Related papers: Reflections on Termination of Linear Loops
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…
We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
We study the problem of deciding universal termination of linear and affine loops over the reals in the bit-model of real computation. We show that both problems are as close to decidable as one can expect them to be: there exist sound…
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 linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of…
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…
We present an efficient approach to prove termination of monotone programs with integer variables, an expressive class of loops that is often encountered in computer programs. Our approach is based on a lightweight static analysis method…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
We consider the problem of deciding termination of single-path while loops with integer variables, affine updates, and affine guard conditions. The question is whether such a loop terminates on all integer initial values. This problem is…
Recent developments in data-driven control have revived interest in the behavioral approach to systems theory, where systems are defined as sets of trajectories rather than being described by a specific model or representation. However,…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
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.…
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…
We present the first approach to prove non-termination of integer programs that is based on loop acceleration. If our technique cannot show non-termination of a loop, it tries to accelerate it instead in order to find paths to other…
Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…