Topic
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.
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03 Jun 2019
TL;DR: This talk will summarize the works towards finding a particular boundary between different self- assembly classes and some trade-offs between different types of self-assembly instructions.
Abstract: In the theory of computation, the Chomsky hierarchy provides a way to characterize the complexity of different formal languages. For each class in the hierarchy, there is a specific type of automaton which recognizes all languages in the class. There different types of automaton can be viewed as standard requirements in order to recognize languages in these classes. In self-assembly, the main task is to generate patterns and shapes within certain resource limitations. Is it possible to separate these tasks into different classes? If yes, can we find a standard set of self-assembly instructions capable of performing all tasks in each class? In this talk, I will summarize the works towards finding a particular boundary between different self-assembly classes and some trade-offs between different types of self-assembly instructions.
TL;DR: In this article, two classes of generalized semi-Thue systems are introduced and two infinite hierarchies of languages are obtained in this way, and the capacity of these generative mechanisms and the closure properties of the obtained families of languages were investigated.
Abstract: In this paper, two classes of generalized semi-Thue systems are introduced. Two infinite hierarchies of languages are obtained in this way. The capacity of these generative mechanisms and the closure properties of the obtained families of languages are investigated.
Journal Article•
TL;DR: It is shown that a context–free string-graph grammar (one hyperedge is replaced at a time) can be used to model discontinuous constituents in natural languages.
Abstract: Discontinuous constituents are a frequent problem in natural language analyses. A constituent is called discontinuous if it is interrupted by other constituents. In German they can appear with separable verb prefixes or relative clauses in the Nachfeld. They can not be captured by a context-free Chomsky grammar. A subset of hypergraph grammars are string-graph grammars where the result of a derivation must be formed like a string i.e. terminal edges are connected to two nodes and are lined up in a row. Nonterminal edges do not have to fulfill this property. In this paper it is shown that a context-free string-graph grammar (one hyperedge is replaced at a time) can be used to model discontinuous constituents in natural languages.
Posted Content•
TL;DR: This paper shows that several definitions of “regular language” or “local rule” that are equivalent in d=1 lead to distinct classes in d≥2, and explores the closure properties and computational complexity of these classes, including undecidability and L, NL, and NP-completeness results.
Abstract: In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them.
In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of ``regular language'' or ``local rule'' that are equivalent in d=1 lead to distinct classes in d >= 2. We explore the closure properties and computational complexity of these classes, including undecidability and L-, NL- and NP-completeness results.
We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in d >= 2 has a periodic point of a given period, and that certain ``local lattice languages'' are not finite-time images or limit sets of any CA. We also show that the entropy of a d-dimensional CA's finite-time image cannot decrease faster than t^{-d} unless it maps every initial condition to a single homogeneous state.