Significant efforts are being directed to build new hardware technologies comprising of artificial neurons and synaptic devices that mimic the architecture of the brain for non-Von Neumann computation [1-5]. The computational capability of such networks arises from synaptic devices that can adapt its conductance based on the time of signaling of its two neurons according to rules such as spike timing dependent plasticity (STDP)  (Figure 1,2). Prior attempts to develop such synaptic devices have relied on using RRAM devices with current-limiting bipolar diodes. Plasticity was demonstrated by applying complicated waveforms or using complex signaling schemes that require precise clocking [1-5]. By leveraging the intrinsic switching properties of nanoscale Pr0.7Ca0.3MnO3 (PCMO) thin film devices [7-9], we show that (1) very simple programming waveforms that mimic the action potential of biological neurons are sufficient to realize biological plasticity and (2) up-to 64×64 cross-bar arrays of synaptic devices are feasible without any external current-limiting bipolar diodes.