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Dynamic techniques are a scalable and effective way to analyze concurrent programs. Instead of analyzing all behaviors of a program, these techniques detect errors by focusing on a single program execution. Often a crucial step in these techniques is to define a causal ordering between events in the execution, which is then computed using vector clocks, a simple data structure that stores logical times of threads. The two basic operations of vector clocks, namely join and copy, require $\Theta(k)$ time, where $k$ is the number of threads. Thus they are a computational bottleneck when $k$ is large. In this work, we introduce tree clocks, a new data structure that replaces vector clocks for computing causal orderings in program executions. Joining and copying tree clocks takes time that is roughly proportional to the number of entries being modified, and hence the two operations do not suffer the a-priori $\Theta(k)$ cost per application. We show that when used to compute the classic happens-before (HB) partial order, tree clocks are optimal, in the sense that no other data structure can lead to smaller asymptotic running time. Moreover, we demonstrate that tree clocks can be used to compute other partial orders, such as schedulable-happens-before (SHB) and the standard Mazurkiewicz (MAZ) partial order, and thus are a versatile data structure. Our experiments show that just by replacing vector clocks with tree clocks, the computation becomes from $2.02 \times$ faster (MAZ) to $2.66 \times$ (SHB) and $2.97 \times$ (HB) on average per benchmark. These results illustrate that tree clocks have the potential to become a standard data structure with wide applications in concurrent analyses.

Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback on how they are doing with their proofs. When constructing a problem, the instructor specifies the dependency graph of the lines of the proof, so that any correct arrangement of the lines can receive full credit. This innovation can improve assessment tools by increasing the types of questions we can ask students about proofs, and can give greater access to proof knowledge by increasing the amount that students can learn on their own with the help of a computer.

Multi-threaded programs are challenging to write. Developers often need to reason about a prohibitively large number of thread interleavings to reason about the behavior of software. A non-interference property like atomicity can reduce this interleaving space by ensuring that any execution is equivalent to an execution where all atomic blocks are executed serially. We consider the well studied notion of conflict serializability for dynamically checking atomicity. Existing algorithms detect violations of conflict serializability by detecting cycles in a graph of transactions observed in a given execution. The number of edges in such a graph can grow quadratically with the length of the trace making the analysis not scalable. In this paper, we present AeroDrome, a novel single pass linear time algorithm that uses vector clocks to detect violations of conflict serializability in an online setting. Experiments show that AeroDrome scales to traces with a large number of events with significant speedup.

We investigate the decidability of automatic program verification for programs that manipulate heaps, and in particular, decision procedures for proving memory safety for them. We extend recent work that identified a decidable subclass of uninterpreted programs to a class of alias-aware programs that can update maps. We apply this theory to develop verification algorithms for memory safety--- determining if a heap-manipulating program that allocates and frees memory locations and manipulates heap pointers does not dereference an unallocated memory location. We show that this problem is decidable when the initial allocated heap forms a forest data-structure and when programs are streaming-coherent, which intuitively restricts programs to make a single pass over a data-structure. Our experimental evaluation on a set of library routines that manipulate forest data-structures shows that common single-pass algorithms on data-structures often fall in the decidable class, and that our decision procedure is efficient in verifying them., Comment: StreamVerif tool for automata-based verification of uninterpreted programs can be found at https://github.com/umangm/streamverif

Dynamic race detection is the problem of determining if an observed program execution reveals the presence of a data race in a program. The classical approach to solving this problem is to detect if there is a pair of conflicting memory accesses that are unordered by Lamport's happens-before (HB) relation. HB based race detection is known to not report false positives, i.e., it is sound. However, the soundness guarantee of HB only promises that the first pair of unordered, conflicting events is a schedulable data race. That is, there can be pairs of HB-unordered conflicting data accesses that are not schedulable races because there is no reordering of the events of the execution, where the events in race can be executed immediately after each other. We introduce a new partial order, called schedulable happens-before (SHB) that exactly characterizes the pairs of schedulable data races --- every pair of conflicting data accesses that are identified by SHB can be scheduled, and every HB-race that can be scheduled is identified by SHB. Thus, the SHB partial order is truly sound. We present a linear time, vector clock algorithm to detect schedulable races using SHB. Our experiments demonstrate the value of our algorithm for dynamic race detection --- SHB incurs only little performance overhead and can scale to executions from real-world software applications without compromising soundness.

We consider the problem of detecting data races in program traces that have been compressed using straight line programs (SLP), which are special context-free grammars that generate exactly one string, namely the trace that they represent. We consider two classical approaches to race detection --- using the happens-before relation and the lockset discipline. We present algorithms for both these methods that run in time that is linear in the size of the compressed, SLP representation. Typical program executions almost always exhibit patterns that lead to significant compression. Thus, our algorithms are expected to result in large speedups when compared with analyzing the uncompressed trace. Our experimental evaluation of these new algorithms on standard benchmarks confirms this observation.

Writing reliable concurrent software remains a huge challenge for today's programmers. Programmers rarely reason about their code by explicitly considering different possible inter-leavings of its execution. We consider the problem of detecting data races from individual executions in a sound manner. The classical approach to solving this problem has been to use Lamport's happens-before (HB) relation. Until now HB remains the only approach that runs in linear time. Previous efforts in improving over HB such as causally-precedes (CP) and maximal causal models fall short due to the fact that they are not implementable efficiently and hence have to compromise on their race detecting ability by limiting their techniques to bounded sized fragments of the execution. We present a new relation weak-causally-precedes (WCP) that is provably better than CP in terms of being able to detect more races, while still remaining sound. Moreover it admits a linear time algorithm which works on the entire execution without having to fragment it., Comment: 22 pages, 8 figures, 1 algorithm, 1 table