Output-Oblivious Stochastic Chemical Reaction Networks
We classify the functions f:N^2 -> N which are stably computable by output-oblivious Stochastic Chemical Reaction Networks (CRNs), i.e., systems of reactions in which output species are never reactants. While it is known that precisely the semilinear functions are stably computable by CRNs, such CRNs sometimes rely on initially producing too many output species, and then consuming the excess in order to reach a correct stable state. These CRNs may be difficult to integrate into larger systems: if the output of a CRN C becomes the input to a downstream CRN C', then C' could inadvertently consume too many outputs before C stabilizes. If, on the other hand, C is output-oblivious then C' may consume C's output as soon as it is available. In this work we prove that a semilinear function f:N^2 -> N is stably computable by an output-oblivious CRN with a leader if and only if it is both increasing and either grid-affine (intuitively, its domains are congruence classes), or the minimum of a finite set of fissure functions (intuitively, functions behaving like the min function).
Chemical Reaction Networks
Stable Function Computation
Output-Oblivious
Output-Monotonic
Theory of computation~Computability
Theory of computation~Formal languages and automata theory
21:1-21:16
Regular Paper
A full version of the paper is available at https://arxiv.org/abs/1812.04401.
Ben
Chugg
Ben Chugg
The University of British Columbia, Canada
Supported by an NSERC Undergraduate Student Research Award.
Hooman
Hashemi
Hooman Hashemi
The University of British Columbia, Canada
Anne
Condon
Anne Condon
The University of British Columbia, Canada
https://orcid.org/0000-0003-1458-1259
Supported by an NSERC Discovery Grant.
10.4230/LIPIcs.OPODIS.2018.21
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Ben Chugg, Hooman Hashemi, and Anne Condon
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