Research Paper#Theoretical Computer Science, Kleene Algebra, Complexity Theory🔬 ResearchAnalyzed: Jan 3, 2026 19:25
PSPACE-Completeness of Relational Kleene Algebra with Graph Loop
Analysis
This paper establishes the PSPACE-completeness of the equational theory of relational Kleene algebra with graph loop, a significant result in theoretical computer science. It extends this result to include other operators like top, tests, converse, and nominals. The introduction of loop-automata and the reduction to the language inclusion problem for 2-way alternating string automata are key contributions. The paper also differentiates the complexity when using domain versus antidomain in Kleene algebra with tests (KAT), highlighting the nuanced nature of these algebraic systems.
Key Takeaways
- •The equational theory of relational Kleene algebra with graph loop is PSPACE-complete.
- •This PSPACE-completeness holds even with extensions like top, tests, converse, and nominals.
- •The paper introduces loop-automata and uses them to reduce the problem to the language inclusion problem for 2-way alternating string automata.
- •The complexity differs for KAT with domain (PSPACE-complete) versus KAT with antidomain (ExpTime-complete).
Reference
“The paper shows that the equational theory of relational Kleene algebra with graph loop is PSpace-complete.”