Related papers: Approximations of generating functions and a few c…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function…
The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many…
Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the "splicing operation", a cut-and-paste binary string…
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals.…
We derive the algebraic generating function for inversion sequences avoiding the patterns $201$ and $210$ by describing a set of succession rules, converting them to a system of generating function equations with one catalytic variable, and…
Integer sequences are of central importance to the modeling of concepts admitting complete finitary descriptions. We introduce a novel view on the learning of such concepts and lay down a set of benchmarking tasks aimed at conceptual…
Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular…
Document databases are increasingly popular in various applications, but their queries are challenging to write due to the flexible and complex data model underlying document databases. This paper presents a synthesis technique that aims to…
Divide-and-conquer functions satisfy equations in F(z),F(z^2),F(z^4)... Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By…
We provide an algorithm for computing semi-Fourier sequences for expressions constructed from arithmetic operations, exponentiations and integrations. The semi-Fourier sequence is a relaxed version of Fourier sequence for polynomials…
The On-Line Encyclopedia of Integer Sequences (OEIS) is a web-accessible database cataloging interesting integer sequences and associated theorems. With more than 12,000 citations, the OEIS is one of the most highly cited resources in all…
We determine all pairs of positive integers $(a,b)$ such that $a+b$ and $a \times b$ have the same decimal digits in reverse order: \[ (2,2), (9,9), (3,24), (2,47), (2,497), (2,4997), (2,49997), \ldots \] We use deterministic finite…
We develop an approach to estimate the probability that a program sampled from a large language model is correct. Given a natural language description of a programming problem, our method samples both candidate programs as well as candidate…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to…
In this paper we present a general method for information extraction that exploits the features of data compression techniques. We first define and focus our attention on the so-called "dictionary" of a sequence. Dictionaries are…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…