Related papers: When can we decide that a P-finite sequence is pos…

Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…

We derive the P-finite recurrences for classes of sequences with ordinary generating function containing roots of polynomials. The focus is on establishing the D-finite differential equations such that the familiar steps of reducing their…

It is well known that algebraic power series are differentially finite (D-finite): they satisfy linear differential equations with polynomial coefficients. The converse problem, whether a given D-finite power series is algebraic or…

In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…

We establish conditions under which the fundamental group of a graph of finite $p$-groups is necessarily residually $p$-finite. The technique of proof is independent of previously established results of this type, and the result is also…

Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…

In this paper we present a method to pass from a recurrence relation having constant coefficients (in short, a C-recurrence) to a finite succession rule defining the same number sequence. We recall that succession rules are a recently…

In this paper we propose a sequence of tests which gives a definitive test for checking $2\times M$ separability. The test is definitive in the sense that each test corresponds to checking membership in a cone, and that the closure of the…

We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…

The long run behaviour of linear dynamical systems is often studied by looking at eventual properties of matrices and recurrences that underlie the system. A basic problem that lies at the core of many questions in this setting is the…

Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works…

In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\(f\) to have exactly…

We propose a numerical method, based on the shift-and-invert power iteration, that answers whether a symmetric matrix is positive definite ("yes") or not ("no"). Our method uses randomization. But, it returns the correct answer with high…

While it is trivial to multiply two C-finite sequences (just like integers), it is not quite so trivial to "factorize" them, or to decide whether they are "prime". The former is plain linear algebra, while the latter is heavy-duty…

We prove that checking if a partial matrix is partial totally positive is co-NP-complete. This contrasts with checking a conventional matrix for total positivity, for which we provide a cubic time algorithm. Checking partial sign regularity…

We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly $2272$ noncorrelated binary pattern sequences of length $\leq 4$. If we restrict our…

New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…

We show that positivity on $\mathbb{R}_+^n$ and on $\mathbb{R}^n$ of real symmetric polynomials of degree at most $p$ in $n\ge2$ variables is solvable by algorithms running in $\mathrm{poly}(n)$ time. For real symmetric quartics, we find…

This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…

The termination behavior of probabilistic programs depends on the outcomes of random assignments. Almost sure termination (AST) is concerned with the question whether a program terminates with probability one on all possible inputs.…