Related papers: Automatic Counting of Generalized Latin Rectangles…
We introduce the class of P-finite automata. These are a generalisation of weighted automata, in which the weights of transitions can depend polynomially on the length of the input word. P-finite automata can also be viewed as simple…
We prove a general result on completing objects similar to Latin rectangles in which the number of occurrences of each symbol is prescribed, each cell contains multiple symbols, and no cell contains repeated symbols. This generalizes…
Rowland and Zeilberger devised an approach to algorithmically determine the modulo $p^r$ reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting $p$-schemes…
We show the power of Bruno Buchberger's seminal Groebner Basis algorithm, interfaced, seamlessly, with what we call symbolic dynamical programming, to automatically generate algebraic equations satisfied by the generating functions…
In this paper we present an efficient computational and symbolic algorithms for solving a backward pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS) such as MAPLE, MACSYMA, MATHEMATICA,…
Many combinatorial sequences (for example, the Catalan and Motzkin numbers) may be expressed as the constant term of $P(x)^k Q(x)$, for some Laurent polynomials $P(x)$ and $Q(x)$ in the variable $x$ with integer coefficients. Denoting such…
In this paper we use the framework of automatic sequences to study combinatorial sequences modulo prime powers. Given a sequence whose generating function is the diagonal of a rational power series, we provide a method, based on work of…
A Latin square of order $n$ is an $n\times n$ matrix in which each row and column contains each of $n$ symbols exactly once. For $\epsilon>0$, we show that with high probability a uniformly random Latin square of order $n$ has no proper…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
In this paper we propose an algorithm for enumerating diagonal Latin squares of small order. It relies on specific properties of diagonal Latin squares to employ symmetry breaking techniques, and on several heuristic optimizations and bit…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
Let $L$ be an $n\times n$ array whose top left $r\times s$ subarray is filled with $k$ different symbols, each occurring at most once in each row and at most once in each column. We find necessary and sufficient conditions that ensure the…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the…
Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant.…
We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing…