A Saturation Method for Collapsible Pushdown Systems

We introduce a natural extension of collapsible pushdown systems called annotated pushdown systems that replaces collapse links with stack annotations. We believe this new model has many advantages. We present a saturation method for global backwards reachability analysis of these models that can also be used to analyse collapsible pushdown systems. Beginning with an automaton representing a set of configurations, we build an automaton accepting all configurations that can reach this set. We also improve upon previous saturation techniques for higher-order pushdown systems by significantly reducing the size of the automaton constructed and simplifying the algorithm and proofs.

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

[2]  C.-H. Luke Ong,et al.  Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems , 2008, Log. Methods Comput. Sci..

[3]  Robin Milner,et al.  Theories for the Global Ubiquitous Computer , 2004, FoSSaCS.

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

[5]  C.-H. Luke Ong,et al.  Verifying higher-order functional programs with pattern-matching algebraic data types , 2011, POPL '11.

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

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

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

[9]  Andreas Podelski,et al.  ACSAR: Software Model Checking with Transfinite Refinement , 2007, SPIN.

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

[11]  Javier Esparza,et al.  Efficient Algorithms for Model Checking Pushdown Systems , 2000, CAV.

[12]  Mohamed Faouzi Atig,et al.  Global Model Checking of Ordered Multi-Pushdown Systems , 2010, FSTTCS.

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

[14]  Arnaud Carayol,et al.  Regular Sets of Higher-Order Pushdown Stacks , 2005, MFCS.

[15]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

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

[17]  Sriram K. Rajamani,et al.  The SLAM project: debugging system software via static analysis , 2002, POPL '02.

[18]  Jaikumar Radhakrishnan,et al.  FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science , 2004, Lecture Notes in Computer Science.

[19]  C.-H. Luke Ong,et al.  Analysing Mu-Calculus Properties of Pushdown Systems , 2010, SPIN.

[20]  Antoine Meyer,et al.  Symbolic Reachability Analysis of Higher-Order Context-Free Processes , 2004, FSTTCS.

[21]  Javier Esparza,et al.  Symbolic Context-Bounded Analysis of Multithreaded Java Programs , 2008, SPIN.

[22]  C.-H. Luke Ong,et al.  Recursion Schemes and Logical Reflection , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

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

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

[25]  Arnaud Carayol,et al.  The Caucal Hierarchy of Infinite Graphs in Terms of Logic and Higher-Order Pushdown Automata , 2003, FSTTCS.

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

[27]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[28]  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).

[29]  Mohamed Nassim Seghir,et al.  A Lightweight Approach for Loop Summarization , 2011, ATVA.

[30]  Pawel Parys.  Collapse Operation Increases Expressive Power of Deterministic Higher Order Pushdown Automata , 2011, STACS.

[31]  Kousha Etessami,et al.  Verifying Probabilistic Procedural Programs , 2004, FSTTCS.

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

[33]  C.-H. Luke Ong,et al.  A saturation method for the modal μ-calculus over pushdown systems , 2011, Inf. Comput..

[34]  Michel Rigo,et al.  Abstract numeration systems and tilings , 2005 .

[35]  Anil Seth,et al.  An Alternative Construction in Symbolic Reachability Analysis of Second Order Pushdown Systems , 2008, Int. J. Found. Comput. Sci..

[36]  Thierry Cachat,et al.  Games on pushdown graphs and extensions , 2003 .

[37]  Javier Esparza,et al.  Efficient Algorithms for Alternating Pushdown Systems with an Application to the Computation of Certificate Chains , 2006, ATVA.

[38]  Somesh Jha,et al.  Weighted pushdown systems and their application to interprocedural dataflow analysis , 2003, Sci. Comput. Program..

[39]  Werner Damm,et al.  The IO- and OI-Hierarchies , 1982, Theor. Comput. Sci..