Deterministic chaos for parallel invertible logic

Invertible logic is an unconventional computing paradigm that enables bidirectional logic operations between inputs and outputs, and holds significant promise for solving critical complex problems. Here we propose a network of coupled chaotic systems that function as deterministic analogues of probabilistic ``$p$-bits,'' to implement parallel invertible logic. In the forward mode, the network has the capability to process inputs to implement the fundamental logic operations NOR/NAND, and their complementary operations OR/AND, in parallel. In the reverse mode, the states of the input nodes yield all possible logical inputs consistent with the truth table of the logic functions for a given output, with the network again having the capacity to implement inverse logic operations in parallel. Our basic idea leverages the existence of distinct attractor geometries, with varying residence times in state-space partitions, and exploits the transitions between these attractors to consistently mirror the logic operations, both in direct and inverse mode. Lastly, we provide proof-of-principle electronic circuit experiments to verify the concept, demonstrate the robustness of the architecture and its potential to be realized in physical implementations.