Reachability Analysis of Pushdown Automata: Application to Model-Checking

We apply the symbolic analysis principle to pushdown systems. We represent (possibly infinite) sets of configurations of such systems by means of finite-state automata. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification (such as model-checking for branching-time logics), we consider the more general class of alternating pushdown systems and use alternating finite-state automata as a representation structure for sets of their configurations. We give a simple and natural procedure to compute sets of predecessors using this representation structure. We incorporate this procedure into the automata-theoretic approach to model-checking to define new model-checking algorithms for pushdown systems against both linear and branching-time properties. From these results we derive upper bounds for several model-checking problems as well as matching lower bounds.

[1]  Amir Pnueli,et al.  Symbolic Controller Synthesis for Discrete and Timed Systems , 1994, Hybrid Systems.

[2]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[3]  E. Allen Emerson,et al.  Automated Temporal Reasoning about Reactive Systems , 1996, Banff Higher Order Workshop.

[4]  Bernhard Steffen,et al.  Model Checking for Context-Free Processes , 1992, CONCUR.

[5]  A. Prasad Sistla,et al.  Automatic verification of finite state concurrent system using temporal logic specifications: a practical approach , 1983, POPL '83.

[6]  Friedrich Otto,et al.  String-Rewriting Systems , 1993, Text and Monographs in Computer Science.

[7]  J. Meigs,et al.  WHO Technical Report , 1954, The Yale Journal of Biology and Medicine.

[8]  Julian Bradfield.  Verifying Temporal Properties of Systems , 1992, Progress in Theoretical Computer Science.

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

[10]  E BryantRandal.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992 .

[11]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[12]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[13]  Moshe Y. Vardi.  A temporal fixpoint calculus , 1988, POPL '88.

[14]  Moshe Y. Vardi.  Alternating Automata and Program Verification , 1995, Computer Science Today.

[15]  Kenneth L. McMillan,et al.  Symbolic model checking: an approach to the state explosion problem , 1992 .

[16]  Igor Walukiewicz,et al.  Pushdown Processes: Games and Model-Checking , 1996, Inf. Comput..

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

[18]  Patrice Godefroid,et al.  Symbolic Verification of Communication Protocols with Infinite State Spaces Using QDDs (Extended Abstract) , 1996, CAV.

[19]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[20]  Patrice Godefroid,et al.  Symbolic Verification of Communication Protocols with Infinite State Spaces using QDDs , 1999, Formal Methods Syst. Des..

[21]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[22]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[23]  Bernhard Steffen,et al.  Composition, Decomposition and Model Checking of Pushdown Processes , 1995, Nord. J. Comput..