Related papers: On Termination of Integer Linear Loops
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…
We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…
An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so; it…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
Interrupts have been widely used in safety-critical computer systems to handle outside stimuli and interact with the hardware, but reasoning about interrupt-driven software remains a difficult task. Although a number of static verification…
After a review of linear imperfections and their causes, we discuss how to model them, the diagnostic equipment needed to monitor them, and the correction algorithms to fix the problem they cause. We first address linear systems - beam…
Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of polynomials that automatically generates a Gr\"obner basis…
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…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…
The structure of the F5 algorithm to compute Gr\"obner bases makes it very efficient. However, while it is believed to terminate for so-called regular sequences, it is not clear whether it terminates for all inputs. This paper has two major…
In the paper, some special linear combinations of the terms of rational cycles of generalized Collatz sequences are studied. It is proved that if the coefficients of the linear combinations satisfy some conditions then these linear…
This paper proposes a technique to specify and verify whether a loop can be parallelised. Our approach can be used as an additional step in a parallelising compiler to verify user annotations about loop dependences. Essentially, our…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
We present a new and faster algorithm for the 4-block integer linear programming problem, overcoming the long-standing runtime barrier faced by previous algorithms that rely on Graver complexity or proximity bounds. The 4-block integer…
Based on the geometric {\it Triangle Algorithm} for testing membership of a point in a convex set, we present a novel iterative algorithm for testing the solvability of a real linear system $Ax=b$, where $A$ is an $m \times n$ matrix of…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be…
This paper proposes a verification method for sparse linear systems $Ax=b$ with general and nonsingular coefficients. A verification method produces the error bound for a given approximate solution. Conventional methods use one of two…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…