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A new concept of weighted pair graphs (WPGs) is proposed to represent a newreconstructibility definition for Boolean control networks (BCNs), which is ageneralization of the reconstructibility definition given in [Fornasini &Valcher, TAC2013, Def. 4]. Based on the WPG representation, an effectivealgorithm for determining the new reconstructibility notion for BCNs isdesigned with the help of the theories of finite automata and formal languages.We prove that a BCN is not reconstructible iff its WPG has a complete subgraph.Besides, we prove that a BCN is reconstructible in the sense of [Fornasini &Valcher, TAC2013, Def. 4] iff its WPG has no cycles, which is simpler to bechecked than the condition in [Fornasini & Valcher, TAC2013, Thm. 4].

A weighted pair graph representation for reconstructibility of Boolean control networks