### Abstract

In this paper, we give a computational solution for the reachability problem of subconservative discrete chemical reaction networks (d-CRNs), namely whether there exists a valid state transition (reaction) sequence between a given initial and a target state. Using subconservativity, we characterize the reachable set of the d-CRN with well-defined simplexes. Moreover, upper bounds are derived for the possible length of cycle-free state transition sequences. We show that the reachability and the related coverability problem in the case of subconservative d-CRNs can be decided in polynomial time by tracing them back to fixed dimensional integer programming (IP) feasibility problems over a bounded integer lattice. The proposed computation model is also employed for determining feasible series of reactions between given (sets of) states. We also show that if the rank of the stoichiometric matrix is less than or equal to 2, then the reachability problem is equivalent to the existence of a non-negative integer solution of the corresponding state equation.

Original language | English |
---|---|

Pages (from-to) | 705-736 |

Number of pages | 32 |

Journal | Match |

Volume | 81 |

Issue number | 3 |

Publication status | Published - Jan 1 2019 |

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### ASJC Scopus subject areas

- Chemistry(all)
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Match*,

*81*(3), 705-736.

**Reachability analysis of subconservative discrete chemical reaction networks.** / Szlobodnyik, Gergely; Szederkényi, G.; Johnston, Matthew D.

Research output: Contribution to journal › Article

*Match*, vol. 81, no. 3, pp. 705-736.

}

TY - JOUR

T1 - Reachability analysis of subconservative discrete chemical reaction networks

AU - Szlobodnyik, Gergely

AU - Szederkényi, G.

AU - Johnston, Matthew D.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we give a computational solution for the reachability problem of subconservative discrete chemical reaction networks (d-CRNs), namely whether there exists a valid state transition (reaction) sequence between a given initial and a target state. Using subconservativity, we characterize the reachable set of the d-CRN with well-defined simplexes. Moreover, upper bounds are derived for the possible length of cycle-free state transition sequences. We show that the reachability and the related coverability problem in the case of subconservative d-CRNs can be decided in polynomial time by tracing them back to fixed dimensional integer programming (IP) feasibility problems over a bounded integer lattice. The proposed computation model is also employed for determining feasible series of reactions between given (sets of) states. We also show that if the rank of the stoichiometric matrix is less than or equal to 2, then the reachability problem is equivalent to the existence of a non-negative integer solution of the corresponding state equation.

AB - In this paper, we give a computational solution for the reachability problem of subconservative discrete chemical reaction networks (d-CRNs), namely whether there exists a valid state transition (reaction) sequence between a given initial and a target state. Using subconservativity, we characterize the reachable set of the d-CRN with well-defined simplexes. Moreover, upper bounds are derived for the possible length of cycle-free state transition sequences. We show that the reachability and the related coverability problem in the case of subconservative d-CRNs can be decided in polynomial time by tracing them back to fixed dimensional integer programming (IP) feasibility problems over a bounded integer lattice. The proposed computation model is also employed for determining feasible series of reactions between given (sets of) states. We also show that if the rank of the stoichiometric matrix is less than or equal to 2, then the reachability problem is equivalent to the existence of a non-negative integer solution of the corresponding state equation.

UR - http://www.scopus.com/inward/record.url?scp=85064416763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064416763&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85064416763

VL - 81

SP - 705

EP - 736

JO - Match

JF - Match

SN - 0340-6253

IS - 3

ER -