Inspired by the experiments in the emerging area of DNA computing, a somewhat unusual type of a computation strategy was recently proposed by one of us: generate a (large) set of candidate solutions of a problem, then remove the non-solutions such that what remains is the set of solutions. This has been called a computation by carving. This idea leads both to a speculation with possible important consequences and to interesting theoretical computer science (formal language) questions. The speculation is that in this way we can "compute" non-recursively enumerable languages, because the family of recursively enumerable languages is not closed under complementation. The formal language theory questions concern sequences of languages with certain regularities, needed as languages to be extracted from the total language of candidate solutions of a problem. Specifically, we consider sequences of languages obtained by starting from a given regular language and iteratively applying to it a...

The purpose of this paper is the study of the smallest family of transductions containing length-preserving rational transductions and closed under union, composition and iteration. We give several characterizations of this class using restricted classes of length-preserving rational transductions, by showing the connections with "context-sensitive transductions" and transductions associated with recognizable picture languages. We also study the classes obtained by only using length-preserving rational functions and we show the relations with "deterministic context-sensitive transductions". 1 Introduction The family of rational languages turns out to be one of the most important classes within the Chomsky hierarchy. Finite automata that are the main object for studying rational languages are now used in the most domains of computer science. Rational transductions introduced by C. C. Elgot and J. E. Mezei [5] are a natural extension of rational languages and were very useful to represe...

We consider bidirectional cooperating distributed (BCD) grammar systems in the sense of Asveld. Independently of their mode , , =, , or t, BCD grammar systems with two components characterize the recursively enumerable languages even with right-linear rules and without -productions. This sharply contrasts earlier results on solely generating or accepting grammars, where right-linear rules always only lead to regular languages. Further restrictions lead to language families closely related to Lindenmayer language families. Moreover, we can solve some open problems in the theory of bidirectional grammars in this way. 1 Introduction Formal language theory mainly investigates the descriptional power of various language defining devices. In this paper, bidirectional cooperating distributed grammar systems are considered. In this way, the present work continues and brings together at least five different research directions in formal language theory: Cooperating distributed (CD) grammar ...

We proceed our work on iterated transductions by studying the closure under union and composition of some classes of iterated functions. We analyze this closure for the classes of lengthpreserving rational functions, length-preserving subsequential functions and length-preserving sequential functions with terminal states. All the classes we obtain are equal. We also study the connection with deterministic context-sensitive languages.

The purpose of this paper is to show connections between iterated rational transductions and linear space computations. Hence, we study the smallest family of transductions containing length-preserving rational transductions and closed under union, composition and iteration. We give several characterizations of this class using restricted classes of length-preserving rational transductions, by showing the connections with ``context-sensitive transductions'' and transductions associated with recognizable picture languages.