Strengthened Results on Nonregular PDL

We continue the ongoing investigation of decidability and undecidability of nonregular extensions of propositional dynamic logic (PDL), by proving two results. The first strengthens the undecidability result of Harel and Singerman regarding one-letter Fibonacci-like extensions, by showing undecidability for a more general class of exponentially growing sequences. The second strengthens the decidability result of Harel and Raz for languages accepted by simple-minded pushdown automata, by showing that the important thing for decidability is that the stack behavior depends only on the input symbol.