Ramsey-Based Inclusion Checking for Dense-Stack Visibly Pushdown Automata

Visibly pushdown automata are popular as they are closed under Boolean operations and determinization. There exist multiple notions of timed pushdown systems like recursive timed automata, densetime pushdown automata. We explore a generalization of visibly pushdown automata over infinite words with parity acceptance condition –in which stack elements have real valued time stamps–named dense-stack visibly pushdown automata. We prove its closure under union and intersection and show that inclusion checking for this class is decidable using Ramsey-based techniques.