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.

Translations of network languages

Abstract: In this paper, we describe new results of research on geometrical properties of complex control systems, the so-called Linguistic Geometry. This research includes the development of syntactic tools for knowledge representation and reasoning about large-scale hierarchical complex systems. It relies on the formalization of search heuristics of high-skilled human experts that have resulted in the development of successful applications in different areas. A hierarchy of subsystems of a complex system, the networks of paths, is represented as a hierarchy of formal languages. In this paper, we investigate transformations of these networks while a system moves from one state to another. The investigation consists of formal, constructive separation of changed and unchanged parts of system representation, the hierarchy of languages. Thus, we address a problem relative to the well-known Frame Problem for planning systems. A partial solution is presented in the form of the theorem about translations of network languages. Formal considerations are illustrated by example of Air Force robotic vehicles.

Inductive Inference Machines That Can Refute Hypothesis Spaces

Abstract: This paper intends to give a theoretical foundation of machine discovery from examples. We point out that the essence of a logic of machine discovery is the refutability of the entire spaces of hypotheses. We discuss this issue in the framework of inductive inference of length-bounded elementary formal systems (EFS's, for short), which are a kind of logic programs over strings of characters and correspond to context-sensitive grammars in Chomsky hierarchy.

Automata That Take Advice

Abstract: Karp and Lipton introduced advice-taking Turing machines to capture nonuniform complexity classes. We study this concept for automata-like models and compare it to other nonuniform models studied in connection with formal languages in the literature. Based on this we obtain complete separations of the classes of the Chomsky hierarchy relative to advices.

Nonterminal Complexity of Programmed Grammars

Abstract: We show that, in the case of context-free programmed grammars with appearance checking working under free derivations, three nonterminals are enough to generate every recursively enumerable language. This improves the previously published bound of eight for the nonterminal complexity of these grammars. This also yields an improved nonterminal complexity bound of four for context-free matrix grammars with appearance checking. Moreover, we establish nonterminal complexity bounds for context-free programmed and matrix grammars working under leftmost derivations.

On Cellular Automata with a Finite Number of State Changes

Abstract: On Cellular Automata with a Finite Number of State Changes. The number of state changes is introduced as a complexity measure for the recognition of languages in cellular automata. The relation of the simplest class — i.e. the one with a constant number of changes per single automaton — to the Chomsky hierarchy is investigated and a comparison with sequential tape complexity is made.