
Conditional Lower Bound for InclusionBased Pointsto Analysis
Inclusionbased (i.e., Andersenstyle) pointsto analysis is a fundament...
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The FineGrained and Parallel Complexity of Andersen's Pointer Analysis
Pointer analysis is one of the fundamental problems in static program an...
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Subcubic Certificates for CFL Reachability
Many problems in interprocedural program analysis can be modeled as the ...
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FlowCFL: A Framework for Typebased Reachability Analysis in the Presence of Mutable Data
Reachability analysis is a fundamental program analysis with a wide vari...
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The FineGrained Complexity of Andersen's Pointer Analysis
Pointer analysis is one of the fundamental problems in static program an...
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Optimal Bound on the Combinatorial Complexity of Approximating Polytopes
Convex bodies play a fundamental role in geometric computation, and appr...
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Approximate Voronoi cells for lattices, revisited
We revisit the approximate Voronoi cells approach for solving the closes...
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Optimal Dyck Reachability for DataDependence and Alias Analysis
A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graph where the edges are labeled with different types of opening and closing parentheses, and the reachability information is computed via paths whose parentheses are properly matched. We present new results for Dyck reachability problems with applications to alias analysis and datadependence analysis. Our main contributions, that include improved upper bounds as well as lower bounds that establish optimality guarantees, are as follows. First, we consider Dyck reachability on bidirected graphs, which is the standard way of performing fieldsensitive pointsto analysis. Given a bidirected graph with n nodes and m edges, we present: (i) an algorithm with worstcase running time O(m + n ·α(n)), where α(n) is the inverse Ackermann function, improving the previously known O(n^2) time bound; (ii) a matching lower bound that shows that our algorithm is optimal wrt to worstcase complexity; and (iii) an optimal averagecase upper bound of O(m) time, improving the previously known O(m ·log n) bound. Second, we consider the problem of contextsensitive datadependence analysis, where the task is to obtain analysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is only linear, and only wrt the number of call sites. Third, we prove that combinatorial algorithms for Dyck reachability on general graphs with truly subcubic bounds cannot be obtained without obtaining subcubic combinatorial algorithms for Boolean Matrix Multiplication, which is a longstanding open problem. We also show that the same hardness holds for graphs of constant treewidth.
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