# Parametric updates in parametric timed automata

## TL;DR

This paper introduces a new subclass of Parametric Timed Automata with parametric clock updates, enabling decidability of the EF-emptiness problem and exact synthesis of parameter valuations for reachability.

## Contribution

It defines a novel subclass of PTAs with parametric updates where EF-emptiness is decidable and allows exact synthesis, a first in extended PTAs.

## Key findings

- Decidability of EF-emptiness in the new subclass.
- Exact synthesis of parameter valuations for reachability.
- First non-trivial subclass of extended PTAs with this property.

## Abstract

We introduce a new class of Parametric Timed Automata (PTAs) where we allow clocks to be compared to parameters in guards, as in classic PTAs, but also to be updated to parameters. We focus here on the EF-emptiness problem: "is the set of parameter valuations for which some given location is reachable in the instantiated timed automaton empty?". This problem is well-known to be undecidable for PTAs, and so it is for our extension. Nonetheless, if we update all clocks each time we compare a clock with a parameter and each time we update a clock to a parameter, we obtain a syntactic subclass for which we can decide the EF-emptiness problem and even perform the exact synthesis of the set of rational valuations such that a given location is reachable. To the best of our knowledge, this is the first non-trivial subclass of PTAs, actually even extended with parametric updates, for which this is possible.