__Molecular Computing and Probabilistic Circuits__

**Jehoshua (Shuki) Bruck**

**Caltech**

Why
does the functioning of biological systems seem miraculous? One reason is that
we do not know how to design systems that do what cells do, namely molecular
computing. In contrast, we know how to design highly complex information
systems. The fundamental reason for the successful evolution of information
systems is the development of mathematical abstractions that enable efficient
and robust design processes. In particular, Claude Shannon in his classical 1938
Master’s Thesis demonstrated that all Boolean functions can be computed by relay
circuits, leading to the development of digital logic and resulting in computer
chips with over a billion transistors. Motivated by the challenge of analyzing
stochastic gene regulatory networks, we generalize the notion of logic design
to probabilistic logic design. Specifically, we consider relay circuits where deterministic
switches are replaced by probabilistic switches. We present efficient
algorithms for synthesizing probabilistic relay circuits that can compute arbitrary
probability distributions.