We consider two decision problems for linear recurrence sequences (LRS) over the
integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the …

We consider the problem of expected cost analysis over nondeterministic probabilistic
programs, which aims at automated methods for analyzing the resource-usage of such …

Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem asks
whether all terms of the sequence are positive. We show that, for simple LRS (those whose …

We consider the decidability and complexity of the Ultimate Positivity Problem, which asks
whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are …

A sequence of real numbers is said to be positive if all terms are positive, and ultimately
positive if all but finitely many terms are positive. In this article we survey recent progress on …

It is a longstanding open problem whether there is an algorithm to decide the Skolem
Problem for linear recurrence sequences (LRS) over the integers, namely whether a given …

This paper investigates the problem of reasoning about non-linear behavior of simple
numerical loops. Our approach builds on classical techniques for analyzing the behavior of …

We consider the following decision problem: given a finite Markov chain with distinguished
source and target states, and given a rational number r, does there exist an integer n such …

In program verification, one method for reasoning about loops is to convert them into sets of
recurrences, and then try to solve these recurrences by computing their closed-form …

A finite-state Markov chain M can be regarded as a linear transform operating on the set of
probability distributions over its node set. The iterative applications of M to an initial …