LAUSR

In this letter, in discrete-event systems modeled by labeled finite-state automata (LFSAs), we show new thinking on the tools of detector and concurrent composition and derive two new algorithms for verifying strong periodic detectability (SPD) without any assumption that run in $\mathsf {NL}$ ; we also reconsider the tool of observer and derive a new algorithm for verifying strong periodic D-detectability (SPDD) without any assumption that runs in $\mathsf {PSPACE}$ . These results strengthen the $\mathsf {NL}$ upper bound on verifying SPD and the $\mathsf {PSPACE}$ upper bound on verifying SPDD for deadlock-free and divergence-free LFSAs in the literature. In our algorithms, the two assumptions are removed by verifying the negations of these properties.