SCIENCE CHINA Information Sciences, Volume 61, Issue 1: 012102(2018) https://doi.org/10.1007/s11432-016-9027-y

## Updatable timed automata with one updatable clock

• AcceptedFeb 9, 2017
• PublishedSep 1, 2017
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### Abstract

Updatable timed automata (UTAs) proposed by Bouyer et.al., is an extension of timed automata (TAs) having the extra ability to update clocks in a more elaborate way than simply reset them to zero. The reachability of UTAs is generally undecidable, which can be easily gained by regarding a pair of clocks as updatable counters. This paper investigates a subclass of UTAs by restricting the number of updatable clocks to be one. We will show that (1) the reachability of general UTAs with one updatable clock (UTA1s) is still undecidable, and (2) that of UTA1s under diagonal-free constraints is decidable, and the complexity is Pspace-complete. The former is achieved by encoding Minsky machines to the general UTA1s, where two counters are simulated by the updatable clock. The latter is gained by regarding a region of a UTA1 to be an unbounded digiword, and encoding sets of digiwords that are accepted by a one counter automaton where regions are generated as the value of the counter.

### Acknowledgment

This work was supported by NSFC-JSPS Bilateral Joint Research Project (Grant No. 61511140100), and National Natural Science Foundation of China (Grant Nos. 61472240, 61602224, 91318301).

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• Figure 1

An Example for UTA1s.

• Figure 2

Value passing from a normal clock to the updatable clock.

• Figure 3

Value passing from the updatable clock to a normal clock.

• Figure 4

(a) Doubling $d$ to $2d$; (b) halving $d$ to $d/2$; (c) tripling $d$ to $3d$; (d) thirding $d$ to $d/3$.

• Figure 5

The intervals when $n=6$.

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