Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%.
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Distributing Graph States Across Quantum Networks
Graph states form an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes—quantum computers within which local operations are free—and EPR pairs shared between nodes that can continually be generated. We prove upper bounds for our approach on the number of EPR pairs consumed, completion time, and amount of classical communication required, all of which are equal to or better than that of prior work [10]. We also reduce the problem of minimizing the completion time to distribute a graph state using our approach to a network flow problem having polynomial time complexity.
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- Award ID(s):
- 1955744
- NSF-PAR ID:
- 10343102
- Date Published:
- Journal Name:
- 2021 IEEE International Conference on Quantum Computing and Engineering (QCE)
- Page Range / eLocation ID:
- 324 to 333
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/QCE52317.2021.00049
