# Monotone Circuits

@article{Chaffey2020MonotoneC, title={Monotone Circuits}, author={Thomas Chaffey and Rodolphe Sepulchre}, journal={ArXiv}, year={2020}, volume={abs/2012.11533} }

Maximal monotonicity is explored as a generalization of the linear theory of passivity, which allows for algorithmic system analysis of an important physical property. The theory is developed for nonlinear 1-port circuits, modelled as port interconnections of the four fundamental elements: resistors, capacitors, inductors and memristors. An algorithm for computing the steady state periodic behavior of such a circuit is presented.

## 3 Citations

### Splitting algorithms and circuit analysis

- Computer ScienceArXiv
- 2022

This extended abstract presents new splitting algorithms specially suited to these structures, for interconnections of monotone and anti-monotone relations.

### Proof complexity of natural formulas via communication arguments

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2020

The result implies that the bit pigeonhole requires exponential tree-like Th( k) proofs, where Th(k) is the semantic proof system operating with polynomial inequalities of degree at most k and k = O(log1--ϵ n) for some ϵ > 0.

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