Here we discuss synaptic temporal integrators capable of computing plasticity functions between principal neurons which are inhibitory to yield a useful network dynamic. We model inhibitory spike-timing-dependent plasticity (iSTDP), parameterized by two thresholds of a pre- and post-synaptic leaky integrator. Because inhibitory synapses between principal neurons do not occur onto spines, but instead onto larger compartments of the dendritic shaft, the integrator in our model is slower than those used to model excitatory synapses onto spines. We implemented continuous iSTDP in our simulation of an all-inhibitory network and demonstrate here for the first time its ability to eliminate loops. We show how this specific circuit topology emerges and is closely related to that observed in models of recurrent excitatory networks. In addition, we show how this topology can generate a type of dynamics called winnerless in a subcortical brain structure called striatum, which also displays a loop-free topology. These properties are reviewed in the context of dynamic programming and the striatum's modulation of global brain topology via inhibitory gating of thalamus under the control of dopamine rewards-based learning.