Abstract: 
In temporallogic model checking, we verify the correctness of a program with respect to a desired behavior by checking whether a structure that models the program satisfies a temporallogic formula that specifies the behavior. The main practical limitation of model checking is caused by the size of the state space of the program, which grows exponentially with the number of concurrent components. This problem, known as the stateexplosion problem, becomes more difficult when we consider realtime model checking, where the program and the specification involve quantitative references to time. In particular, when use timed automata to describe realtime programs and we specify timed behaviors in the logic TCTL, a realtime extension of the temporal logic CTL with clock variables, then the state space under consideration grows exponentially not only with the number of concurrent components, but also with the number of clocks and the length of the clock constraints used in the program and the specification. Two powerful methods for coping with the stateexplosion problem are onthefly and spaceefficient model checking. In onthefly model checking, we explore only the portion of the state space of the program whose exploration is essential for determining the satisfaction of the specification. In spaceefficient model checking, we store in memory the minimal information required, preferring to spend time on reconstructing information rather than spend space on storing it. In this work we develop an automatatheoretic approach to TCTL model checking that combines both methods. We suggest, for the first time, a PSPACE onthefly modelchecking algorithm for TCTL.
