Abstract Interpretation from a Topological Perspective

Interpretation from a Topological Perspective David A. Schmidt Kansas State University, Manhattan, Kansas, USA Abstract. Topology is the study of property sets (open sets) and continuous functions on them. Despite its applicability to abstract interpretation, topology is little used, and this paper tries to rectify the sitWe develop abstract interpretation from topological principles by relaxing the definitions of open set and continuity; key results still hold. We study families of closed and open sets and show they generate post- and pre-condition analyses, respectively. Giacobazzi's forwardsand backwards-complete functions are characterized by the topologically closed and continuous maps. Finally, we show that Smyth's upper and lower topologies for powersets induce the overapproximating and underting transition functions used for abstract-model checking.

• Type: Conference
• Year: 2009
• Where: SAS
• Authors: David A. Schmidt
• Keywords: Develop Abstract Interpretation, Formal Methods, Open Sets, SAS 2009, Underting Transition Functions