@book{BenschBoldtBordihnetal.2004, author = {Bensch, Suna and Boldt, Oliver and Bordihn, Henning and J{\"u}rgensen, Helmut}, title = {Workshop "Formale Methoden der Linguistik" und "14. Theorietag Automaten und Formale Sprachen"}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, volume = {2004, 2}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, publisher = {Univ.}, address = {Potsdam}, issn = {0946-7580}, pages = {144 S.}, year = {2004}, language = {de} } @article{BordihnHolzerKutrib2005, author = {Bordihn, Henning and Holzer, Markus and Kutrib, Martin}, title = {Unsolvability levels of operation problems for subclasses of context-free languages}, issn = {0129-0541}, year = {2005}, abstract = {We investigate the operation problem for linear and deterministic context-free languages: Fix an operation on formal languages. Given linear (deterministic, respectively) context-free languages, is the application of this operation to the given languages still a linear (deterministic, respectively) context-free language? Besides the classical operations, for which the linear and deterministic context-free languages are not closed, we also consider the recently introduced root and power operation. We show non-semidecidability, to be more precise, we show completeness for the second level of the arithmetic hierarchy for all of the aforementioned operations, except for the power operation, if the underlying alphabet contains at least two letters. The result for the power opera, tion solves an open problem stated in Theoret. Comput. Sci. 314 (2004) 445-449}, language = {en} } @article{BordihnKutribMalcher2011, author = {Bordihn, Henning and Kutrib, Martin and Malcher, Andreas}, title = {Undecidability and hierarchy results for parallel communicating finite automata}, series = {International journal of foundations of computer science}, volume = {22}, journal = {International journal of foundations of computer science}, number = {7}, publisher = {World Scientific}, address = {Singapore}, issn = {0129-0541}, doi = {10.1142/S0129054111008891}, pages = {1577 -- 1592}, year = {2011}, abstract = {Parallel communicating finite automata (PCFAs) are systems of several finite state automata which process a common input string in a parallel way and are able to communicate by sending their states upon request. We consider deterministic and nondeterministic variants and distinguish four working modes. It is known that these systems in the most general mode are as powerful as one-way multi-head finite automata. It is additionally known that the number of heads corresponds to the number of automata in PCFAs in a constructive way. Thus, undecidability results as well as results on the hierarchies induced by the number of heads carry over from multi-head finite automata to PCFAs in the most general mode. Here, we complement these undecidability and hierarchy results also for the remaining working modes. In particular, we show that classical decidability questions are not semi-decidable for any type of PCFAs under consideration. Moreover, it is proven that the number of automata in the system induces infinite hierarchies for deterministic and nondeterministic PCFAs in three working modes.}, 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{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{BordihnHolzer2006, author = {Bordihn, Henning and Holzer, Markus}, title = {Programmed grammars and their relation to the LBA problem}, series = {Acta informatica}, volume = {43}, journal = {Acta informatica}, publisher = {Elsevier}, address = {New York}, issn = {0001-5903}, doi = {10.1007/s00236-006-0017-9}, pages = {223 -- 242}, year = {2006}, abstract = {We consider generating and accepting programmed grammars with bounded degree of non-regulation, that is, the maximum number of elements in success or in failure fields of the underlying grammar. In particular, it is shown that this measure can be restricted to two without loss of descriptional capacity, regardless of whether arbitrary derivations or left-most derivations are considered. Moreover, in some cases, precise characterizations of the linear bounded automaton problem in terms of programmed grammars are obtained. Thus, the results presented in this paper shed new light on some longstanding open problem in the theory of computational complexity.}, language = {en} } @misc{BordihnNagyVaszil2018, author = {Bordihn, Henning and Nagy, Benedek and Vaszil, Gy{\"o}rgy}, title = {Preface: Non-classical models of automata and applications VIII}, series = {RAIRO-Theoretical informatics and appli and applications}, volume = {52}, journal = {RAIRO-Theoretical informatics and appli and applications}, number = {2-4}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0988-3754}, doi = {10.1051/ita/2018019}, pages = {87 -- 88}, year = {2018}, language = {en} } @article{Bordihn2005, author = {Bordihn, Henning}, title = {On the number of components in cooperating distributed grammar systems}, issn = {0304-3975}, year = {2005}, abstract = {It is proved that the number of components in context-free cooperating distributed (CD) grammar systems can be reduced to 3 when they are working in the so-called sf-mode of derivation, which is the cooperation protocol which has been considered first for CD grammar systems. In this derivation mode, a component continues the derivation until and unless there is a nonterminal in the sentential form which cannot be rewritten according to that component. Moreover, it is shown that CD grammar systems in sf-mode with only one component can generate only the context-free languages but they can generate non-context-free languages if two components are used. The sf-mode of derivation is compared with other well-known cooperation protocols with respect to the hierarchies induced by the number of components. (C) 2004 Elsevier B.V. All rights reserved}, language = {en} } @article{BordihnHolzer2021, author = {Bordihn, Henning and Holzer, Markus}, title = {On the number of active states in finite automata}, series = {Acta informatica}, volume = {58}, journal = {Acta informatica}, number = {4}, publisher = {Springer}, address = {Berlin ; Heidelberg [u.a.]}, issn = {0001-5903}, doi = {10.1007/s00236-021-00397-8}, pages = {301 -- 318}, year = {2021}, abstract = {We introduce a new measure of descriptional complexity on finite automata, called the number of active states. Roughly speaking, the number of active states of an automaton A on input w counts the number of different states visited during the most economic computation of the automaton A for the word w. This concept generalizes to finite automata and regular languages in a straightforward way. We show that the number of active states of both finite automata and regular languages is computable, even with respect to nondeterministic finite automata. We further compare the number of active states to related measures for regular languages. In particular, we show incomparability to the radius of regular languages and that the difference between the number of active states and the total number of states needed in finite automata for a regular language can be of exponential order.}, 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} }