Countdown games, and simulation on (succinct) one-counter nets

by   Petr Jancar, et al.

We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (LMCS 2016) [HLMT16] for simulation preorder of succinct one-counter nets (i.e., one-counter automata with no zero tests where counter increments and decrements are integers written in binary), by showing that all relations between bisimulation equivalence and simulation preorder are EXPSPACE-hard for these nets. We describe a reduction from reachability games whose EXPSPACE-completeness in the case of succinct one-counter nets was shown by Hunter [RP 2015], by using other results. We also provide a direct self-contained EXPSPACE-completeness proof for a special case of such reachability games, namely for a modification of countdown games that were shown EXPTIME-complete by Jurdzinski, Sproston, Laroussinie [LMCS 2008]; in our modification the initial counter value is not given but is freely chosen by the first player. We also present a new simplified proof of the belt theorem that gives a simple graphic presentation of simulation preorder on one-counter nets and leads to a polynomial-space algorithm; it is an alternative to the proof from [HLMT16].



There are no comments yet.


page 1

page 2

page 3

page 4


EXPSPACE-hardness of behavioural equivalences of succinct one-counter nets

We note that the remarkable EXPSPACE-hardness result in [Göller, Haase, ...

Continuous One-Counter Automata

We study the reachability problem for continuous one-counter automata, C...

Squares: A Fast Counter-Based RNG

In this article, we present a new counter-based random number generator ...

Revisiting Synthesis for One-Counter Automata

One-counter automata are obtained by extending classical finite-state au...

Universality Problem for Unambiguous VASS

We study languages of unambiguous VASS, that is, Vector Addition Systems...

Dynamic Toolbox for ETRINV

Recently, various natural algorithmic problems have been shown to be ∃R-...

The Emptiness Problem for Valence Automata over Graph Monoids

This work studies which storage mechanisms in automata permit decidabili...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.