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Cellular spaces are shown to possess properties favorable to reconfiguration. As a first step in the direction of reconfigurable cellular spaces, this paper demonstrates the implementation of arbitrary finite-state machines in self-diagnosing cellular spaces. The results cover single cell failures caused by erroneous state transitions or by erroneous outputs. One of the attractive features of the implementation is the absence of any hard core components. As an intermediate step, it is shown how to transform any given cellular space into a self-diagnosing cellular space. The results demonstrate that the control structure (which is a finite-state machine) of any computing device can be implemented as a self-diagnosing entity without hard core.