Thu 11 Jan 2018 10:55 - 11:20 at Watercourt - Program Analysis I Chair(s): Tachio Terauchi

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 data-dependence 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 field-sensitive points-to analysis. Given a bidirected graph with $n$ nodes and $m$ edges, we present: (i)~an algorithm with worst-case running time $O(m + n \cdot \alpha(n))$, where $\alpha(n)$ 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 worst-case complexity; and (iii)~an optimal average-case upper bound of $O(m)$ time, improving the previously known $O(m \cdot \log n)$ bound.

Second, we consider the problem of context-sensitive data-dependence 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 sub-cubic bounds cannot be obtained without obtaining sub-cubic combinatorial algorithms for Boolean Matrix Multiplication, which is a long-standing open problem. Thus we establish that the existing combinatorial algorithms for Dyck reachability are (conditionally) optimal for general graphs.

Finally, we provide a prototype implementation of our algorithms for both alias analysis and data-dependence analysis. Our experimental evaluation demonstrates that the new algorithms significantly outperform all existing methods on the two problems, over real-world benchmarks.

Thu 11 Jan

Displayed time zone: Tijuana, Baja California change

10:30 - 12:10
Program Analysis IResearch Papers at Watercourt
Chair(s): Tachio Terauchi Waseda University
10:30
25m
Talk
Inference of Static Semantics for Incomplete C Programs
Research Papers
Pre-print
10:55
25m
Talk
Optimal Dyck Reachability for Data-dependence and Alias Analysis
Research Papers
Krishnendu Chatterjee IST Austria, Andreas Pavlogiannis IST Austria, Bhavya Choudhary IIT Bombay
11:20
25m
Talk
Data-centric Dynamic Partial Order Reduction
Research Papers
Marek Chalupa Masaryk University, Krishnendu Chatterjee IST Austria, Andreas Pavlogiannis IST Austria, Kapil Vaidya IIT Bombay, Nishant Sinha IBM Research
11:45
25m
Talk
Analytical Modeling of Cache Behavior for Affine Programs
Research Papers
Wenlei Bao Ohio State University, Sriram Krishnamoorthy Pacific Northwest National Laboratories, Louis-Noël Pouchet Colorado State University, P. Sadayappan Ohio State University