Permutation rewriting and algorithmic verification

Proposes a natural subclass of regular languages, called alphabetic pattern constraints (APC), which is effectively closed under permutation rewriting, i.e. under iterative application of rules of the form ab/spl rarr/ba. It is well-known that regular languages do not have this closure property in general. Our result can be applied for example to regular model checking, for verifying properties of parametrized linear networks of regular processes and for modeling and verifying properties of asynchronous distributed systems. We also consider the complexity of testing membership in APC, and show that the question is complete for PSPACE when the input is an NFA (nondeterministic finite automaton) and complete for NLOGSPACE when it is a DFA (deterministic finite automaton). Moreover, we show that both the inclusion problem and the question of closure under permutation rewriting are PSPACE-complete when we restrict ourselves to the APC class.

[1]  Parosh Aziz Abdulla,et al.  On-the-Fly Analysis of Systems with Unbounded, Lossy FIFO Channels , 1998, CAV.

[2]  Marcus Nilsson,et al.  Regular Model Checking , 2000, CAV.

[3]  Amir Pnueli,et al.  Liveness and Acceleration in Parameterized Verification , 2000, CAV.

[4]  Anca Muscholl,et al.  Message Sequence Graphs and Decision Problems on Mazurkiewicz Traces , 1999, MFCS.

[5]  Marcus Nilsson,et al.  Transitive Closures of Regular Relations for Verifying Infinite-State Systems , 2000, TACAS.

[6]  Anca Muscholl,et al.  Deciding Properties for Message Sequence Charts , 1998, FoSSaCS.

[7]  Stephan Merz,et al.  Model Checking , 2000 .

[8]  Pierre Wolper,et al.  A partial approach to model checking , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

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

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

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

[12]  Laurent Fribourg,et al.  Reachability sets of parameterized rings as regular languages , 1997, INFINITY.

[13]  Pierre Wolper,et al.  A Partial Approach to Model Checking , 1994, Inf. Comput..

[14]  Amir Pnueli,et al.  Symbolic Model Checking with Rich ssertional Languages , 1997, CAV.

[15]  Anca Muscholl,et al.  Deciding Properties of Message Sequence Charts , 2003, Scenarios: Models, Transformations and Tools.

[16]  Doron A. Peled,et al.  All from One, One for All: on Model Checking Using Representatives , 1993, CAV.

[17]  Wolfgang Thomas,et al.  Classifying Regular Events in Symbolic Logic , 1982, J. Comput. Syst. Sci..

[18]  Anca Muscholl,et al.  Über die Erkennbarkeit unendlicher Spuren , 1994 .

[19]  Wojciech Zielonka,et al.  The Book of Traces , 1995 .

[20]  Amir Pnueli,et al.  Symbolic model checking with rich assertional languages , 2001, Theor. Comput. Sci..

[21]  Parosh Aziz Abdulla,et al.  Handling Global Conditions in Parameterized System Verification , 1999, CAV.

[22]  Pierre Wolper,et al.  An Algorithmic Approach for Checking Closure Properties of Temporal Logic Specifications and Omega-Regular Languages , 1998, Theor. Comput. Sci..

[23]  A. Mazurkiewicz.  Concurrent Program Schemes and their Interpretations , 1977 .

[24]  Antti Valmari,et al.  A stubborn attack on state explosion , 1990, Formal Methods Syst. Des..

[25]  Pierre Wolper,et al.  Verifying Systems with Infinite but Regular State Spaces , 1998, CAV.

[26]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[27]  Antti Valmari.  A stubborn attack on state explosion , 1992, Formal Methods Syst. Des..

[28]  A. Pnueli,et al.  Symbolic Model Checking withRich , 2022 .