Ranks of compositionally closed minimal reaction systems

Husain Intekhab (), Johnny Lim () and Wen Chean Teh ()
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Husain Intekhab: Universiti Sains Malaysia
Johnny Lim: Universiti Sains Malaysia
Wen Chean Teh: Universiti Sains Malaysia

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 819-828

Abstract: Abstract A reaction system is a computational model motivated by the functioning of living cells. In previous studies, Ehrenfeucht et al. have classified the functions specified by minimal reaction systems. Several studies have focused on the reaction system ranks of functions specified by minimal reaction systems, where the rank pertains to the minimum size of a specifying reaction system. This paper focuses on reaction system rank for a class of union-additive functions specified by minimal reaction systems introduced by Salomaa, which are closed under composition. More precisely, we establish a sufficient condition for the equality of reaction system ranks for functions belonging to the class. Then we study the reaction system ranks of such functions with signature sizes one and two, as well as those with one-to-one signatures, specifically over ternary and quaternary alphabets. Lastly, we establish a lower upper bound of reaction system ranks of such functions with one-to-one signatures for $$|S| \ge 5.$$ | S | ≥ 5 .

Keywords: Combinatorics; Natural computing; Biochemical reaction model; Minimal reaction system; Reaction system rank; 05B40; 68R05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00411-4

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