State-based opacity of labeled real-time automata

State -based opacity is a special type of opacity as a confidentiality property, which describes whether an external intruder cannot be sure whether secret states of a system have been visited by observing its generated outputs, given that the intruder knows complete knowledge of the system's structure but can only see generated outputs. When the time of visiting secret states is specified as the initial time, the current time, any past time, and at most ������ observational steps prior to the current time, the notions of state -based opacity can be formulated as initialstate opacity, current -state opacity, infinite -step opacity, and ������-step opacity, respectively. In this paper, we formulate the four versions of opacity for labeled real-time automata which are a widely -used model of real-time systems, and give N2EXPTIME verification algorithms for the four notions by defining appropriate notions of observer and reverse observer for labeled realtime automata that are proven to be computable in N2EXPTIME.