Weakly-Synchronized Ground Tree Rewriting

(with Applications to Verifying Multithreaded Programs)
  • Anthony Widjaja Lin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


Ground tree rewrite systems (GTRS) are a well-known treeextension of prefix-rewrite systems on words (a.k.a. pushdown systems), where subtrees (instead of word prefixes) are rewritten. GTRS can model programs with unbounded recursion depth and thread-spawning, wherein the threads have a tree-shaped dependency graph. We consider the extension of GTRS with a finite (global) control unit for synchronizing among the active threads, a.k.a. state-extended GTRS (sGTRS). Since sGTRS is Turing-complete, we restrict the finite control unit to dags possibly with self-loops, a.k.a. weakly-synchronized GTRS (wGTRS). wGTRS can be regarded as a generalization of context-bounded analysis of multipushdown systems with dynamic thread spawning. We show that reachability, repeated reachability, and the complement of model checking deterministic LTL over weakly-synchronized GTRS (wGTRS) are NP-complete by a polynomial reduction to checking existential Presburger formulas, for which highly optimized solvers are available.


Model Check Transition System Production Rule Full Version Tree Automaton 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anthony Widjaja Lin
    • 1
  1. 1.Department of Computer ScienceOxford UniversityUK

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