Related papers: Counting and Generating Terms in the Binary Lambda…

We study the relationship between the growth rate of an integer sequence and harmonic and functional properties of the corresponding sequence of characters. In particular we show that every polynomial sequence contains a set that is…

A novel approach to automated learning of syntactic rules governing natural languages is proposed, based on using probabilities assigned to sentences (and potentially longer word sequences) by transformer neural network language models to…

We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…

This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…

In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…

We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…

Despite their growing capabilities, language models still frequently reproduce content from their training data, generate repetitive text, and favor common grammatical patterns and vocabulary. A possible cause is the decoding strategy: the…

The ability of large language models to generate complex texts allows them to be widely integrated into many aspects of life, and their output can quickly fill all network resources. As the impact of LLMs grows, it becomes increasingly…

We study the question of whether for each n there is another integer m with lambda(m)=lambda(n), where lambda is Carmichael's function. We give a "near" proof of the fact that this is the case unconditionally, and a complete conditional…

The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be…

Many problems in Computer Science can be abstracted to the following question: given a set of objects and rules respectively, which new objects can be produced? In the paper, we consider a succinct version of the question: given a set of…

Lambda words are sequences obtained by encoding the differences between ordered elements of the form i+j\theta, where i and j are non-negative integers and 1 < \theta <2. Lambda words are right-infinite words defined over an infinite…

Twins in a finite word are formed by a pair of identical subwords placed at disjoint sets of positions. We investigate the maximum length of twins in a random word over a $k$-letter alphabet. The obtained lower bounds for small values of…

We use generating functions to enumerate Arndt compositions, that is, integer compositions where there is a descent between every second pair of parts, starting with the first and second part, and so on. In 2013, J\"org Arndt noted that…

We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…

We develop a technique for generalising from data in which models are samplers represented as program text. We establish encouraging empirical results that suggest that Markov chain Monte Carlo probabilistic programming inference techniques…

Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…

We propose generative models for three types of extra-grammatical word formation phenomena abounding in English slang: Blends, Clippings, and Reduplicatives. Adopting a data-driven approach coupled with linguistic knowledge, we propose…

We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric…

Some consider large-scale language models that can generate long and coherent pieces of text as dangerous, since they may be used in misinformation campaigns. Here we formulate large-scale language model output detection as a hypothesis…