On Pure Multi-Pushdown Automata that Perform Complete-Pushdown Pops

This paper introduces and discusses pure multi-pushdown automata that remove symbols from their pushdowns only by performing complete-pushdown pops. During this operation, the entire pushdown is compared with a prefix of the input, and if they match, the pushdown is completely emptied and the input is advanced by the prefix. The paper proves that these automata define an infinite hierarchy of language families identical with the infinite hierarchy of language families resulting from right linear simple matrix grammars. If these automata are allowed to join their pushdowns and create new pushdowns, then they define another infinite hierarchy of language families according to the number of pushdowns.