TY - JOUR A1 - Bordihn, Henning T1 - Active symbols in grammars with valuations JF - Theoretical computer science N2 - Grammars with valuations are context-free rewriting mechanisms where the derivation process is controlled by a recursive function that evaluates strings. They have been introduced by Jurgen Dassow as models for the molecular replication process taking into account its selective character. A symbol is active in a grammar with valuation if it can be rewritten non-identically. This paper studies the effect of restricting the number of active symbols in grammars with valuations and several variants thereof to their generative power. It is investigated in which cases the number of active symbols induces infinite strict hierarchies and when the hierarchies collapse. The induced language families are compared among one another. (C) 2016 Elsevier B.V. All rights reserved. KW - Formal languages KW - Biologically inspired formal systems KW - Descriptional complexity Y1 - 2017 U6 - https://doi.org/10.1016/j.tcs.2016.11.008 SN - 0304-3975 SN - 1879-2294 VL - 682 SP - 42 EP - 48 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Pablo Alarcon, Pedro A1 - Arroyo, Fernando A1 - Bordihn, Henning A1 - Mitrana, Victor A1 - Mueller, Mike T1 - Ambiguity of the multiple interpretations on regular languages JF - Fundamenta informaticae N2 - 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. KW - Multiple interpretation scheme KW - regular language KW - o-ambiguity KW - internal ambiguity KW - external ambiguity Y1 - 2015 U6 - https://doi.org/10.3233/FI-2015-1200 SN - 0169-2968 SN - 1875-8681 VL - 138 IS - 1-2 SP - 85 EP - 95 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Bordihn, Henning T1 - Context-freeness of the power of context-free languages is undecidable N2 - The power of a language L is the set of all powers of the words in L. In this paper, the following decision problem is investigated. Given a context-free language L, is the power of L context-free? We show that this problem is decidable for languages over unary alphabets, but it is undecidable whenever languages over alphabets with at least two letters are considered. (C) 2003 Elsevier B.V. All rights reserved Y1 - 2004 SN - 0304-3975 ER - TY - THES A1 - Bordihn, Henning T1 - Contributions to the syntactical analysis beyond context-freeness T1 - Beiträge zur syntaktischen Analyse nicht-kontextfreier Sprachen N2 - Parsability approaches of several grammar formalisms generating also non-context-free languages are explored. Chomsky grammars, Lindenmayer systems, grammars with controlled derivations, and grammar systems are treated. Formal properties of these mechanisms are investigated, when they are used as language acceptors. Furthermore, cooperating distributed grammar systems are restricted so that efficient deterministic parsing without backtracking becomes possible. For this class of grammar systems, the parsing algorithm is presented and the feature of leftmost derivations is investigated in detail. N2 - Ansätze zum Parsing verschiedener Grammatikformalismen, die auch nicht-kontextfreie Sprachen erzeugen können, werden diskutiert. Chomsky-Grammatiken, Lindenmayer-Systeme, Grammatiken mit gesteuerten Ersetzungen und Grammatiksysteme werden behandelt. Formale Eigenschaften dieser Mechanismen als Akzeptoren von Sprachen werden untersucht. Weiterhin werden kooperierende verteilte (CD) Grammatiksysteme derart beschränkt, dass effizientes deterministisches Parsing ohne Backtracking möglich ist. Für diese Klasse von Grammatiksystemen wird der Parsingalgorithmus vorgestellt und die Rolle von Linksableitungen wird detailliert betrachtet. KW - Parsing KW - Akzeptierende Grammatiken KW - Gesteuerte Ableitungen KW - Grammatiksysteme KW - Linksableitungen KW - Parsing KW - Accepting Grammars KW - Controlled Derivations KW - Grammar Systems KW - Leftmost Derivations Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59719 ER - TY - JOUR A1 - Bordihn, Henning A1 - Holzer, Markus A1 - Kutrib, Martin T1 - Decidability of operation problems for TOL languages and subclasses JF - Information and computation N2 - We investigate the decidability of the operation problem for TOL languages and subclasses. Fix an operation on formal languages. Given languages from the family considered (OL languages, TOL languages, or their propagating variants), is the application of this operation to the given languages still a language that belongs to the same language family? Observe, that all the Lindenmayer language families in question are anti-AFLs, that is, they are not closed under homomorphisms, inverse homomorphisms, intersection with regular languages, union, concatenation, and Kleene closure. Besides these classical operations we also consider intersection and substitution, since the language families under consideration are not closed under these operations, too. We show that for all of the above mentioned language operations, except for the Kleene closure, the corresponding operation problems of OL and TOL languages and their propagating variants are not even semidecidable. The situation changes for unary OL languages. In this case we prove that the operation problems with respect to Kleene star, complementation, and intersection with regular sets are decidable. KW - L systems KW - Operation problem KW - Decidability KW - Unary languages Y1 - 2011 U6 - https://doi.org/10.1016/j.ic.2010.11.008 SN - 0890-5401 VL - 209 IS - 3 SP - 344 EP - 352 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Bordihn, Henning A1 - Holzer, Markus A1 - Kutrib, Martin T1 - Determination of finite automata accepting subregular languages N2 - We investigate the descriptional complexity of the nondeterministic finite automaton (NFA) to the deterministic finite automaton (DFA) conversion problem, for automata accepting subregular languages such as combinational languages, definite languages and variants thereof, (strictly) locally testable languages, star-free languages, ordered languages, prefix-, suffix-, and infix-closed languages, and prefix-, Suffix-, and infix-free languages. Most of the bounds for the conversion problem are shown to be tight ill the exact number of states, that is, the number is sufficient and necessary in the worst case. Otherwise tight bounds in order of magnitude are shown. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/03043975 U6 - https://doi.org/10.1016/j.tcs.2009.05.019 SN - 0304-3975 ER - TY - JOUR A1 - Bordihn, Henning A1 - Vaszil, György T1 - Deterministic Lindenmayer systems with dynamic control of parallelism JF - International journal of foundations of computer science N2 - M-rate 0L systems are interactionless Lindenmayer systems together with a function assigning to every string a set of multisets of productions that may be applied simultaneously to the string. Some questions that have been left open in the forerunner papers are examined, and the computational power of deterministic M-rate 0L systems is investigated, where also tabled and extended variants are taken into consideration. KW - parallel rewriting KW - Lindenmayer systems KW - restricted parallelism KW - determinism KW - developmental systems KW - formal languages Y1 - 2019 U6 - https://doi.org/10.1142/S0129054120400031 SN - 0129-0541 SN - 1793-6373 VL - 31 IS - 1 SP - 37 EP - 51 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Bordihn, Henning A1 - Dassow, Juergen A1 - Holzer, Markus T1 - Extending regular expressions with homomorphic replacement N2 - We define H- and EH-expressions as extensions of regular expressions by adding homomorphic and iterated homomorphic replacement as new operations, resp. The definition is analogous to the extension given by Gruska in order to characterize context-free languages. We compare the families of languages obtained by these extensions with the families of regular, linear context-free, context-free, and EDT0L languages. Moreover, relations to language families based on patterns, multi-patterns, pattern expressions, H-systems and uniform substitutions are also investigated. Furthermore, we present their closure properties with respect to TRIO operations and discuss the decidability status and complexity of fixed and general membership, emptiness, and the equivalence problem. Y1 - 2010 UR - http://www.rairo-ita.org/ U6 - https://doi.org/10.1051/Ita/2010013 SN - 0988-3754 ER - TY - JOUR A1 - Bordihn, Henning A1 - Mitrana, Victor A1 - Paun, Andrei A1 - Paun, Mihaela T1 - Hairpin completions and reductions BT - semilinearity properties JF - Natural computing : an innovative journal bridging biosciences and computer sciences ; an international journal N2 - 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. KW - DNA hairpin formation KW - Hairpin completions KW - Hairpin reductions KW - Semilinearity property Y1 - 2020 U6 - https://doi.org/10.1007/s11047-020-09797-0 SN - 1572-9796 VL - 20 IS - 2 SP - 193 EP - 203 PB - Springer Science + Business Media B.V. CY - Dordrecht ER - TY - JOUR A1 - Bordihn, Henning A1 - Fernau, Henning A1 - Holzer, Markus A1 - Manca, Vincenzo A1 - Martin-Vide, Carlos T1 - Iterated sequential transducers as language generating devices JF - Theoretical computer science N2 - Iterated finite state sequential transducers are considered as language generating devices. The hierarchy induced by the size of the state alphabet is proved to collapse to the fourth level. The corresponding language families are related to the families of languages generated by Lindenmayer systems and Chomsky grammars. Finally, some results on deterministic and extended iterated finite state transducers are established. KW - finite state sequential transducers KW - state complexity KW - Lindenmayer systems Y1 - 2006 U6 - https://doi.org/10.1016/j.tcs.2006.07.059 SN - 0304-3975 VL - 369 IS - 1 SP - 67 EP - 81 PB - Elsevier CY - Amsterdam ER -