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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.
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
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.
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.
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.
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.
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.
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.
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.
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.