Ordered Tree-Pushdown Systems

We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a decidable reachability problem. This follows from a preservation of recognizability result for the backward reachability relation of such systems. As an application, we show that our simple model can encode several formalisms generalizing pushdown systems, such as ordered multi-pushdown systems, annotated higher-order pushdown systems, the Krivine machine, and ordered annotated multi-pushdown systems. In each case, our procedure yields tight complexity.

[1]  Matthew Hague,et al.  Saturation of Concurrent Collapsible Pushdown Systems , 2013, FSTTCS.

[2]  Naoki Kobayashi,et al.  Saturation-Based Model Checking of Higher-Order Recursion Schemes , 2013, CSL.

[3]  Pierre Wolper,et al.  A direct symbolic approach to model checking pushdown systems , 1997, INFINITY.

[4]  Arnaud Carayol,et al.  Saturation algorithms for model-checking pushdown systems , 2014, AFL.

[5]  Benedikt Bollig,et al.  Emptiness of Multi-pushdown Automata Is 2ETIME-Complete , 2008, Developments in Language Theory.

[6]  Andrzej S. Murawski,et al.  Collapsible Pushdown Automata and Recursion Schemes , 2008, 2008 23rd Annual IEEE Symposium on Logic in Computer Science.

[7]  Igor Walukiewicz,et al.  Unsafe Grammars and Panic Automata , 2005, ICALP.

[8]  C.-H. Luke Ong,et al.  A Saturation Method for the Modal Mu-Calculus with Backwards Modalities over Pushdown Systems , 2010, ArXiv.

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

[10]  Pawel Parys,et al.  Strictness of the Collapsible Pushdown Hierarchy , 2012, MFCS.

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

[12]  Irène Guessarian,et al.  Pushdown tree automata , 1983, Mathematical systems theory.

[13]  C.-H. Luke Ong,et al.  The Safe Lambda Calculus , 2007, TLCA.

[14]  Olivier Serre,et al.  C-SHORe: a collapsible approach to higher-order verification , 2013, ICFP.

[15]  Igor Walukiewicz,et al.  Simply typed fixpoint calculus and collapsible pushdown automata , 2016, Math. Struct. Comput. Sci..

[16]  Jean-Louis Krivine,et al.  A call-by-name lambda-calculus machine , 2007, High. Order Symb. Comput..

[17]  Igor Walukiewicz,et al.  Krivine machines and higher-order schemes , 2011, Inf. Comput..

[18]  Klaus Aehlig.  A Finite Semantics of Simply-Typed Lambda Terms for Infinite Runs of Automata , 2007, Log. Methods Comput. Sci..

[19]  Mohamed Faouzi Atig,et al.  Model-Checking of Ordered Multi-Pushdown Automata , 2012, Log. Methods Comput. Sci..

[20]  Olivier Serre,et al.  A Saturation Method for Collapsible Pushdown Systems , 2012, ICALP.

[21]  Anil Seth.  Global Reachability in Bounded Phase Multi-stack Pushdown Systems , 2010, CAV.

[22]  Pawel Urzyczyn,et al.  Higher-Order Pushdown Trees Are Easy , 2002, FoSSaCS.

[23]  C. Aiswarya,et al.  MSO Decidability of Multi-Pushdown Systems via Split-Width , 2012, CONCUR.

[24]  Javier Esparza,et al.  A BDD-Based Model Checker for Recursive Programs , 2001, CAV.