Elsevier

Theoretical Computer Science

Volume 574, 6 April 2015, Pages 1-17
Theoretical Computer Science

A decidable class of planar linear hybrid systems

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Abstract

In this paper, we show the decidability of a new subclass of linear hybrid automata. These automata are planar, that is, consist of two state variables, monotonic along some direction in the plane and have identity resets, that is, the values of the continuous variables are not reset to a different value on a discrete transition. Our proof uses a combination of a tree construction capturing the edge-to-edge reachability and a finite bisimulation construction. Our class strictly contains the class of two dimensional piecewise constant derivative systems for which decidability of the reachability problem is known.

Keywords

Hybrid systems
Decidability
Planar systems
Piecewise constant derivatives
Bisimulations
Reachability
Verification
Safety

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