Context-aware counter abstraction

The trend towards multi-core computing has made concurrent software an important target of computer-aided verification. Unfortunately, Model Checkers for such software suffer tremendously from combinatorial state space explosion. We show how to apply counter abstraction to real-world concurrent programs to factor out redundancy due to thread replication. The traditional global state representation as a vector of local states is replaced by a vector of thread counters, one per local state. In practice, straightforward implementations of this idea are unfavorably sensitive to the number of local states. We present a novel symbolic exploration algorithm that avoids this problem by carefully scheduling which counters to track at any moment during the search. We have carried out experiments on Boolean programs, an abstraction promoted by the success of the Slam project. The experiments give evidence of the applicability of our method to realistic programs, and of the often huge savings obtained in comparison to plain symbolic state space exploration, and to exploration optimized by partial-order methods. To our knowledge, our tool marks the first implementation of counter abstraction to programs with non-trivial local state spaces, resulting in a Model Checker for concurrent Boolean programs that promises true scalabilit

Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs

We show that the class of chordal claw-free graphs admits LREC=-definable canonization. LREC= is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm for the class of chordal claw-free graphs, and that LREC= captures logarithmic space on this graph class. Since LREC= is contained in fixed-point logic with counting, we also obtain that fixed-point logic with counting captures polynomial time on the class of chordal claw-free graphs

Sequence queries on temporal graphs

Graphs that evolve over time are called temporal graphs. They can be used to describe and represent real-world networks, including transportation networks, social networks, and communication networks, with higher fidelity and accuracy. However, research is still limited on how to manage large scale temporal graphs and execute queries over these graphs efficiently and effectively. This thesis investigates the problems of temporal graph data management related to node and edge sequence queries. In temporal graphs, nodes and edges can evolve over time. Therefore, sequence queries on nodes and edges can be key components in managing temporal graphs. In this thesis, the node sequence query decomposes into two parts: graph node similarity and subsequence matching. For node similarity, this thesis proposes a modified tree edit distance that is metric and polynomially computable and has a natural, intuitive interpretation. Note that the proposed node similarity works even for inter-graph nodes and therefore can be used for graph de-anonymization, network transfer learning, and cross-network mining, among other tasks. The subsequence matching query proposed in this thesis is a framework that can be adopted to index generic sequence and time-series data, including trajectory data and even DNA sequences for subsequence retrieval. For edge sequence queries, this thesis proposes an efficient storage and optimized indexing technique that allows for efficient retrieval of temporal subgraphs that satisfy certain temporal predicates. For this problem, this thesis develops a lightweight data management engine prototype that can support time-sensitive temporal graph analytics efficiently even on a single PC