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Many synthesis and verification problems can be reduced to determining the truth of formulas over the real numbers. These formulas often involve constraints with integrals in them. To this end, we extend the framework of δ-decision procedures with techniques for handling integrals of user-specified real functions. We implement this decision procedure in the tool ∫dReal, which is built on top of dReal. We evaluate ∫dReal on a suite of problems that include formulas verifying the fairness of algorithms and the privacy and the utility of privacy mechanisms and formulas that synthesize parameters for the desired utility of privacy mechanisms. The performance of the tool in these experiments demonstrates the effectiveness of ∫dReal. 

Security properties of real-time systems often involve reasoning about hyper-properties, as opposed to properties of single executions or trees of executions. These hyper-properties need to additionally be expressive enough to reason about real-time constraints. Examples of such properties include information flow, side channel attacks and service-level agreements. In this paper we study computational problems related to a branching-time, hyper-property extension of metric temporal logic (MTL) that we call HCMTL*. We consider both the interval-based and point-based semantics of this logic. The verification problem that we consider is to determine if a given HCMTL* formula ℑ is true in a system represented by a timed automaton. We show that this problem is undecidable. We then show that the verification problem is decidable if we consider executions upto a fixed time horizon T. Our decidability result relies on reducing the verification problem to the truth of an MSO formula over reals with a bounded time interval. 

We consider the problem of checking the differential privacy of online randomized algorithms that process a stream of inputs and produce outputs corresponding to each input. This paper generalizes an automaton model called DiP automata [10] to describe such algorithms by allowing multiple real-valued storage variables. A DiP automaton is a parametric automaton whose behavior depends on the privacy budget ∈. An automaton A will be said to be differentially private if, for some D, the automaton is D∈-differentially private for all values of ∈ > 0. We identify a precise characterization of the class of all differentially private DiP automata. We show that the problem of determining if a given DiP automaton belongs to this class is PSPACE-complete. Our PSPACE algorithm also computes a value for D when the given automaton is differentially private. The algorithm has been implemented, and experiments demonstrating its effectiveness are presented. 

Deadlocks are one of the most notorious concurrency bugs, and significant research has focused on detecting them efficiently. Dynamic predictive analyses work by observing concurrent executions, and reason about alternative interleavings that can witness concurrency bugs. Such techniques offer scalability and sound bug reports, and have emerged as an effective approach for concurrency bug detection, such as data races. Effective dynamic deadlock prediction, however, has proven a challenging task, as no deadlock predictor currently meets the requirements of soundness, high-precision, and efficiency. In this paper, we first formally establish that this tradeoff is unavoidable, by showing that (a) sound and complete deadlock prediction is intractable, in general, and (b) even the seemingly simpler task of determining the presence of potential deadlocks, which often serve as unsound witnesses for actual predictable deadlocks, is intractable. The main contribution of this work is a new class of predictable deadlocks, called sync(hronization)-preserving deadlocks. Informally, these are deadlocks that can be predicted by reordering the observed execution while preserving the relative order of conflicting critical sections. We present two algorithms for sound deadlock prediction based on this notion. Our first algorithm SPDOffline detects all sync-preserving deadlocks, with running time that is linear per abstract deadlock pattern, a novel notion also introduced in this work. Our second algorithm SPDOnline predicts all sync-preserving deadlocks that involve two threads in a strictly online fashion, runs in overall linear time, and is better suited for a runtime monitoring setting. We implemented both our algorithms and evaluated their ability to perform offline and online deadlock-prediction on a large dataset of standard benchmarks. Our results indicate that our new notion of sync-preserving deadlocks is highly effective, as (i) it can characterize the vast majority of deadlocks and (ii) it can be detected using an online, sound, complete and highly efficient algorithm.