# Non-Causal Computation

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## Abstract

**:**

## 1. Introduction

## 2. Logical Consistency

## 3. Non-Causal Circuit Model

## 4. Computational Advantage

## 5. Other Non-Causal Computational Models

## 6. Conclusions and Open Questions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Causal and non-causal computation. The arrows point in the direction of computation. (

**a**) The values that are assigned to the variables of a computational model at time t depend on ${\rho}_{t-1}$. (

**b**) Cyclic dependencies of the values that are assigned to the variables at different steps during the computation.

**Figure 2.**(

**a**) Overdetermined circuit: The bit 0 is mapped to 1 and vice versa; i.e., there is no consistent assignment of a value that travels on the wire. (

**b**) Information antinomy: Both 0 and 1 could potentially travel on the wire, yet the circuit does not specify which.

**Figure 3.**(

**a**) Open circuit $\mathcal{C}$ with input a. (

**b**) Closed circuit ${\mathcal{C}}_{i}$ with $a=i\to {c}_{a}={c}_{i}$. (

**c**) The big box represents a non-causal comb (note that combs obey causality; the higher-order transformations described here are equivalent to combs, yet where the causality assumption is dropped) that transforms a gate (${H}^{\prime}$) to a new gate, the composition.

**Figure 4.**Fixed point search for a black box with one and a black box with two fixed points. (

**a**) The output x is the fixed point c added to the input a. (

**b**) Circuit for finding a fixed point for a black box with two fixed points.

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**MDPI and ACS Style**

Baumeler, Ä.; Wolf, S.
Non-Causal Computation. *Entropy* **2017**, *19*, 326.
https://doi.org/10.3390/e19070326

**AMA Style**

Baumeler Ä, Wolf S.
Non-Causal Computation. *Entropy*. 2017; 19(7):326.
https://doi.org/10.3390/e19070326

**Chicago/Turabian Style**

Baumeler, Ämin, and Stefan Wolf.
2017. "Non-Causal Computation" *Entropy* 19, no. 7: 326.
https://doi.org/10.3390/e19070326