We revisit the classic problem of proving safety over parameterised
concurrent systems, i.e., an infinite family of finite-state
concurrent systems that are represented by some finite (symbolic)
means. An example of such an infinite family is a dining philosopher
protocol with any number $n$ of processes ($n$ being the parameter
that defines the infinite family). Regular model checking is a
well-known generic framework for modelling parameterised concurrent
systems, where an infinite set of configurations (resp.~transitions)
is represented by a regular set (resp.~regular transducer). Although
verifying safety properties in the regular model checking framework is
undecidable in general, many sophisticated semi-algorithms have been
developed in the past fifteen years that can successfully prove safety
in many practical instances. In this paper, we propose a simple
solution to synthesise regular inductive invariants that makes use of
Angluin's classic $L^*$ algorithm (and its variants). We provide a
termination guarantee when the set of configurations reachable from a
given set of initial configurations is regular. We have tested $L^*$
algorithm on standard (as well as new) examples in regular model
checking including the dining philosopher protocol, the dining
cryptographer protocol, and several mutual exclusion protocols
(e.g. Bakery, Burns, Szymanski, and German). Our experiments show
that, despite the simplicity of our solution, it can perform at least
as well as existing semi-algorithms.