Synchronizing Automata over Nested Words

Abstract. We extend the concept of a synchronizing word from finitestate automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i.e., takes the NWA from all control states to a single control state. We show that although the shortest synchronizing word for an NWA, if it exists, can be (at most) exponential in the size of the NWA, the existence of such a word can still be decided in polynomial time. As our main contribution, we show that deciding the existence of a short synchronizing word (of at most given length) becomes PSPACE-complete (as opposed to NP-complete for DFA). The upper bound makes a connection to pebble games and Strahler numbers, and the lower bound goes via cost-optimal synchronizing words for DFA, an intermediate problem that we also show PSPACE-complete.

• Type: Journal
• Year: 2016
• Where: FOSSACS
• Authors: Dmitry Chistikov, Pavel Martyugin, Mahsa Shirmohammadi
• Keywords: FOSSACS 2016, Software Engineering