Related papers: Non-Termination Sets of Simple Linear Loops
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…
Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
Program termination is a hot research topic in program analysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the…
A Code loop on a binary linear code that is doubly even with a factor set is shown to be a central loop, conjugacy closed loop, Burn loop and extra loop. General forms of the identities that define the factor set of a code are deduced.
The stable torsion length in a group is the stable word length with respect to the set of all torsion elements. We show that the stable torsion length vanishes in crystallographic groups. We then give a linear programming algorithm to…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
A fundamental result in linear algebra states that if a homogenous linear equation system has only the trivial solution, then there are at most as many variables as equations. We prove the following generalisation of this phenomenon. If a…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
Probably building non procedural languages is the most prospective way for parallel programming just because non procedural means no fixed way for execution. The article consists of 3 parts. In first part we consider formal systems for…
Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task already for syntactically restricted classes of loops. Rather…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
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…
While loops are present in virtually all imperative programming languages. They are important both for practical reasons (performing a number of iterations not known in advance) and theoretical reasons (achieving Turing completeness). In…
We introduce IsalProgram (Instruction Set and Language for Programming), a novel assembly-like programming language with three distinctive theoretical properties: (1) it is a regular language in the sense of formal language theory, meaning…
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs. To this end, a variety of acceleration techniques has been proposed. However, so far all of them have been monolithic, i.e., a…