Probability 1 computation with chemical reaction networks ∗ Rachel Cummings

The computational power of stochastic chemical reaction networks (CRNs) varies significantly with the output convention and whether or not error is permitted. Focusing on probability 1 computation, we demonstrate a striking difference between stable computation that converges to a state where the output cannot change, and the notion of limit-stable computation where the output eventually stops changing with probability 1. While stable computation is known to be restricted to semilinear predicates (essentially piecewise linear), we show that limit-stable computation encompasses the set of predicates in ∆2 in the arithmetical hierarchy (a superset of Turing-computable). In finite time, our construction achieves an error-correction scheme for Turing universal computation. This work refines our understanding of the tradeoffs between error and computational power in CRNs. ∗The first author was supported by NSF grants CCF-1049899 and CCF-1217770, the second author was supported by NSF grants CCF-1219274 and CCF-1162589 and the Molecular Programming Project under NSF grant 1317694, and the third author was supported by NIGMS Systems Biology Center grant P50 GM081879. †Northwestern University, Evanston, IL, USA, [email protected] ‡California Institute of Technology, Pasadena, CA, USA, [email protected] §University of California, San Francisco, San Francisco, CA, USA, [email protected]