Model Checking Languages of Data Words

We consider the model-checking problem for data multi-pushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent programs with dynamic process creation. To specify properties of data words, we use monadic second-order (MSO) logic, which comes with a predicate to test two word positions for data equality. While satisfiability for MSO logic is undecidable (even for weaker fragments such as first-order logic), our main result states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.

[1]  Manindra Agrawal,et al.  FST TCS 2002: Foundations of Software Technology and Theoretical Computer Science , 2002, Lecture Notes in Computer Science.

[2]  Bruno Courcelle,et al.  Graph Rewriting: An Algebraic and Logic Approach , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[3]  Parosh Aziz Abdulla,et al.  Forcing Monotonicity in Parameterized Verification: From Multisets to Words , 2009, SOFSEM.

[4]  Thomas Schwentick,et al.  Two-variable logic on data words , 2011, TOCL.

[5]  Benedikt Bollig,et al.  Realizability of Dynamic MSC Languages , 2010, CSR.

[6]  Parosh Aziz Abdulla,et al.  Advanced Ramsey-Based Büchi Automata Inclusion Testing , 2011, CONCUR.

[7]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[8]  Stéphane Demri,et al.  Model Checking Freeze LTL over One-Counter Automata , 2008, FoSSaCS.

[9]  LazićRanko,et al.  LTL with the freeze quantifier and register automata , 2009 .

[10]  Claire David,et al.  On the Satisfiability of Two-Variable Logic over Data Words , 2010, LPAR.

[11]  Michael Kaminski,et al.  Context-free languages over infinite alphabets , 1998, Acta Informatica.

[12]  Stéphane Demri,et al.  LTL with the Freeze Quantifier and Register Automata , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[13]  Juhani Karhumäki,et al.  Computer Science - Theory and Applications , 2014, Lecture Notes in Computer Science.

[14]  Nissim Francez,et al.  Finite-Memory Automata , 1994, Theor. Comput. Sci..

[15]  Supratik Mukhopadhyay,et al.  Dynamic Message Sequence Charts , 2002, FSTTCS.

[16]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[17]  Orna Grumberg,et al.  Variable Automata over Infinite Alphabets , 2010, LATA.

[18]  Stéphane Demri,et al.  When Model-Checking Freeze LTL over Counter Machines Becomes Decidable , 2010, FoSSaCS.

[19]  Benedikt Bollig.  An Automaton over Data Words That Captures EMSO Logic , 2011, CONCUR.

[20]  Nikos Tzevelekos.  Fresh-register automata , 2011, POPL '11.

[21]  Wojciech Rytter,et al.  On the Maximal Number of Cubic Runs in a String , 2010, LATA.

[22]  Michael Kaminski,et al.  Finite-Memory Automata with Non-Deterministic Reassignment , 2010, Int. J. Found. Comput. Sci..

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

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

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

[26]  Bernhard Rumpe,et al.  SOFSEM 2010: Theory and Practice of Computer Science, 36th Conference on Current Trends in Theory and Practice of Computer Science, Spindleruv Mlýn, Czech Republic, January 23-29, 2010. Proceedings , 2010, SOFSEM.

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

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

[29]  Thomas Schwentick,et al.  Two-variable logic and key constraints on data words , 2011, ICDT '11.