Fixed Points and Noetherian Topologies

Aliaume Lopez (1, 2)

1 LMF - Laboratoire Méthodes Formelles
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

Abstract Noetherian spaces are a generalisation of well-quasi-orderings to topologies, that can be used to prove termination of programs. They find applications in the verification of transition systems, some of which are better described using topology. The goal of this paper is to allow the systematic description of computations using inductively defined datatypes via Noetherian spaces. This is achieved through a fixed point theorem based on a topological minimal bad sequence argument.

Keywords: Noetherian spaces topology well-quasi-orderings initial algebras Kruskal's Theorem Higman's Lemma; Noetherian spaces; topology; well-quasi-orderings; initial algebras; Kruskal's Theorem; Higman's Lemma

Domains: Logic in Computer Science [cs.LO]; General Topology [math.GN]

Aliaume Lopez. Fixed Points and Noetherian Topologies. FoSSaCS, Apr 2023, Paris, France. pp.456-476, ⟨10.1007/978-3-031-30829-1_22⟩. ⟨hal-04284124⟩