Related papers: Formal Languages in Dynamical Systems
The new approach to representation of syntax of formal languages-- a formalism of syntax diagrams is offered. Syntax diagrams look a convenient language for the description of syntactic relations in the languages having nonlinear…
It is proposed that the theory of dynamical systems offers appropriate tools to model many phonological aspects of both speech production and perception. A dynamic account of speech rhythm is shown to be useful for description of both…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis…
Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are…
Understanding learning as a dynamic process is challenging due to the interaction of multiple factors, including cognitive load, internal state change, and subjective evaluation. Existing approaches often address these elements in…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We…
Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing…
We study analysis of complex systems using a Quantitative Theory of Meaning developed as an extention of Shannon's Communication Theory. The approach consideres complexity not in terms of the manifestation of its effects which are…
The intricate hierarchical structure of syntax is fundamental to the intricate and systematic nature of human language. This study investigates the premise that language models, specifically their attention distributions, can encapsulate…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to…
Transformer-based language models are effective but complex, and understanding their inner workings and reasoning mechanisms is a significant challenge. Previous research has primarily explored how these models handle simple tasks like name…
The method of constructing of Grothendieck's topology basing on a neighbourhood grammar, defined on the category of syntax diagrams is described in the article. Syntax diagrams of a formal language are the multigraphs with nodes, signed by…
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
Characterizing the computational power of neural network architectures in terms of formal language theory remains a crucial line of research, as it describes lower and upper bounds on the reasoning capabilities of modern AI. However, when…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…