Related papers: Inference of termination conditions for numerical …
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…
In this paper, we investigate the problem of mining numerical data in the framework of Formal Concept Analysis. The usual way is to use a scaling procedure --transforming numerical attributes into binary ones-- leading either to a loss of…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
We present cTI, the first system for universal left-termination inference of logic programs. Termination inference generalizes termination analysis and checking. Traditionally, a termination analyzer tries to prove that a given class of…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
We present a new characterization of termination of general logic programs. Most existing termination analysis approaches rely on some static information about the structure of the source code of a logic program, such as modes/types,…
There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that…
Termination of logic programs with negated body atoms (here called general logic programs) is an important topic. One reason is that many computational mechanisms used to process negated atoms, like Clark's negation as failure and Chan's…
A fundamental problem in program verification concerns the termination of simple linear loops of the form x := u ; while Bx >= b do {x := Ax + a} where x is a vector of variables, u, a, and c are integer vectors, and A and B are integer…
We propose an early termination technique for mixed integer conic programming for use within branch-and-bound based solvers. Our approach generalizes previous early termination results for ADMM-based solvers to a broader class of…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the…
The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for…
Nielsen transformations form the basis of a simple and widely used procedure for solving word equations. We make progress on the problem of determining when this procedure terminates in the presence of length constraints. To do this, we…
Termination properties of actual Prolog systems with constraints are fragile and difficult to analyse. The lack of the occurs-check, moded and overloaded arithmetical evaluation via is/2 and the occasional nontermination of finite domain…
In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
Tiwari proved that termination of linear programs (loops with linear loop conditions and updates) over the reals is decidable through Jordan forms and eigenvectors computation. Braverman proved that it is also decidable over the integers.…
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…
Formal specification techniques allow expressing idealized specifications, which abstract from restrictions that may arise in implementations. However, partial implementations are universal in software development due to practical…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…