ABSTRACT: A standard technique from the hashing literature is to use two hash functions h1(x) and h2(x) to simulate additional hash functions of the form gi(x) = h1(x) + ih2(x). We demonstrate that this technique can be usefully applied to Bloom filters and related data structures. Specifically, only two hash functions are necessary to effectively implement a Bloom filter without any loss in the asymptotic false positive probability. This leads to less computation and potentially less need for

Abstract. The most expensive operation in explicit state model checking is the hash computation required to store the explored states in a hash table. One way to reduce this computation is to compute the hash incrementally by only processing those portions of the state that are modified in a transition. This paper presents an incremental heap canonicalization algorithm that aids in such an incremental hash computation. Like existing heap canonicalization algorithms, the incremental algorithm reduces the state space explored by detecting heap symmetries. On the other hand, the algorithm ensures that for small changes in the heap the resulting canonical representations differ only by relatively small amounts. This reduces the amount of hash computation a model checker has to perform after every transition, resulting in significant speedup of state space exploration. This paper describes the algorithm and its implementation in two explicit state model checkers, CMC and Zing. 1

Abstract. In order to apply formal methods in practice, the practitioner has to comprehend a vast amount of research literature and realistically evaluate practical merits of different approaches. In this paper we focus on explicit finite state model checking and study this area from practitioner’s point of view. We provide a systematic overview of techniques for fighting state space explosion and we analyse trends in the research. We also report on our own experience with practical performance of techniques. Our main conclusion and recommendation for practitioner is the following: be critical to claims of dramatic improvement brought by a single sophisticated technique, rather use many different simple techniques and combine them. 1

Abstract. A Bloom filter is a very compact data structure that supports approximate membership queries on a set, allowing false positives. We propose several new variants of Bloom filters and replacements with similar functionality. All of them have a better cache-efficiency and need less hash bits than regular Bloom filters. Some use SIMD functionality, while the others provide an even better space efficiency. As a consequence, we get a more flexible trade-off between false positive rate, spaceefficiency, cache-efficiency, hash-efficiency, and computational effort. We analyze the efficiency of Bloom filters and the proposed replacements in detail, in terms of the false positive rate, the number of expected cachemisses, and the number of required hash bits. We also describe and experimentally evaluate the performance of highly-tuned implementations. For many settings, our alternatives perform better than the methods proposed so far. 1

Abstract. 3Spin and 3Murphi are modified versions of the Spin model checker and the Murϕ verifier. Our modifications enhance the probabilistic algorithms and data structures for storing visited states, making them more effective and more usable for verifying huge transition systems. The tools also support a verification methodology designed to minimize time to finding errors, or to reaching desired certainty of error-freedom. This methodology calls for bitstate hashing, hash compaction, and integrated analyses of both to provide feedback and advice to the user. 3Spin and 3Murphi are the only tools to offer this support, and do so with the most powerful and flexible currently-available implementations of the underlying algorithms and data structures. 1

Abstract—We present a per-flow packet sampling method that enables the real-time classification of high-speed network traffic. Our method, based upon the partial sampling of each flow (i.e., performing sampling at only early stages in each flow’s lifetime), provides a sufficient reduction in total traffic (e.g., a factor of five in packets, a factor of ten in bytes) as to allow practical implementations at one Gigabit/s, and, using limited hardware assistance, ten Gigabit/s. I.

Abstract. Existing techniques for approximate storage of visited states in a model checker are too special-purpose and too DRAM-intensive. Bitstate hashing, based on Bloom filters, is good for exploring most of very large state spaces, and hash compaction is good for high-assurance verification of more tractable problems. We describe a scheme that is good at both, because it adapts at run time to the number of states visited. It does this within a fixed memory space and with remarkable speed and accuracy. In many cases, it is faster than existing techniques, because it only ever requires one random access to main memory per operation; existing techniques require several to have good accuracy. Adapting to accomodate more states happens in place using streaming access to memory; traditional rehashing would require extra space, random memory accesses, and hash computation. The structure can also incorporate search stack matching for partial-order reductions, saving the need for extra resources dedicated to an additional structure. Our scheme is well-suited for a future in which random accesses to memory are more of a limiting factor than the size of memory. 1

This thesis is about the design and analysis of Bloom filter and multiple choice hash table variants for application settings with extreme resource requirements. We employ a very flexible methodology, combining theoretical, numerical, and empirical techniques to obtain constructions that are both analyzable and practical. First, we show that a wide class of Bloom filter variants can be effectively implemented using very easily computable combinations of only two fully random hash functions. From a theoretical perspective, these results show that Bloom filters and related data structures can often be substantially derandomized with essentially no loss in performance. From a practical perspective, this derandomization allows for a significant speedup in certain query intensive applications. The rest of this work focuses on designing space-efficient, open-addressed, multiple choice hash tables for implementation in high-performance router hardware. Using multiple hash functions conserves space, but requires every hash table operation to consider multiple hash buckets, forcing a tradeoff between the slow speed of examining these buckets serially