Abstract
We study the computational complexity of some important problems on reaction systems (RSs), a biologically motivated model introduced by Ehrenfeucht and Rozenberg in [7], that were overseen in the literature. To this end we focus on the complexity of (i) equivalence and multi-step simulation properties, (ii) special structural and behavioural RS properties such as, e.g., isotonicity, antitonicity, etc., and minimality with respect to reactant and/or inhibitor sets, and (iii) threshold properties. The complexities vary from deterministic polynomial time solvability to coNP- and PSPACE-completeness. Finally, as a side result on the complexity of threshold problems we improve the previously known threshold values for the no-concurrency, the comparability, and the redundancy property studied in [2].
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- 1.
If the RS has to be strict the threshold for TOT is \((2^n-1)(3^n-3\cdot 2^n+2^{\lceil \frac{n}{2}\rceil }+2^{\lfloor \frac{n}{2}\rfloor })+1\), see [2].
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Holzer, M., Rauch, C. (2021). On the Computational Complexity of Reaction Systems, Revisited. In: Santhanam, R., Musatov, D. (eds) Computer Science – Theory and Applications. CSR 2021. Lecture Notes in Computer Science(), vol 12730. Springer, Cham. https://doi.org/10.1007/978-3-030-79416-3_10
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