@article{BordihnVaszil2021,
  author    = {Bordihn, Henning and Vaszil, Gy{\"o}rgy},
  title     = {Reversible parallel communicating finite automata systems},
  series = {Acta informatica},
  volume    = {58},
  journal   = {Acta informatica},
  number    = {4},
  publisher = {Springer},
  address   = {Berlin ; Heidelberg ; New York, NY},
  issn      = {0001-5903},
  doi       = {10.1007/s00236-021-00396-9},
  pages     = {263 -- 279},
  year      = {2021},
  abstract  = {We study the concept of reversibility in connection with parallel communicating systems of finite automata (PCFA in short). We define the notion of reversibility in the case of PCFA (also covering the non-deterministic case) and discuss the relationship of the reversibility of the systems and the reversibility of its components. We show that a system can be reversible with non-reversible components, and the other way around, the reversibility of the components does not necessarily imply the reversibility of the system as a whole. We also investigate the computational power of deterministic centralized reversible PCFA. We show that these very simple types of PCFA (returning or non-returning) can recognize regular languages which cannot be accepted by reversible (deterministic) finite automata, and that they can even accept languages that are not context-free. We also separate the deterministic and non-deterministic variants in the case of systems with non-returning communication. We show that there are languages accepted by non-deterministic centralized PCFA, which cannot be recognized by any deterministic variant of the same type.},
  language  = {en}
}
@article{LippoldEidnerKumkeetal.2017,
  author    = {Lippold, Holger and Eidner, Sascha and Kumke, Michael Uwe and Lippmann-Pipke, Johanna},
  title     = {Dynamics of metal-humate complexation equilibria as revealed by isotope exchange studies - a matter of concentration and time},
  series = {Geochimica et cosmochimica acta : journal of the Geochemical Society and the Meteoritical Society},
  volume    = {197},
  journal   = {Geochimica et cosmochimica acta : journal of the Geochemical Society and the Meteoritical Society},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0016-7037},
  doi       = {10.1016/j.gca.2016.10.019},
  pages     = {62 -- 70},
  year      = {2017},
  abstract  = {Complexation with dissolved humic matter can be crucial in controlling the mobility of toxic or radioactive contaminant metals. For speciation and transport modelling, a dynamic equilibrium process is commonly assumed, where association and dissociation run permanently. This is, however, questionable in view of reported observations of a growing resistance to dissociation over time. In this study, the isotope exchange principle was employed to gain direct insight into the dynamics of the complexation equilibrium, including kinetic inertisation phenomena. Terbium(III), an analogue of trivalent actinides, was used as a representative of higher-valent metals. Isotherms of binding to (flocculated) humic acid, determined by means of Tb-160 as a radiotracer, were found to be identical regardless of whether the radioisotope was introduced together with the bulk of stable Tb-159 or subsequently after pre-equilibration for up to 3 months. Consequently, there is a permanent exchange of free and humic-bound Tb since all available binding sites are occupied in the plateau region of the isotherm. The existence of a dynamic equilibrium was thus evidenced. There was no indication of an inertisation under these experimental conditions. If the small amount of Tb-160 was introduced prior to saturation with Tb-159, the expected partial desorption of Tb-160 occurred at much lower rates than observed for the equilibration process in the reverse procedure. In addition, the rates decreased with time of pre-equilibration. Inertisation phenomena are thus confined to the stronger sites of humic molecules (occupied at low metal concentrations). Analysing the time-dependent course of isotope exchange according to first-order kinetics indicated that up to 3 years are needed to attain equilibrium. Since, however, metal-humic interaction remains reversible, exchange of metals between humic carriers and mineral surfaces cannot be neglected on the long time scale to be considered in predictive transport models.},
  language  = {en}
}
@article{KellerRoellyValleriani2015,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {On time duality for Markov Chains},
  series = {Stochastic models},
  volume    = {31},
  journal   = {Stochastic models},
  number    = {1},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {1532-6349},
  doi       = {10.1080/15326349.2014.969736},
  pages     = {98 -- 118},
  year      = {2015},
  abstract  = {For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are in time duality. We introduce a new condition called permuted balance that generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided.},
  language  = {en}
}