Chomsky hierarchy

About: Chomsky hierarchy is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 31067 citations. The topic is also known as: Chomsky–Schützenberger hierarchy.

Reaction Automata

Abstract: Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that feature (string) language acceptors with multiset manipulation as a computing mechanism, and show that reaction automata are computationally Turing universal. Further, some subclasses of reaction automata with space complexity are investigated and their language classes are compared to the ones in the Chomsky hierarchy.

Restarting Automata for Picture Languages: A Survey on Recent Developments

Abstract: Much work has been done to obtain classes of picture languages that would correspond to the classes of the Chomsky hierarchy for string languages, and finally the class REC of recognizable picture languages has been agreed on as the class that corresponds to the ‘regular string languages.’ This class has several nice characterizations in terms of regular expressions, tiling automata, and on-line tesselation automata, and it has nice closure properties, but it also has two main drawbacks: all its characterizations are highly nondeterministic in nature, and it contains languages that are NP-complete. Consequentially, various deterministic subclasses of REC have been defined. Mainly, however, these definitions are quite complex, and it is not clear which of the resulting classes should be considered as ‘the’ class of deterministic recognizable picture languages. Here we present some recent developments obtained in a research project that aims at finding a deterministic model of a two-dimensional automaton that has the following desirable properties:

Prolegomenon to the relation between social theory and method

Abstract: Building on the work of Noam Chomsky (1963), this paper presents a hierarchy of grammars and associated computational automata in order to inform social theory construction and method. A detailed exposition of linguistic forms within the grammar hierarchy reveals clear analogues with common social scientific paradigms. Two of these paradigms (which are termed structural and process approaches) are already being widely exploited by formal methodological techniques. A third paradigm, which is rooted in a tradition of interpretive sociology, has been more resistant to formalization. Using arguments from theoretical computer science, the paper suggests that existing quantitative methodologies can be extended to accommodate qualitative arguments which subsume empirical domains as diverse as natural language and structurational phenomena.

Fair expressions and regular languages over lists

Abstract: In this paper a formalism is proposed, named fair expressions, partly introduced in [Bre94], that extends regular expressions to lists, having strings as components. This formalism uses classical regular operators, i.e. catenation and its closure, and novel ones, namely the operator of merge and its closure, which are natural for lists. Fair expressions allow to define languages of lists, named fair languages, which can be compared to word languages by flattening the lists into strings. In this paper the basic properties of fair languages are briefly summarized and also extended with respect to previous works [Bre94]: hierarchy, semilinearity, closure, decidability and comparison with the Chomsky hierarchy are dealt with. The family offair languages is however far larger than the regular one; as a novel contribution this paper investigates its subfamilies that are comparable with regular languages. The main result that the regular subfamilies offair languages constitute a proper hierarchy. These subfamilies are then characterized and their properties are explored, showing that they are, in general, more mathematically tractable than fair languages. The conclusion lists comparisons with related works, open problems and research directions.