Visibly Pushdown Games

The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is given by a visibly pushdown language. We establish that, unlike pushdown games with pushdown winning conditions, visibly pushdown games are decidable and are 2Exptime-complete. We also show that pushdown games against Ltl specifications and Caret specifications are 3Exptime-complete. Finally, we establish the topological complexity of visibly pushdown languages by showing that they are a subclass of Boolean combinations of Σ3 sets. This leads to an alternative proof that visibly pushdown automata are not determinizable and also shows that visibly pushdown games are determined.

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

[2]  I. Walukiewicz.  A landscape with games in the background , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[3]  Amir Pnueli,et al.  On the synthesis of a reactive module , 1989, POPL '89.

[4]  Igor Walukiewicz,et al.  Pushdown Games with Unboundedness and Regular Conditions , 2003, FSTTCS.

[5]  Rajeev Alur,et al.  Visibly pushdown languages , 2004, STOC '04.

[6]  W. Browder,et al.  Annals of Mathematics , 1889 .

[7]  Olivier Serre,et al.  Games with winning conditions of high Borel complexity , 2006, Theor. Comput. Sci..

[8]  Wieslaw Zielonka,et al.  Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees , 1998, Theor. Comput. Sci..

[9]  Wolfgang Thomas,et al.  Languages, Automata, and Logic , 1997, Handbook of Formal Languages.

[10]  Thomas W. Reps,et al.  Precise interprocedural dataflow analysis via graph reachability , 1995, POPL '95.

[11]  A. Prasad Sistla,et al.  On Model-Checking for Fragments of µ-Calculus , 1993, CAV.

[12]  Igor Walukiewicz,et al.  Pushdown Processes: Games and Model-Checking , 1996, Inf. Comput..

[13]  Wolfgang Thomas,et al.  A Short Introduction to Infinite Automata , 2001, Developments in Language Theory.

[14]  Wolfgang Thomas,et al.  Solving Pushdown Games with a Sigma3 Winning Condition , 2002, CSL.

[15]  Sriram K. Rajamani,et al.  Bebop: A Symbolic Model Checker for Boolean Programs , 2000, SPIN.