PSPACE-Completeness of Relational Kleene Algebra with Graph Loop

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.