Related papers: Lindenmayer systems as a model of computations
Human language and logic abilities are computationally quantified within the well-studied grammar-automata hierarchy. We identify three hierarchical tiers and two corresponding transitions and show their correspondence to specific abilities…
We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…
Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based…
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
The article provides the theoretical framework of Probabilistic Shoenfield Machines (PSMs), an extension of the classical Shoenfield Machine that models randomness in the computation process. PSMs are introduced in contexts where…
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…
The {\em diagonalization technique} was invented by Georg Cantor to show that there are more real numbers than algebraic numbers and is very crucial in {\em theoretical computer science}. In this work, we enumerate all of the…
Large Language Models are useless for linguistics, as they are probabilistic models that require a vast amount of data to analyse externalized strings of words. In contrast, human language is underpinned by a mind-internal computational…
Large Language Models (LLMs) have demonstrated remarkable reasoning abilities, prompting interest in their application as black-box optimizers. This paper asserts that LLMs possess the capability for zero-shot optimization across diverse…
The Extended Church-Turing Thesis (ECTT) posits that all effective information processing, including unbounded and non-uniform interactive computations, can be described in terms of interactive Turing machines with advice. Does this…
Natural Language Processing (NLP) has become one of the leading application areas in the current Artificial Intelligence boom. Transfer learning has enabled large deep learning neural networks trained on the language modeling task to vastly…
Language models (LMs) are statistical models that calculate probabilities over sequences of words or other discrete symbols. Currently two major paradigms for language modeling exist: count-based n-gram models, which have advantages of…
Given an input string s and a specific Lindenmayer system (the so-called Fibonacci grammar), we define an automaton which is capable of (i) determining whether s belongs to the set of strings that the Fibonacci grammar can generate (in…
Lossy channel systems (LCSs) are systems of finite state automata that communicate via unreliable unbounded fifo channels. In order to circumvent the undecidability of model checking for nondeterministic LCSs, probabilistic models have been…
Memcomputing is a novel non-Turing paradigm of computation that uses interacting memory cells (memprocessors for short) to store and process information on the same physical platform. It was recently proved mathematically that memcomputing…
In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this…
As the core component of Natural Language Processing (NLP) system, Language Model (LM) can provide word representation and probability indication of word sequences. Neural Network Language Models (NNLMs) overcome the curse of dimensionality…
The Curry-Howard correspondence is often called the proofs-as-programs result. I offer a generalization of this result, something which may be called machines as programs. Utilizing this insight, I introduce two new Turing Machines called…
The capabilities of large language models (LLMs) have sparked debate over whether such systems just learn an enormous collection of superficial statistics or a set of more coherent and grounded representations that reflect the real world.…