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 - TY - JOUR A1 - Bordihn, Henning T1 - On the number of components in cooperating distributed grammar systems N2 - 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 Y1 - 2005 SN - 0304-3975 ER - TY - JOUR A1 - Bordihn, Henning A1 - Holzer, Markus A1 - Kutrib, Martin T1 - Unsolvability levels of operation problems for subclasses of context-free languages N2 - 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 Y1 - 2005 SN - 0129-0541 ER - TY - BOOK A1 - Bensch, Suna A1 - Boldt, Oliver A1 - Bordihn, Henning A1 - Jürgensen, Helmut T1 - Workshop "Formale Methoden der Linguistik" und "14. Theorietag Automaten und Formale Sprachen" T3 - Preprint / Universität Potsdam, Institut für Informatik Y1 - 2004 SN - 0946-7580 VL - 2004, 2 PB - Univ. CY - Potsdam 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 - GEN A1 - Bordihn, Henning A1 - Nagy, Benedek A1 - Vaszil, György T1 - Preface: Non-classical models of automata and applications VIII T2 - RAIRO-Theoretical informatics and appli and applications Y1 - 2018 U6 - https://doi.org/10.1051/ita/2018019 SN - 0988-3754 SN - 1290-385X VL - 52 IS - 2-4 SP - 87 EP - 88 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Bordihn, Henning A1 - Bottoni, Paolo A1 - Labella, Anna A1 - Mitrana, Victor T1 - Networks of picture processors as problem solvers JF - Soft Computing N2 - 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. KW - Picture KW - Picture processor KW - Hiding processor KW - Picture matching KW - (k,l)-Local language Y1 - 2016 U6 - https://doi.org/10.1007/s00500-016-2206-y SN - 1432-7643 SN - 1433-7479 VL - 21 SP - 5529 EP - 5541 PB - Springer CY - New York 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 - Bensch, Suna A1 - Bordihn, Henning A1 - Holzer, Markus A1 - Kutrib, Martin T1 - On input-revolving deterministic and nondeterministic finite automata N2 - We introduce and investigate input-revolving finite automata, which are (nondeterministic) finite state automata with the additional ability to shift the remaining part of the input. Three different modes of shifting are considered, namely revolving to the left, revolving to the right, and circular-interchanging. We investigate the computational capacities of these three types of automata and their deterministic variants, comparing any of the six classes of automata with each other and with further classes of well-known automata. In particular, it is shown that nondeterminism is better than determinism, that is, for all three modes of shifting there is a language accepted by the nondeterministic model but not accepted by any deterministic automaton of the same type. Concerning the closure properties most of the deterministic language families studied are not closed under standard operations. For example, we show that the family of languages accepted by deterministic right-revolving finite automata is an anti-AFL which is not closed under reversal and intersection. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/08905401 U6 - https://doi.org/10.1016/J.Ic.2009.03.002 SN - 0890-5401 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 - 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 - Kutrib, Martin A1 - Malcher, Andreas T1 - On the computational capacity of parallel communicating finite automata JF - International journal of foundations of computer science N2 - Systems of parallel finite automata communicating by states are investigated. We consider deterministic and nondeterministic devices and distinguish four working modes. It is known that systems in the most general mode are as powerful as one-way multi-head finite automata. Here we solve some open problems on the computational capacity of systems working in the remaining modes. In particular, it is shown that deterministic returning and non-returning devices are equivalent, and that there are languages which are accepted by deterministic returning and centralized systems but cannot be accepted by deterministic non-returning centralized systems. Furthermore, we show that nondeterministic systems are strictly more powerful than their deterministic variants in all the four working modes. Finally, incomparability with the classes of (deterministic) (linear) context-free languages as well as the Church-Rosser languages is derived. KW - Automata systems KW - cooperating systems KW - formal languages KW - theory of computation Y1 - 2012 U6 - https://doi.org/10.1142/S0129054112500062 SN - 0129-0541 VL - 23 IS - 3 SP - 713 EP - 732 PB - World Scientific CY - Singapore 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 - Kutrib, Martin A1 - Malcher, Andreas T1 - Undecidability and hierarchy results for parallel communicating finite automata JF - International journal of foundations of computer science N2 - 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. KW - Automata systems KW - cooperating systems KW - formal languages KW - decidability questions Y1 - 2011 U6 - https://doi.org/10.1142/S0129054111008891 SN - 0129-0541 VL - 22 IS - 7 SP - 1577 EP - 1592 PB - World Scientific CY - Singapore ER - 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 - Bordihn, Henning A1 - Holzer, Markus T1 - Programmed grammars and their relation to the LBA problem JF - Acta informatica N2 - 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. KW - programmed grammars KW - accepting grammars KW - LBA problem KW - degree of non-regulation KW - leftmost derivations Y1 - 2006 U6 - https://doi.org/10.1007/s00236-006-0017-9 SN - 0001-5903 VL - 43 SP - 223 EP - 242 PB - Elsevier CY - New York ER - TY - JOUR A1 - Bordihn, Henning A1 - Vaszil, György T1 - Reversible parallel communicating finite automata systems JF - Acta informatica N2 - 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. KW - Finite automata KW - Reversibility KW - Systems of parallel communicating KW - automata Y1 - 2021 U6 - https://doi.org/10.1007/s00236-021-00396-9 SN - 0001-5903 SN - 1432-0525 VL - 58 IS - 4 SP - 263 EP - 279 PB - Springer CY - Berlin ; Heidelberg ; New York, NY ER - TY - JOUR A1 - Bordihn, Henning A1 - Holzer, Markus T1 - On the number of active states in finite automata JF - Acta informatica N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1007/s00236-021-00397-8 SN - 0001-5903 SN - 1432-0525 VL - 58 IS - 4 SP - 301 EP - 318 PB - Springer CY - Berlin ; Heidelberg [u.a.] ER - TY - JOUR A1 - Bordihn, Henning A1 - Mitrana, Victor T1 - On the degrees of non-regularity and non-context-freeness JF - Journal of computer and system sciences N2 - 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. KW - context-free grammar KW - degree of non-regularity KW - context-sensitive KW - grammar KW - degree of non-context-freeness Y1 - 2020 U6 - https://doi.org/10.1016/j.jcss.2019.09.003 SN - 0022-0000 SN - 1090-2724 VL - 108 SP - 104 EP - 117 PB - Elsevier CY - San Diego, Calif. [u.a.] ER -