eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-09-04
3:1
3:18
10.4230/LIPIcs.DNA.2020.3
article
Composable Computation in Leaderless, Discrete Chemical Reaction Networks
Hashemi, Hooman
1
Chugg, Ben
2
Condon, Anne
1
https://orcid.org/0000-0003-1458-1259
The University of British Columbia, Vancouver, Canada
Stanford University, CA, USA
We classify the functions f:ℕ^d → ℕ that are stably computable by leaderless, output-oblivious discrete (stochastic) Chemical Reaction Networks (CRNs). CRNs that compute such functions are systems of reactions over species that include d designated input species, whose initial counts represent an input x ∈ ℕ^d, and one output species whose eventual count represents f(x). Chen et al. showed that the class of functions computable by CRNs is precisely the semilinear functions. In output-oblivious CRNs, the output species is never a reactant. Output-oblivious CRNs are easily composable since a downstream CRN can consume the output of an upstream CRN without affecting its correctness. Severson et al. showed that output-oblivious CRNs compute exactly the subclass of semilinear functions that are eventually the minimum of quilt-affine functions, i.e., affine functions with different intercepts in each of finitely many congruence classes. They call such functions the output-oblivious functions. A leaderless CRN can compute only superadditive functions, and so a leaderless output-oblivious CRN can compute only superadditive, output-oblivious functions. In this work we show that a function f:ℕ^d → ℕ is stably computable by a leaderless, output-oblivious CRN if and only if it is superadditive and output-oblivious.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol174-dna26/LIPIcs.DNA.2020.3/LIPIcs.DNA.2020.3.pdf
Chemical Reaction Networks
Stable Function Computation
Output-Oblivious
Output-Monotonic