On properties of languages accepted by deterministic pushdown automata with translucent input letters

We study deterministic pushdown automata operating with translucent input letters. These devices can be obtained by equipping classical deterministic pushdown automata with a translucency function which, depending on the current state, establishes the set of invisible input symbols: such invisible symbols are skipped in the current move and dealt with in subsequent sweeps, while the first visible symbol from the current input head position rightward is processed and consumed. Deterministic pushdown automata with translucent input letters can be returning, meaning that a new input sweep starts from the leftmost input symbol left on the tape immediately after processing a visible symbol, or non-returning. We show some incomparability results between the acceptance capabilities of returning and non-returning deterministic pushdown automata with translucent input letters and those of non-returning deterministic and nondeterministic finite state automata with translucent input letters. Then, we prove the non-closure of the families of languages accepted by returning and non-returning deterministic pushdown automata with translucent input letters under: concatenation, Kleene star, length-preserving and inverse homomorphism, reversal, and intersection with regular languages. In particular, arguments used to prove the non-closure under intersection with regular languages enable us to answer a question left open in the literature, on the recognition power of non-returning deterministic finite state automata with translucent input letters.