@article{PabloAlarconArroyoBordihnetal.2015,
  author    = {Pablo Alarcon, Pedro and Arroyo, Fernando and Bordihn, Henning and Mitrana, Victor and Mueller, Mike},
  title     = {Ambiguity of the multiple interpretations on regular languages},
  series = {Fundamenta informaticae},
  volume    = {138},
  journal   = {Fundamenta informaticae},
  number    = {1-2},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0169-2968},
  doi       = {10.3233/FI-2015-1200},
  pages     = {85 -- 95},
  year      = {2015},
  abstract  = {A multiple interpretation scheme is an ordered sequence of morphisms. The ordered multiple interpretation of a word is obtained by concatenating the images of that word in the given order of morphisms. The arbitrary multiple interpretation of a word is the semigroup generated by the images of that word. These interpretations are naturally extended to languages. Four types of ambiguity of multiple interpretation schemata on a language are defined: o-ambiguity, internal ambiguity, weakly external ambiguity and strongly external ambiguity. We investigate the problem of deciding whether a multiple interpretation scheme is ambiguous on regular languages.},
  language  = {en}
}
@article{BordihnMitranaPaunetal.2020,
  author    = {Bordihn, Henning and Mitrana, Victor and Paun, Andrei and Paun, Mihaela},
  title     = {Hairpin completions and reductions},
  series = {Natural computing : an innovative journal bridging biosciences and computer sciences ; an international journal},
  volume    = {20},
  journal   = {Natural computing : an innovative journal bridging biosciences and computer sciences ; an international journal},
  number    = {2},
  publisher = {Springer Science + Business Media B.V.},
  address   = {Dordrecht},
  issn      = {1572-9796},
  doi       = {10.1007/s11047-020-09797-0},
  pages     = {193 -- 203},
  year      = {2020},
  abstract  = {This paper is part of the investigation of some operations on words and languages with motivations coming from DNA biochemistry, namely three variants of hairpin completion and three variants of hairpin reduction. Since not all the hairpin completions or reductions of semilinear languages remain semilinear, we study sufficient conditions for semilinear languages to preserve their semilinearity property after applying the non-iterated hairpin completion or hairpin reduction. A similar approach is then applied to the iterated variants of these operations. Along these lines, we define the hairpin reduction root of a language and show that the hairpin reduction root of a semilinear language is not necessarily semilinear except the universal language. A few open problems are finally discussed.},
  language  = {en}
}
@article{BordihnMitranaNegruetal.2018,
  author    = {Bordihn, Henning and Mitrana, Victor and Negru, Maria C. and Paun, Andrei and Paun, Mihaela},
  title     = {Small networks of polarized splicing processors are universal},
  series = {Natural computing : an innovative journal bridging biosciences and computer sciences ; an international journal},
  volume    = {17},
  journal   = {Natural computing : an innovative journal bridging biosciences and computer sciences ; an international journal},
  number    = {4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1567-7818},
  doi       = {10.1007/s11047-018-9691-0},
  pages     = {799 -- 809},
  year      = {2018},
  abstract  = {In this paper, we consider the computational power of a new variant of networks of splicing processors in which each processor as well as the data navigating throughout the network are now considered to be polarized. While the polarization of every processor is predefined (negative, neutral, positive), the polarization of data is dynamically computed by means of a valuation mapping. Consequently, the protocol of communication is naturally defined by means of this polarization. We show that networks of polarized splicing processors (NPSP) of size 2 are computationally complete, which immediately settles the question of designing computationally complete NPSPs of minimal size. With two more nodes we can simulate every nondeterministic Turing machine without increasing the time complexity. Particularly, we prove that NPSP of size 4 can accept all languages in NP in polynomial time. Furthermore, another computational model that is universal, namely the 2-tag system, can be simulated by NPSP of size 3 preserving the time complexity. All these results can be obtained with NPSPs with valuations in the set as well. We finally show that Turing machines can simulate a variant of NPSPs and discuss the time complexity of this simulation.},
  language  = {en}
}
@article{BordihnMitrana2020,
  author    = {Bordihn, Henning and Mitrana, Victor},
  title     = {On the degrees of non-regularity and non-context-freeness},
  series = {Journal of computer and system sciences},
  volume    = {108},
  journal   = {Journal of computer and system sciences},
  publisher = {Elsevier},
  address   = {San Diego, Calif. [u.a.]},
  issn      = {0022-0000},
  doi       = {10.1016/j.jcss.2019.09.003},
  pages     = {104 -- 117},
  year      = {2020},
  abstract  = {We study the derivational complexity of context-free and context-sensitive grammars by counting the maximal number of non-regular and non-context-free rules used in a derivation, respectively. The degree of non-regularity/non-context-freeness of a language is the minimum degree of non-regularity/non-context-freeness of context-free/context-sensitive grammars generating it. A language has finite degree of non-regularity iff it is regular. We give a condition for deciding whether the degree of non-regularity of a given unambiguous context-free grammar is finite. The problem becomes undecidable for arbitrary linear context-free grammars. The degree of non-regularity of unambiguous context-free grammars generating non-regular languages as well as that of grammars generating deterministic context-free languages that are not regular is of order Omega(n). Context-free non-regular languages of sublinear degree of non-regularity are presented. A language has finite degree of non-context-freeness if it is context-free. Context-sensitive grammars with a quadratic degree of non-context-freeness are more powerful than those of a linear degree.},
  language  = {en}
}
@article{BordihnBottoniLabellaetal.2017,
  author    = {Bordihn, Henning and Bottoni, Paolo and Labella, Anna and Mitrana, Victor},
  title     = {Networks of picture processors as problem solvers},
  series = {Soft Computing},
  volume    = {21},
  journal   = {Soft Computing},
  publisher = {Springer},
  address   = {New York},
  issn      = {1432-7643},
  doi       = {10.1007/s00500-016-2206-y},
  pages     = {5529 -- 5541},
  year      = {2017},
  abstract  = {We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts at each step, simultaneously, all subpictures of identical (progressively decreasing) size from the input picture and sends them to the other subnetwork which checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterward, we present a solution based on networks containing both evolutionary and hiding processors running in O(n + m + kl) computational (processing and communication) steps, for any size (n, m) of the input pic-ture and (k, l) of the pattern. From the proofs of these results, we infer that any (k, l)-local language with 1 <= k <= 3 can be decided in O(n + m + l) computational steps by networks with evolutionary processors only, while any (k, l)-local language with arbitrary k, l can be decided in O(n + m + kl) computational steps by networks containing both evolutionary and hiding processors.},
  language  = {en}
}