@article{Denecke2019,
  author    = {Denecke, Klaus-Dieter},
  title     = {The partial clone of linear formulas},
  series = {Siberian mathematical journal},
  volume    = {60},
  journal   = {Siberian mathematical journal},
  number    = {4},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446619040037},
  pages     = {572 -- 584},
  year      = {2019},
  abstract  = {A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′).},
  language  = {en}
}
@article{LekkoksungDenecke2019,
  author    = {Lekkoksung, Nareupanat and Denecke, Klaus-Dieter},
  title     = {The partial clone of linear tree languages},
  series = {Siberian mathematical journal},
  volume    = {60},
  journal   = {Siberian mathematical journal},
  number    = {3},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446619030121},
  pages     = {497 -- 507},
  year      = {2019},
  abstract  = {A term, also called a tree, is said to be linear, if each variable occurs in the term only once. The linear terms and sets of linear terms, the so-called linear tree languages, play some role in automata theory and in the theory of formal languages in connection with recognizability. We define a partial superposition operation on sets of linear trees of a given type and study the properties of some many-sorted partial clones that have sets of linear trees as elements and partial superposition operations as fundamental operations. The endomorphisms of those algebras correspond to nondeterministic linear hypersubstitutions.},
  language  = {en}
}