Proof of transitive closure property of directed acyclic graphs

Authors:
Fares Fraij;Steve Roach
Affiliations:
Al-Hussein Bin Talal University, Ma'an, Jordan;The University of Texas at El Paso, El Paso, TX
Venue:
Proceedings of the Eighth International Workshop on the ACL2 Theorem Prover and its Applications
Year:
2009

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Abstract

This paper presents a formal correctness proof for some properties of restricted finite directed acyclic graphs (DAGs). A restricted graph has a single root and arbitrary siblings. The siblings are assigned integers, string values, or restricted DAGs. Leafs must be assigned string values. The main property is the transitive closure. Our restricted graphs and the properties are formalized in ACL2, and an ACL2 book has been prepared for reuse.