相关论文: Democratic sequences
In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics…
This article proposes the use of pseudorandom decimal sequences that have gone through an additional random mapping for the design of cryptographic keys. These sequences are generated by starting with inverse prime expansions in base 3 and…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a…
Let \(\mathcal{P}(n)\) be the set of partitions of the positive integer \(n\). For \(\alpha=(\alpha_1,...,\alpha_t) \in \mathcal{P}(n)\) define the diagonal sequence \(\delta(\alpha)=(d_k(\alpha))_{k \geq 1}\) via \( d_k(\alpha) =…
We show that explicit pragmatic inference aids in correctly generating and following natural language instructions for complex, sequential tasks. Our pragmatics-enabled models reason about why speakers produce certain instructions, and…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feasible region}. We show that this feasible region is a…
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
Causal decoder-only transformer models used for generative language modelling, such as Generative Pre-trained Transformers (GPT), are trained to predict the next token in a sequence based only on its previous tokens. Despite this simple…
We prove that for a positive integer a the integer sequence P(n) satisfying for all n, -infty<n<infty, the recurrence P(n)=a+P(n-phi(a)), phi(a) the Euler function, generates in increasing order all integers P(n) coprime to a.The finite…
The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…
We study a fixed-window counting system in which integers are represented by words of constant length while the alphabet grows as needed. This viewpoint arises from De Bruijn sequences: for fixed order $n$, the reverse prefer-max sequence…
Expressive reading, considered the defining attribute of oral reading fluency, comprises the prosodic realization of phrasing and prominence. In the context of evaluating oral reading, it helps to establish the speaker's comprehension of…
Summary: We present a new method to incrementally construct the FM-index for both short and long sequence reads, up to the size of a genome. It is the first algorithm that can build the index while implicitly sorting the sequences in the…
It is known that binary words containing no $k$ consecutive 1s are enumerated by $k$-step Fibonacci numbers. In this note we discuss the expected value of a random bit in a random word of length $n$ having this property.
We use the ``map of elections'' approach of Szufa et al. (AAMAS-2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which…
The wayward quality of continuous prompts stresses the importance of their interpretability as unexpected and unpredictable behaviors appear following training, especially in the context of large language models automating people-sensitive…
Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. When such a sequence can be…
Previous authors have shown how to build FM-indexes efficiently in external memory, but querying them efficiently remains an open problem. Searching na\"{i}vely for a pattern $P$ requires (\Theta (|P|)) random access. In this paper we show…
A \Def{composition} of a positive integer $n$ is a $k$-tuple $(\l_1, \l_2, \dots, \l_k) \in \Z_{> 0}^k$ such that $n = \l_1 + \l_2 + \dots + \l_k$. Our goal is to enumerate those compositions whose parts $\l_1, \l_2, \dots, \l_k$ avoid a…
Bernoulli sieve is a recursive construction of a random composition (ordered partition) of integer $n$. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of component…