Related papers: Eventual Linear Ranking Functions
The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many…
We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…
The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting…
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…
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…
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 parameterized, well-founded relations such that an assignment to…
The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and…
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 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…
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…
We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…
Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for…
While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…
Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different…
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…
Vector addition systems are an important model in theoretical computer science and have been used for the analysis of systems in a variety of areas. Termination is a crucial property of vector addition systems and has received considerable…
Finding whether a linear-constraint loop has a linear ranking function is an important key to understanding the loop behavior, proving its termination and establishing iteration bounds. If no preconditions are provided, the decision problem…
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…