Related papers: Variants of Higher-Dimensional Automata
In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata. In this paper, we compare the descriptional power of these models with…
We show that every two-way deterministic finite automaton (2DFA) that solves one-way liveness on height h has Omega(h^2) states. This implies a quadratic lower bound for converting one-way nondeterministic finite automata to 2DFAs, which…
A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
We present several new results and connections between various extensions of finite automata through the study of vector automata and homing vector automata. We show that homing vector automata outperform extended finite automata when both…
Recent advancements in open-source Visual Language Models (VLMs) such as LLaVA, Qwen-VL, and Llama have catalyzed extensive research on their integration with diverse systems. The internet-scale general knowledge encapsulated within these…
The paper is devoted to two types of algebraic models of automata. The usual (first type) model leads to the developed decomposition theory (Krohn-Rhodes theory). We introduce another type of automata model and study how these automata are…
We examine different generalizations of checking stack automata by allowing multiple input heads and multiple stacks, and characterize their computing power in terms of two-way multi-head finite automata and space-bounded Turing machines.…
Deep neural networks (DNNs) have proven their capabilities in many areas in the past years, such as robotics, or automated driving, enabling technological breakthroughs. DNNs play a significant role in environment perception for the…
It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized…
Recently, a new paradigm was introduced in automata theory. The main idea is to classify regular languages according to their propensity to be sorted, establishing a deep connection between automata theory and data compression [J. ACM…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…
While Monte Carlo Tree Search (MCTS) shows promise in Large Language Model (LLM) based Automatic Heuristic Design (AHD), it suffers from a critical over-exploitation tendency under the limited computational budgets required for heuristic…
Computing sparse redundant representations is an important problem both in applied mathematics and neuroscience. In many applications, this problem must be solved in an energy efficient way. Here, we propose a hybrid distributed algorithm…
Over the last decades the development of ASP has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting…
When does a deterministic computational model define a probability distribution? What are its properties? This work formalises and settles this stochasticity problem for weighted automata, and its generalisation cost register automata…
General-purpose large language models (LLMs) are increasingly deployed in verticals such as telecommunications, where adaptation is hindered by scarce, low-information-density corpora and tight mobile/edge constraints. We propose Data…
Plane-walking automata were introduced by Salo & T\"orma to recognise languages of two-dimensional infinite words (subshifts), the counterpart of $4$-way finite automata for two-dimensional finite words. We extend the model to allow for…
High-dimensional, low sample-size (HDLSS) data problems have been a topic of immense importance for the last couple of decades. There is a vast literature that proposed a wide variety of approaches to deal with this situation, among which…