Parameterized Verification of Infinite-State Processes with Global Conditions

We present a simple and effective approximated backward reachability algorithm for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes may communicate via broadcast, rendez-vous and shared variables. We apply the algorithm to verify mutual exclusion for complex protocols such as Lamport's bakery algorithm both with and without atomicity conditions, a distributed version of the bakery algorithm, and Ricart-Agrawala's distributed mutual exclusion algorithm.

[1]  Amir Pnueli,et al.  Parameterized Verification with Automatically Computed Inductive Assertions , 2001, CAV.

[2]  Helmut Veith,et al.  Environment Abstraction for Parameterized Verification , 2006, VMCAI.

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

[4]  A. Prasad Sistla,et al.  Reasoning about systems with many processes , 1992, JACM.

[5]  Ashok K. Agrawala,et al.  An optimal algorithm for mutual exclusion in computer networks , 1981, CACM.

[6]  Gul Agha,et al.  Concurrent Object-Oriented Programming and Petri Nets , 2001, Lecture Notes in Computer Science.

[7]  Parosh Aziz Abdulla,et al.  Regular Model Checking Without Transducers (On Efficient Verification of Parameterized Systems) , 2007, TACAS.

[8]  Alan Bundy,et al.  Logic Program Synthesis via Proof Planning , 1992, LOPSTR.

[9]  Parosh Aziz Abdulla,et al.  Regular Model Checking without Transducers , 2007 .

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

[11]  Shuvendu K. Lahiri,et al.  Indexed Predicate Discovery for Unbounded System Verification , 2004, CAV.

[12]  Kousha Etessami,et al.  A Hierarchy of Polynomial-Time Computable Simulations for Automata , 2002, CONCUR.

[13]  Kousha Etessami,et al.  Analysis of Recursive Game Graphs Using Data Flow Equations , 2004, VMCAI.

[14]  Peter Z. Revesz,et al.  A Closed-Form Evaluation for Datalog Queries with Integer (Gap)-Order Constraints , 1993, Theor. Comput. Sci..

[15]  Ahmed Rezine,et al.  Parameterized Systems: Generalizing and Simplifying Automatic Verification , 2008 .

[16]  Giorgio Delzanno,et al.  Beyond Parameterized Verification , 2002, TACAS.

[17]  Alain Finkel,et al.  On the verification of broadcast protocols , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[18]  Parosh Aziz Abdulla,et al.  Algorithmic Analysis of Programs with Well Quasi-ordered Domains , 2000, Inf. Comput..

[19]  P. Abdulla,et al.  On the Coverability Problem for Constrained Multiset Rewriting , 2008 .

[20]  Parosh Aziz Abdulla,et al.  Regular Model Checking Made Simple and Efficient , 2002, CONCUR.

[21]  Gregory R. Andrews,et al.  Foundations of Multithreaded, Parallel, and Distributed Programming , 1999 .

[22]  Kedar S. Namjoshi,et al.  On model checking for non-deterministic infinite-state systems , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

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

[24]  Parosh Aziz Abdulla,et al.  Approximated parameterized verification of infinite-state processes with global conditions , 2009, Formal Methods Syst. Des..

[25]  Richard Gerber,et al.  Model-checking concurrent systems with unbounded integer variables: symbolic representations, approximations, and experimental results , 1999, TOPL.

[26]  Giorgio Delzanno Automatic Verification of Parameterized Cache Coherence Protocols , 2000, CAV.

[27]  Mordechai Ben-Ari,et al.  Formal Verification of the Ricart-Agrawala Algorithm , 2000, FSTTCS.

[28]  Pierre Wolper,et al.  Iterating transducers in the large , 2003 .

[29]  Laurent Fribourg,et al.  Symbolic Verification with Gap-Order Constraints , 1996, LOPSTR.

[30]  G. S. Graham A New Solution of Dijkstra ' s Concurrent Programming Problem , 2022 .