  A popular method for modelling reactive systems is to use $\omega$-regular
languages. These languages can be represented as nondeterministic B\"uchi
automata (NBAs) or $\omega$-regular expressions. Existing methods synthesise
expressions from state-based NBAs. Synthesis from transition-based NBAs is
traditionally done by transforming transition-based NBAs into state-based NBAs.
This transformation, however, can increase the complexity of the synthesised
expressions. This paper proposes a novel method for directly synthesising
$\omega$-regular expressions from transition-based NBAs. We prove that the
method is sound and complete. Our empirical results show that the
$\omega$-regular expressions synthesised from transition-based NBAs are more
compact than those synthesised from state-based NBAs. This is particularly the
case for NBAs computed from obligation, reactivity, safety and recurrence-type
LTL formulas, reporting in the latter case an average reduction of over 50%. We
also show that our method successfully synthesises $\omega$-regular expressions
from more LTL formulas when using a transition-based instead of a state-based
NBA.
