Related papers: Termination of Linear Programs with Nonlinear Cons…
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…
Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…
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…
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…
We consider the problem whether termination of affine integer loops is decidable. Since Tiwari conjectured decidability in 2004, only special cases have been solved. We complement this work by proving decidability for the case that the…
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…
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…
The termination problem for affine programs over the integers was left open in\cite{Braverman}. For more that a decade, it has been considered and cited as a challenging open problem. To the best of our knowledge, we present here the most…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…
We consider linear single-path loops of the form \[ \textbf{while} \quad \varphi \quad \textbf{do} \quad \vec{x} \gets A \vec{x} + \vec{b} \quad \textbf{end} \] where $\vec{x}$ is a vector of variables, the loop guard $\varphi$ is a…
We consider the problem of proving termination for triangular weakly non-linear loops (twn-loops) over some ring $\mathcal{S}$ like $\mathbb{Z}$, $\mathbb{Q}$, or $\mathbb{R}$. The guard of such a loop is an arbitrary quantifier-free…
We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all…
We investigate the termination problem of a family of multi-path polynomial programs (MPPs), in which all assignments to program variables are polynomials, and test conditions of loops and conditional statements are polynomial equalities.…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear…
We consider the following problem: given $d \times d$ rational matrices $A_1, \ldots, A_k$ and a polyhedral cone $\mathcal{C} \subset \mathbb{R}^d$, decide whether there exists a non-zero vector whose orbit under multiplication by $A_1,…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
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…