Emptiness of Multi-pushdown Automata Is 2ETIME-Complete

We consider multi-pushdown automata, a multi-stack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first non-empty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptiness problem for multi-pushdown automata is 2ETIME-complete wrt. the number of stacks. Containment in 2ETIME is shown by translating an automaton into a grammar for which we can check if the generated language is empty. The lower bound is established by simulating the behavior of an alternating Turing machine working in exponential space. We also compare multi-pushdown automata with the model of bounded-phase multi-stack (visibly) pushdown automata.

[1]  Salvatore La Torre,et al.  A Robust Class of Context-Sensitive Languages , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[2]  Salvatore La Torre,et al.  An Infinite Automaton Characterization of Double Exponential Time , 2008, CSL.

[3]  Aniello Murano,et al.  2-Visibly Pushdown Automata , 2007, Developments in Language Theory.

[4]  Joost Engelfriet,et al.  Iterated Stack Automata and Complexity Classes , 1991, Inf. Comput..

[5]  Javier Esparza,et al.  Reachability Analysis of Pushdown Automata: Application to Model-Checking , 1997, CONCUR.

[6]  Salvatore La Torre,et al.  Context-Bounded Analysis of Concurrent Queue Systems , 2008, TACAS.

[7]  Luca Breveglieri,et al.  Multi-Push-Down Languages and Grammars , 1996, Int. J. Found. Comput. Sci..

[8]  Antoni Mazurkiewicz,et al.  CONCUR '97: Concurrency Theory , 1997, Lecture Notes in Computer Science.

[9]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.