
SATbased Circuit Local Improvement
Finding exact circuit size is a notorious optimization problem in practi...
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Exact, complete expressions for the thermodynamic costs of circuits
Common engineered systems implement computations using circuits, as do m...
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FineGrained System Identification of Nonlinear Neural Circuits
We study the problem of sparse nonlinear model recovery of high dimensio...
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Optimising Clifford Circuits with Quantomatic
We present a system of equations between Clifford circuits, all derivabl...
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A Minimal Intervention Definition of Reverse Engineering a Neural Circuit
In neuroscience, researchers have developed informal notions of what it ...
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Competition through selective inhibitory synchrony
Models of cortical neuronal circuits commonly depend on inhibitory feedb...
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Neural ideals and stimulus space visualization
A neural code C is a collection of binary vectors of a given length n th...
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The PSPACEhardness of understanding neural circuits
In neuroscience, an important aspect of understanding the function of a neural circuit is to determine which, if any, of the neurons in the circuit are vital for the biological behavior governed by the neural circuit. A similar problem is to determine whether a given small set of neurons may be enough for the behavior to be displayed, even if all other neurons in the circuit are deactivated. Such a subset of neurons forms what is called a degenerate circuit for the behavior being studied. Recent advances in experimental techniques have provided researchers with tools to activate and deactivate subsets of neurons with a very high resolution, even in living animals. The data collected from such experiments may be of the following form: when a given subset of neurons is deactivated, is the behavior under study observed? This setting leads to the algorithmic question of determining the minimal vital or degenerate sets of neurons when one is given as input a description of the neural circuit. The algorithmic problem entails both figuring out which subsets of neurons should be perturbed (activated/deactivated), and then using the data from those perturbations to determine the minimal vital or degenerate sets. Given the large number of possible perturbations, and the recurrent nature of neural circuits, the possibility of a combinatorial explosion in such an approach has been recognized in the biology and the neuroscience literature. In this paper, we prove that the problems of finding minimal or minimumsize degenerate sets, and of finding the set of vital neurons, of a neural circuit given as input, are in fact PSPACEhard. More importantly, we prove our hardness results by showing that a simpler problem, that of simulating such neural circuits, is itself PSPACEhard.
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