A Modal Perspective on Path Constraints

Several classes of path constraints for semistructured data are analysed and a number of decidability and complexity results proved for such constraints. While some of these decidability results were known before, it is believed that the improved complexity bounds are new. Proofs are based on techniques from modal logic and automata theory. This modal logic perspective sheds additional light on the reasons for previously known decidability and complexity results.

[1]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[2]  Steven J. DeRose,et al.  XML Path Language (XPath) , 1999 .

[3]  Peter Øhrstrøm,et al.  Temporal Logic , 1994, Lecture Notes in Computer Science.

[4]  Wenfei Fan,et al.  Path constraints on semistructured and structured data , 1998, PODS '98.

[5]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[6]  Alasdair Urquhart,et al.  Temporal Logic , 1971 .

[7]  Maarten de Rijke,et al.  Path Constraints from a Modal Logic Point of View , 2001, KRDB.

[8]  Joseph Y. Halpern.  The Effect of Bounding the Number of Primitive Propositions and the Depth of Nesting on the Complexity of Modal Logic , 1995, Artif. Intell..

[9]  Valentin Goranko,et al.  Hierarchies of modal and temporal logics with reference pointers , 1996, J. Log. Lang. Inf..

[10]  T. G. Szymanski,et al.  On the Equivalence, Containment, and Covering Problems for the Regular and Context-Free Languages , 1976, J. Comput. Syst. Sci..

[11]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[12]  Rance Cleaveland,et al.  A linear-time model-checking algorithm for the alternation-free modal mu-calculus , 1993, Formal Methods Syst. Des..

[13]  Patrick Blackburn,et al.  Hybrid languages , 1995, J. Log. Lang. Inf..

[14]  José L. Balcázar,et al.  Structural Complexity I , 1988, EATCS Monographs on Theoretical Computer Science Series.

[15]  Dan Suciu,et al.  A query language and optimization techniques for unstructured data , 1996, SIGMOD '96.

[16]  Luca de Alfaro,et al.  Model Checking the World Wide Web , 2001, CAV.

[17]  Edith Hemaspaandra,et al.  The Price of Universality , 1996, Notre Dame J. Formal Log..

[18]  Wenfei Fan,et al.  Path Constraints on Deterministic Graphs , 1998 .

[19]  Elliotte Rusty Harold,et al.  XML in a Nutshell , 2001 .

[20]  Moshe Y. Vardi,et al.  The Hybrid mu-Calculus , 2001 .

[21]  Alberto O. Mendelzon,et al.  Finding Regular Simple Paths in Graph Databases , 1989, SIAM J. Comput..

[22]  I-Peng Lin,et al.  The Complexity of Propositional Modal Theories and the Complexity of Consistency of Propositional Modal Theories , 1994, LFCS.

[23]  Pierre Wolper,et al.  Automata theoretic techniques for modal logics of programs: (Extended abstract) , 1984, STOC '84.

[24]  Vaughan R. Pratt,et al.  Models of program logics , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[25]  Alberto O. Mendelzon,et al.  Querying the World Wide Web , 1996, Fourth International Conference on Parallel and Distributed Information Systems.

[26]  Edith Hemaspaandra.  The Complexity of Poor Man's Logic , 2001, J. Log. Comput..

[27]  William C. Rounds,et al.  Feature Logics , 1997, Handbook of Logic and Language.

[28]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[29]  Serge Abiteboul,et al.  Regular path queries with constraints , 1997, J. Comput. Syst. Sci..

[30]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[31]  李幼升,et al.  Ph , 1989 .

[32]  Georg Gottlob,et al.  Monadic queries over tree-structured data , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[33]  J W Ballard,et al.  Data on the web? , 1995, Science.

[34]  Diego Calvanese,et al.  View-Based Query Answering and Query Containment over Semistructured Data , 2001, DBPL.

[35]  Patrick Hayes,et al.  Rdf Model Theory W3c Working Draft @@@@@ Status of This Document , 2001 .

[36]  Jennifer Widom,et al.  The Lorel query language for semistructured data , 1997, International Journal on Digital Libraries.

[37]  Bruno Courcelle,et al.  The Expression of Graph Properties and Graph Transformations in Monadic Second-Order Logic , 1997, Handbook of Graph Grammars.

[38]  Mordechai Ben-Ari,et al.  Deterministic Propositional Dynamic Logic: Finite Models, Complexity, and Completeness , 1982, J. Comput. Syst. Sci..

[39]  Francesco M. Donini,et al.  Reasoning in description logics , 1997 .

[40]  Dan Suciu,et al.  Containment and equivalence for an XPath fragment , 2002, PODS.

[41]  Luca Cardelli,et al.  A Spatial Logic for Querying Graphs , 2002, ICALP.

[42]  Rohit Parikh.  Propositional logics of programs: systems, models, and complexity , 1980, POPL '80.

[43]  Rance Cleaveland,et al.  A linear-time model-checking algorithm for the alternation-free modal mu-calculus , 1993, Formal Methods Syst. Des..

[44]  Johan van Benthem,et al.  Modal Languages and Bounded Fragments of Predicate Logic , 1998, J. Philos. Log..

[45]  H. James Hoover,et al.  Limits to Parallel Computation: P-Completeness Theory , 1995 .

[46]  George Gargov,et al.  Determinism and Looping in Combinatory PDL , 1988, Theor. Comput. Sci..

[47]  Maarten Marx,et al.  A Road-Map on Complexity for Hybrid Logics , 1999, CSL.