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 - 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 - 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 -