)
Abbreviated titleEuroCG2018
Internet address


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