On-The-Fly Static Analysis via Dynamic Bidirected Dyck Reachability.
CoRR(2023)
摘要
Dyck reachability is a principled, graph-based formulation of a plethora of
static analyses. Bidirected graphs are used for capturing dataflow through
mutable heap data, and are usual formalisms of demand-driven points-to and
alias analyses. The best (offline) algorithm runs in $O(m+n\cdot \alpha(n))$
time, where $n$ is the number of nodes and $m$ is the number of edges in the
flow graph, which becomes $O(n^2)$ in the worst case.
In the everyday practice of program analysis, the analyzed code is subject to
continuous change, with source code being added and removed. On-the-fly static
analysis under such continuous updates gives rise to dynamic Dyck reachability,
where reachability queries run on a dynamically changing graph, following
program updates. Naturally, executing the offline algorithm in this online
setting is inadequate, as the time required to process a single update is
prohibitively large.
In this work we develop a novel dynamic algorithm for bidirected Dyck
reachability that has $O(n\cdot \alpha(n))$ worst-case performance per update,
thus beating the $O(n^2)$ bound, and is also optimal in certain settings. We
also implement our algorithm and evaluate its performance on on-the-fly
data-dependence and alias analyses, and compare it with two best known
alternatives, namely (i) the optimal offline algorithm, and (ii) a fully
dynamic Datalog solver. Our experiments show that our dynamic algorithm is
consistently, and by far, the top performing algorithm, exhibiting speedups in
the order of 1000X. The running time of each update is almost always
unnoticeable to the human eye, making it ideal for the on-the-fly analysis
setting.
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关键词
CFL reachability,dynamic algorithms,static analysis
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