Related papers: Enumerating Lambda Terms by Weighted Length of The…

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…

It is well-known in the field of programming languages that dealing with variable names and binders may lead to conflicts such as undesired captures when implementing interpreters or compilers. This situation has been overcome by resorting…

Performing $n$ steps of $\beta$-reduction to a given term in the $\lambda$-calculus can lead to an increase in the size of the resulting term that is exponential in $n$. The same is true for the possible depth increase of terms along a…

We present a method which displays all palindromes of a given length from De Bruijn words of a certain order, and also a recursive one which constructs all palindromes of length $n+1$ from the set of palindromes of length $n$. We show that…

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 task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…

We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables ($FO^2$). Specifically, given an $FO^2$ sentence $\Gamma$ and a positive integer $n$, how can one enumerate all the…

Let $\widetilde{\alpha}$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetilde{\alpha}$ is $\lfloor L…

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…

The Bernoulli convolution $\nu_\lambda$ with parameter $\lambda\in(0,1)$ is the probability measure supported on $\mathbf{R}$ that is the law of the random variable $\sum\pm\lambda^n$, where the $\pm$ are independent fair coin-tosses. We…

This paper defines two decreasing measures for terms of the simply typed lambda-calculus, called the W-measure and the Tm-measure. A decreasing measure is a function that maps each typable lambda-term to an element of a well-founded…

For $0 < \lambda < 1$ and $n \rightarrow \infty$ pick uniformly at random $\lambda n$ vectors in $\{0,1\}^n$ and let $C$ be the orthogonal complement of their span. Given $0 < \gamma < \frac12$ with $0 < \lambda < h(\gamma)$, let $X$ be the…

Unanticipated connections between different fragments of lambda calculus and different families of embedded graphs (a.k.a. "maps") motivate the problem of enumerating $\beta$-normal linear lambda terms. In this brief note, it is shown (by…

We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…

We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{(\lambda)}(x))^2(1-x)^\alpha (1+x)^\beta\, dx, \end{equation*} where $C_n^{(\lambda)}$ denotes the Gegenbauer-polynomial of index $\lambda>0$ and $\alpha,\beta>-1$. We give…

A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code…

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…

The present work analyzes the redundancy of sets of combinatorial objects produced by a weighted random generation algorithm proposed by Denise et al. This scheme associates weights to the terminals symbols of a weighted context-free…

There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…

Let $s_n$ be the number of words consisting of the ternary alphabet consisting of the digits 0, 1, and 2 such that no subword (or factor) is a square (a word concatenated with itself, e.g., $11$, $1212$, or $102102$). From computational…