Related papers: Nagoya Termination Tool
We present a tool that automates termination proofs for recursive definitions by mining existing termination theorems.
Monotonic semantic path orders and weighted path orders are powerful reduction orders for proving termination of term rewrite systems. In this paper we present their simple unification as reduction orders and reduction pairs. We also…
Term rewriting is a Turing complete model of computation. When taught to students of computer science, key properties of computation as well as techniques to analyze programs on an abstract level are conveyed. This paper gives a swift…
The Weighted Path Order of Yamada is a powerful technique for proving termination. It is also supported by CeTA, a certifier for checking untrusted termination proofs. To be more precise, CeTA contains a verified function that computes for…
We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…
We revisit the static dependency pair method for proving termination of higher-order term rewriting and extend it in a number of ways: (1) We introduce a new rewrite formalism designed for general applicability in termination proving of…
Narrowing and unification are very useful tools for symbolic analysis of rewrite theories, and thus for any model that can be specified in that way. A very clear example of their application is the field of formal cryptographic protocol…
On the one hand, checking specific termination proofs by hand, say using a particular collection of matrix interpretations, can be an arduous and error-prone task. On the other hand, automation of such checks would save time and help to…
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…
The Transformer model has revolutionized Natural Language Processing tasks such as Neural Machine Translation, and many efforts have been made to study the Transformer architecture, which increased its efficiency and accuracy. One potential…
NPtool is a fast and accurate system for extracting noun phrases from English texts for the purposes of e.g. information retrieval, translation unit discovery, and corpus studies. After a general introduction, the system architecture is…
Machine translation (MT) is an important sub-field of natural language processing that aims to translate natural languages using computers. In recent years, end-to-end neural machine translation (NMT) has achieved great success and has…
Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order…
We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…
Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…
There are many techniques and tools for termination of C programs, but up to now they were not very powerful for termination proofs of programs whose termination depends on recursive data structures like lists. We present the first approach…
In recent years, two higher-order extensions of the powerful dependency pair approach for termination analysis of first-order term rewriting have been defined: the static and the dynamic approach. Both approaches offer distinct advantages…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
In a previous work, the first author extended to higher-order rewriting and dependent types the use of size annotations in types, a termination proof technique called type or size based termination and initially developed for ML-like…
Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools…