9.

It is well-known that the automorphism towers of infinite centre-less groups of cardinality κ terminate in less than (2 κ) + steps. But an easy counting argument shows that (2 κ) + is not the best possible bound. However, in this paper, we will show that it is impossible to find an explicit better bound using ZF C.

I survey termination analysis of logic programs with particular attention to methods for automatically proving termination. I introduce the central concepts of automatic termination analysis and give an overview of the research on other types of termination analysis. I describe the main approaches covered in the literature and compare the accuracy and eeciency of each of them.

Proving program termination is key to guaranteeing absence of undesirable behaviour, such as hanging programs and even security vulnerabilities such as denial-of-service attacks. To make termination checks scale to large systems, interprocedural termination analysis seems essential, which is a largely unexplored area of research in termination analysis, where most effort has focussed on difficu...

We investigate the practically crucial property of operational termination of deterministic conditional term rewriting systems (DCTRSs), an important declarative programming paradigm. We show that operational termination can be equivalently characterized by the newly introduced notion of context-sensitive quasi-reductivity. Based on this characterization and an unraveling transformation of DCTR...

In classical planning we are faced with the fol­ lowing formal task: Given a set A of permissible actions, a description a of init ial states and a description of final states, determine a plan I I , i.e. a finite sequence of actions from A, such that execution of II begun in any state satis­ fying is guaranteed to terminate in a state satisfying In this paper we extend the classical model of p...

The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. In this paper, we show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different te...

One of the difficulties of proving program termination is managing the subtle interplay between the finding of a termination argument and the finding of the argument’s supporting invariant. In this paper we propose a new mechanism that facilitates better cooperation between these two types of reasoning. In an experimental evaluation we find that our new method leads to dramatic performance impr...