Related papers: Termination of Linear Loops over the Integers
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty allows us to prove the existence of…
While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility…
We study the computational complexity of the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets, or equivalently the Termination Problem for affine loops with compact semialgebraic guard sets. Consider…
This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the ring $\mathbb{Z}[x]$ of polynomials in one variable. We…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…
Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
The Size-Change Termination principle was first introduced to study the termination of first-order functional programs. In this work, we show that it can also be used to study the termination of higher-order rewriting in a system of…
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime $p$. In particular, in the integer case, we improve a recent bound…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
In the book [FIM], original methods were proposed to determine the invariant measure of random walks in the quarter plane with small jumps, the general solution being obtained via reduction to boundary value problems. Among other things, an…
We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…