Constrained Dynamic Tree Networks

We generalise Constrained Dynamic Pushdown Networks, introduced by Bouajjani et al., to Constrained Dynamic Tree Networks. In this model, we have trees of processes which may monitor their children. We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable. We address the problem of symbolic reachability analysis for this model. More precisely, we consider the problem of computing an effective representation of their reachability sets using finite state automata. We show that backwards reachability sets starting from regular sets of configurations are always regular. We provide an algorithm for computing backwards reachability sets using tree automata.

[1]  Markus Müller-Olm,et al.  Iterable Forward Reachability Analysis of Monitor-DPNs , 2013, Festschrift for Dave Schmidt.

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

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

[4]  Vincent Penelle Rewriting Higher-Order Stack Trees , 2015, CSR.

[5]  Gennaro Parlato,et al.  The tree width of auxiliary storage , 2011, POPL '11.

[6]  Markus Müller-Olm,et al.  Predecessor Sets of Dynamic Pushdown Networks with Tree-Regular Constraints , 2009, CAV.

[7]  Pawel Parys,et al.  The Complexity of the Diagonal Problem for Recursion Schemes , 2017, FSTTCS.

[8]  C.-H. Luke Ong,et al.  Winning Regions of Pushdown Parity Games: A Saturation Method , 2009, CONCUR.

[9]  Stefan Schwoon,et al.  Model checking pushdown systems , 2002 .

[10]  Tayssir Touili,et al.  Verifying parallel programs with dynamic communication structures , 2009, Theor. Comput. Sci..

[11]  Anil Seth Games on Higher Order Multi-stack Pushdown Systems , 2009, RP.

[12]  Javier Esparza,et al.  jMoped: A Test Environment for Java Programs , 2007, CAV.

[13]  C.-H. Luke Ong,et al.  A type-directed abstraction refinement approach to higher-order model checking , 2014, POPL.

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

[15]  Tayssir Touili,et al.  Regular Symbolic Analysis of Dynamic Networks of Pushdown Systems , 2005, CONCUR.

[16]  Philippe Schnoebelen,et al.  The regular viewpoint on PA-processes , 1998, Theor. Comput. Sci..

[17]  Anca Muscholl,et al.  Safety of Parametrized Asynchronous Shared-Memory Systems is Almost Always Decidable , 2015, CONCUR.

[18]  Naoki Kobayashi,et al.  Verification of Higher-Order Concurrent Programs with Dynamic Resource Creation , 2016, APLAS.

[19]  C.-H. Luke Ong,et al.  A traversal-based algorithm for higher-order model checking , 2012, ICFP '12.

[20]  V. Cody Infinite Graphs Generated by Tree Rewriting , 2003 .

[21]  Denis Lugiez Forward Analysis of Dynamic Network of Pushdown Systems is Easier without Order , 2011, Int. J. Found. Comput. Sci..

[22]  Walter S. Brainerd,et al.  Tree Generating Regular Systems , 1969, Inf. Control..

[23]  Naoki Kobayashi A Practical Linear Time Algorithm for Trivial Automata Model Checking of Higher-Order Recursion Schemes , 2011, FoSSaCS.

[24]  Atsushi Igarashi,et al.  Model-Checking Higher-Order Programs with Recursive Types , 2013, ESOP.

[25]  Helmut Seidl,et al.  Contextual Locking for Dynamic Pushdown Networks , 2013, SAS.

[26]  Naoki Kobayashi Model-checking higher-order functions , 2009, PPDP '09.

[27]  Lorenzo Clemente,et al.  The Diagonal Problem for Higher-Order Recursion Schemes is Decidable* , 2016, 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[28]  Helmut Seidl,et al.  Join-Lock-Sensitive Forward Reachability Analysis for Concurrent Programs with Dynamic Process Creation , 2011, VMCAI.

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

[30]  Georg Zetzsche,et al.  An approach to computing downward closures , 2015, ICALP.

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

[32]  Tayssir Touili,et al.  Model checking dynamic pushdown networks , 2014, Formal Aspects of Computing.

[33]  Anca Muscholl,et al.  Reachability for Dynamic Parametric Processes , 2017, VMCAI.

[34]  Kazutaka Matsuda,et al.  Pairwise Reachability Analysis for Higher Order Concurrent Programs by Higher-Order Model Checking , 2014, CONCUR.

[35]  Lorenzo Clemente,et al.  Ordered Tree-Pushdown Systems , 2015, FSTTCS.

[36]  C.-H. Luke Ong,et al.  On Model-Checking Trees Generated by Higher-Order Recursion Schemes , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[37]  Mahesh Viswanathan,et al.  Decidability Results for Well-Structured Transition Systems with Auxiliary Storage , 2007, CONCUR.

[38]  Tayssir Touili,et al.  Verifying Parallel Programs with Dynamic Communication Structures , 2009, CIAA.

[39]  C.-H. Luke Ong,et al.  Unboundedness and downward closures of higher-order pushdown automata , 2015, POPL.

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

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

[42]  Jakob Rehof,et al.  Context-Bounded Model Checking of Concurrent Software , 2005, TACAS.

[43]  Naoki Kobayashi Higher-Order Model Checking: From Theory to Practice , 2011, 2011 IEEE 26th Annual Symposium on Logic in Computer Science.