Related papers: On Termination of Integer Linear Loops
This paper investigates the relation between linear codes and the stabilizer in ${\rm GL}_2(\mathbb{C})$ of their weight enumerators. We prove a result on the finiteness of stabilizers and give a complete classification of linear codes with…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations…
In this paper we study the complexity of the problems: given a loop, described by linear constraints over a finite set of variables, is there a linear or lexicographical-linear ranking function for this loop? While existence of such…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
The termination problem of a logic program can be addressed in either a static or a dynamic way. A static approach performs termination analysis at compile time, while a dynamic approach characterizes and tests termination of a logic…
Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…
Verifiers that can prove programs correct against their full functional specification require, for programs with loops, additional annotations in the form of loop invariants---propeties that hold for every iteration of a loop. We show that…
The integration of Formal Verification tools with Large Language Models (LLMs) offers a path to scale software verification beyond manual workflows. However, current methods remain unreliable: without a solid theoretical footing, the…
Invariants are the predominant approach to verify the correctness of loops. As an alternative, loop contracts, which make explicit the premise and conclusion of the underlying induction proof, can sometimes capture correctness conditions…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects…
In previous work, we presented a symbolic execution method which starts with a concrete model of the program but progressively abstracts away details only when these are known to be irrelevant using interpolation. In this paper, we extend…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
Termination analyses investigate the termination behavior of programs, intending to detect nontermination, which is known to cause a variety of program bugs (e.g. hanging programs, denial-of-service vulnerabilities). Beyond formal…