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Similarity analysis plays a crucial role in various software engineering tasks, such as detecting software changes, version merging, identifying plagiarism, and analyzing binary code. Equivalence analysis, a stricter form of similarity, focuses on determining whether different programs or versions of the same program behave identically. While extensive research exists on code and binary similarity as well as equivalence analysis, there is a lack of quantitative reasoning in these areas. Non-equivalence is a spectrum that requires deeper exploration, as it can manifest in different ways across the input domain space. This paper emphasizes the importance of quantitative reasoning on non-equivalence which arises due to semantic differences. By quantitatively reasoning about non-equivalence, it becomes possible to identify specific input ranges for which programs are equivalent or non-equivalent. We aim to address the gap in quantitative reasoning in symbolic similarity analysis, enabling a more comprehensive understanding of program behavior. 

Starting with a random initial seed, fuzzers search for inputs that trigger bugs or vulnerabilities. However, fuzzers often fail to generate inputs for program paths guarded by restrictive branch conditions. In this paper, we show that by first identifying rare-paths in programs (i.e., program paths with path constraints that are unlikely to be satisfied by random input generation), and then, generating inputs/seeds that trigger rare-paths, one can improve the coverage of fuzzing tools. In particular, we present techniques 1) that identify rare paths using quantitative symbolic analysis, and 2) generate inputs that can explore these rare paths using path-guided concolic execution. We provide these inputs as initial seed sets to three state of the art fuzzers. Our experimental evaluation on a set of programs shows that the fuzzers achieve better coverage with the rare-path based seed set compared to a random initial seed. 

Given a private string q and a remote server that holds a set of public documents D, how can one of the K most relevant documents to q in D be selected and viewed without anyone (not even the server) learning anything about q or the document? This is the oblivious document ranking and retrieval problem. In this paper, we describe Coeus, a system that solves this problem. At a high level, Coeus composes two cryptographic primitives: secure matrix-vector product for scoring document relevance using the widely-used term frequency-inverse document frequency (tf-idf) method, and private information retrieval (PIR) for obliviously retrieving documents. However, Coeus reduces the time to run these protocols, thereby improving the user-perceived latency, which is a key performance metric. Coeus first reduces the PIR overhead by separating out private metadata retrieval from document retrieval, and it then scales secure matrix-vector product to tf-idf matrices with several hundred billion elements through a series of novel cryptographic refinements. For a corpus of English Wikipedia containing 5 million documents, a keyword dictionary with 64K keywords, and on a cluster of 143 machines on AWS, Coeus enables a user to obliviously rank and retrieve a document in 3.9 seconds---a 24x improvement over a baseline system.