Program Complexity of Dynamic LTL Model Checking

Using a recent result by Hesse we show that for any fixed linear-time temporal formula the dynamic model checking problem is in Dyn-TC0, a complexity class introduced by Hesse, Immerman, Patnaik, containing all dynamic problems where the update after an operation has been performed can be computed by a DLOGTIME-uniform constant-depth threshold circuit. The operations permitted to modify the transition system to be verified include insertion and deletion of transitions and relabeling of states.

[1]  Robert K. Brayton,et al.  Incremental Methods for Formal Verification and Logic Synthesis , 1996 .

[2]  Scott A. Smolka,et al.  Incremental Model Checking in the Modal Mu-Calculus , 1994, CAV.

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

[4]  Robert K. Brayton,et al.  Incremental methods for FSM traversal , 1995, Proceedings of ICCD '95 International Conference on Computer Design. VLSI in Computers and Processors.

[5]  Jianwen Su,et al.  Incremental and Decremental Evaluation of Transitive Closure by First-Order Queries , 1995, Inf. Comput..

[6]  Kousha Etessami,et al.  Dynamic tree isomorphism via first-order updates to a relational database , 1998, PODS '98.

[7]  Neil Immerman,et al.  Complete problems for dynamic complexity classes , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[8]  Limsoon Wong,et al.  Incremental Recomputation of Recursive Queries with Nested Sets and Aggregate Functions , 1997, DBPL.

[9]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[10]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[11]  Neil Immerman,et al.  Dyn-FO: A Parallel, Dynamic Complexity Class , 1997, J. Comput. Syst. Sci..

[12]  Neil Immerman,et al.  On Uniformity within NC¹ , 1990, J. Comput. Syst. Sci..

[13]  William Hesse.  Division Is in Uniform TC0 , 2001, ICALP.

[14]  Kousha Etessami,et al.  Counting quantifiers, successor relations, and logarithmic space , 1995, Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference.

[15]  Thomas W. Reps,et al.  On the Computational Complexity of Dynamic Graph Problems , 1996, Theor. Comput. Sci..