Hourglass Automata

TL;DR

This paper introduces hourglass automata, a class of timed automata with reversible clocks, and demonstrates that their language emptiness problem remains decidable with up to two clocks using a novel clock update method.

Contribution

The paper defines hourglass automata and presents a new clock update allowing their expression, proving decidability of language emptiness for up to two clocks.

Findings

Decidability of language emptiness for hourglass automata with up to two clocks.

Introduction of a new clock update for timed automata.

Construction of finite untimed graphs using clock regions.

Abstract

In this paper, we define the class of hourglass automata, which are timed automata with bounded clocks that can be made to progress backwards as well as forwards at a constant rate. We then introduce a new clock update for timed automata that allows hourglass automata to be expressed. This allows us to show that language emptiness remains decidable with this update when the number of clocks is two or less. This is done by showing that we can construct a finite untimed graph using clock regions from any timed automaton that use this new update.