Abstract
We investigate the computational complexity of some problems related to preimages and ancestors of states of reaction systems. In particular, we prove that finding a minimum-cardinality preimage or ancestor, computing their size, or counting them are all intractable problems, with complexity ranging from \(\mathbf{FP}^{\mathbf{NP}[\log n]}\) to \(\mathbf{FPSPACE}(\mathrm{poly})\).
This work has been supported by Fondo d’Ateneo (FA) 2013 of Università degli Studi di Milano-Bicocca: “Complessità computazionale in modelli di calcolo bioispirati: Sistemi a membrane e sistemi a reazioni”, by the Italian MIUR PRIN 2010–2011 grant “Automata and Formal Languages: Mathematical and Applicative Aspects” H41J12000190001, and by the French National Research Agency project EMC (ANR-09-BLAN-0164).
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Dennunzio, A., Formenti, E., Manzoni, L., Porreca, A.E. (2015). Preimage Problems for Reaction Systems. In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_42
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DOI: https://doi.org/10.1007/978-3-319-15579-1_42
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