Condensing Abstract Domains for Logic Program Analysis

Title: Condensing Abstract Domains for Logic Program Analysis

Abstract: This research article explores the concept of condensing abstract domains in the context of logic program analysis. The main idea is to create abstract domains that can accurately represent the semantics of logic languages without losing precision, even when the analysis is goal-independent. This is achieved by systematically refining abstract domains to make them condensing, which means that goal-driven and goal-independent analyses agree, ensuring no loss of precision.

The article introduces the concept of condensation as an abstract domain property and demonstrates that the problem of making an abstract domain condensing can be simplified by focusing on making the domain complete with respect to unification. It also discusses the relationship between condensing abstract domains and quantales, which are models of propositional linear logic.

The research suggests that condensing abstract domains can be systematically derived from any non-condensing domain using a simple domain refinement operator. This approach allows for the development of more accurate and efficient logic program analyses, which is crucial for applications such as automated reasoning and software verification.

Implications: The findings of this research have significant implications for the field of logic program analysis. By introducing the concept of condensing abstract domains, the article provides a new approach to designing accurate and efficient analysis algorithms. This can lead to improved performance in applications that rely on logic program analysis, such as automated reasoning systems and software verification tools.

Furthermore, the research contributes to the ongoing discussion about the relationship between goal-directed and goal-independent analyses in the context of abstract interpretation. By demonstrating that condensing abstract domains can be systematically derived, the article provides a clear framework for understanding and addressing the trade-offs between precision and efficiency in logic program analysis.

Keywords: Abstract interpretation, abstract domain, condensing abstract domain, logic program analysis, linear logic, unification

Link to Article: https://arxiv.org/abs/0204016v1 Authors: arXiv ID: 0204016v1