### Abstract

In this paper we study the reachability problem of sub- A nd superconservative discrete state chemical reaction networks (d-CRNs). It is known that a subconservative network has bounded reachable state space, while that of a superconservative one is unbounded. The reachability problem of superconservative reaction networks is traced back to the reachability of subconservative ones. We consider network structures composed of reactions having at most one input and one output species beyond the possible catalyzers. We give a proof that, assuming all the reactions are charged in the initial and target states, the reachability problems of sub- A nd superconservative reaction networks are equivalent to the existence of nonnegative integer solution of the corresponding d-CRN state equations. Using this result, the reachability problem is reformulated as an Integer Linear Programming (ILP) feasibility problem. Therefore, the number of feasible trajectories satisfying the reachability relation can be counted in polynomial time in the number of species and in the distance of initial and target states, assuming fixed number of reactions in the system.

Original language | English |
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Article number | 1035974 |

Journal | Complexity |

Volume | 2019 |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### ASJC Scopus subject areas

- General

### Cite this

*Complexity*,

*2019*, [1035974]. https://doi.org/10.1155/2019/1035974

**Reachability analysis of low-order discrete state reaction networks obeying conservation laws.** / Szlobodnyik, Gergely; Szederkényi, G.

Research output: Contribution to journal › Article

*Complexity*, vol. 2019, 1035974. https://doi.org/10.1155/2019/1035974

}

TY - JOUR

T1 - Reachability analysis of low-order discrete state reaction networks obeying conservation laws

AU - Szlobodnyik, Gergely

AU - Szederkényi, G.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper we study the reachability problem of sub- A nd superconservative discrete state chemical reaction networks (d-CRNs). It is known that a subconservative network has bounded reachable state space, while that of a superconservative one is unbounded. The reachability problem of superconservative reaction networks is traced back to the reachability of subconservative ones. We consider network structures composed of reactions having at most one input and one output species beyond the possible catalyzers. We give a proof that, assuming all the reactions are charged in the initial and target states, the reachability problems of sub- A nd superconservative reaction networks are equivalent to the existence of nonnegative integer solution of the corresponding d-CRN state equations. Using this result, the reachability problem is reformulated as an Integer Linear Programming (ILP) feasibility problem. Therefore, the number of feasible trajectories satisfying the reachability relation can be counted in polynomial time in the number of species and in the distance of initial and target states, assuming fixed number of reactions in the system.

AB - In this paper we study the reachability problem of sub- A nd superconservative discrete state chemical reaction networks (d-CRNs). It is known that a subconservative network has bounded reachable state space, while that of a superconservative one is unbounded. The reachability problem of superconservative reaction networks is traced back to the reachability of subconservative ones. We consider network structures composed of reactions having at most one input and one output species beyond the possible catalyzers. We give a proof that, assuming all the reactions are charged in the initial and target states, the reachability problems of sub- A nd superconservative reaction networks are equivalent to the existence of nonnegative integer solution of the corresponding d-CRN state equations. Using this result, the reachability problem is reformulated as an Integer Linear Programming (ILP) feasibility problem. Therefore, the number of feasible trajectories satisfying the reachability relation can be counted in polynomial time in the number of species and in the distance of initial and target states, assuming fixed number of reactions in the system.

UR - http://www.scopus.com/inward/record.url?scp=85064385117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064385117&partnerID=8YFLogxK

U2 - 10.1155/2019/1035974

DO - 10.1155/2019/1035974

M3 - Article

AN - SCOPUS:85064385117

VL - 2019

JO - Complexity

JF - Complexity

SN - 1076-2787

M1 - 1035974

ER -