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Published in:
2012 | OriginalPaper | Chapter
Weakly-Synchronized Ground Tree Rewriting
(with Applications to Verifying Multithreaded Programs)
Author : Anthony Widjaja Lin
Published in: Mathematical Foundations of Computer Science 2012
Publisher: Springer Berlin Heidelberg
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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.