DeepAI AI Chat
Log In Sign Up

A simple lower bound for ARRIVAL

08/13/2021
by   Graham Manuell, et al.
0

The ARRIVIAL problem introduced by Dohrau, Gärtner, Kohler, Matoušek and Welzl concerns a train moving on a directed graph proceeding along outward edges according to the position of 'switches' at each vertex, which in turn are toggled whenever the train passes through them. The problem asks whether the train every reaches a designated destination vertex. It is known that ARRIVAL is contained in UP ∩ coUP, while the previously best published lower bound is that it is NL-hard. In this note we provide a simple reduction to the 𝖣𝖨𝖦𝖨𝖢𝖮𝖬𝖯_𝖤𝖷𝖯 problem considered by Aaronson. It follows in particular that ARRIVAL is both CC-hard and PL-hard.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/12/2021

A Subexponential Algorithm for ARRIVAL

The ARRIVAL problem is to decide the fate of a train moving along the ed...
10/25/2020

Even the Easiest(?) Graph Coloring Problem is not Easy in Streaming!

We study a graph coloring problem that is otherwise easy but becomes qui...
02/21/2018

ARRIVAL: Next Stop in CLS

We study the computational complexity of ARRIVAL, a zero-player game on ...
07/28/2019

A Lower Bound on Cycle-Finding in Sparse Digraphs

We consider the problem of finding a cycle in a sparse directed graph G ...
05/26/2020

A lower bound for splines on tetrahedral vertex stars

A tetrahedral complex all of whose tetrahedra meet at a common vertex is...
11/23/2022

The Stochastic Arrival Problem

We study a new modification of the Arrival problem, which allows for nod...