A Small Model Theorem for Rectangular Hybrid Automata Networks

Johnson, Taylor T.; Mitra, Sayan

doi:10.1007/978-3-642-30793-5_2

Abstract:

Rectangular hybrid automata (RHA) are finite state machines with additional skewed clocks that are useful for modeling real-time systems. This paper is concerned with the uniform verification of safety properties of networks with arbitrarily many interacting RHAs. Each automaton is equipped with a finite collection of pointers to other automata that enables it to read their state. This paper presents a small model result for such networks that reduces the verification problem for a system with arbitrarily many processes to a system with finitely many processes. The result is applied to verify and discover counterexamples of inductive invariant properties for distributed protocols like Fischer's mutual exclusion algorithm and the Small Aircraft Transportation System (SATS). We have implemented a prototype tool called Passel relying on the satisfiability modulo theories (SMT) solver Z3 to check inductive invariants automatically.

Reference:

Taylor T. Johnson, Sayan Mitra, "A Small Model Theorem for Rectangular Hybrid Automata Networks", In Proceedings of the IFIP International Conference on Formal Techniques for Distributed Systems, Joint 14th Formal Methods for Open Object-Based Distributed Systems and 32nd Formal Techniques for Networked and Distributed Systems (FORTE/FMOODS 2012), Stockholm, Sweden, pp. , 2012, jun. (Best Paper Award for DisCoTec, Passel tool and specification source, Passel tool overview)

Bibtex Entry:

@inproceedings{johnson2012forte,
        author          =       {Taylor T. Johnson and Sayan Mitra},
        title           =       {A Small Model Theorem for Rectangular Hybrid Automata Networks},
        year            =       {2012},
        booktitle       =       {Proceedings of the IFIP International Conference on Formal Techniques for Distributed Systems, Joint 14th Formal Methods for Open Object-Based Distributed Systems and 32nd Formal Techniques for Networked and Distributed Systems (<a href="http://lucan.sics.se/discotec/?q=fmoodsforte">FORTE/FMOODS 2012</a>)},
    address     =   {Stockholm, Sweden},
        month           =       jun,
        pages           =       {},
        gsid        =   {4606381030313410526},
        abstract        =       {Rectangular hybrid automata (RHA) are finite state machines with additional skewed clocks that are useful for modeling real-time systems.  This paper is concerned with the uniform verification of safety properties of networks with arbitrarily many interacting RHAs.  Each automaton is equipped with a finite collection of pointers to other automata that enables it to read their state.  This paper presents a small model result for such networks that reduces the verification problem for a system with arbitrarily many processes to a system with finitely many processes.  The result is applied to verify and discover counterexamples of inductive invariant properties for distributed protocols like Fischer's mutual exclusion algorithm and the Small Aircraft Transportation System (SATS).  We have implemented a prototype tool called Passel relying on the satisfiability modulo theories (SMT) solver Z3 to check inductive invariants automatically.},
        doi     =   {10.1007/978-3-642-30793-5_2},
        comment     =   {<b>Best Paper Award for DisCoTec</b>, <a href="research/passel/">Passel tool and specification source</a>, <a href="http://publish.illinois.edu/passel-tool/">Passel tool overview</a>},
        pdf = {http://www.taylortjohnson.com/research/johnson2012forte.pdf},
        software = {http://publish.illinois.edu/passel-tool/},
}