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We describe the open-source tool dReal, an SMT solver for nonlinear formulas over the reals. The tool can handle various nonlinear real functions such as polynomials, trigonometric functions, exponential functions, etc. dReal implements the framework of δ-complete decision procedures: It returns either unsat or δ-sat on input formulas, where δ is a(More)
We study SMT problems over the reals containing ordinary differential equations,. They are important for formal verification of realistic hybrid systems and embedded software. We develop δ-complete algorithms for SMT formulas that are purely existentially quantified, as well as ∃∀-formulas whose universal quantification is restricted to the time variables.(More)
Lean is a new open source theorem prover being developed at Microsoft Research and Carnegie Mellon University, with a small trusted kernel based on dependent type theory. It aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction of(More)
By combining algorithmic learning, decision procedures, predicate abstraction, and simple templates, we present an automated technique for finding quantified loop invariants. Our technique can find arbitrary first-order invariants (modulo a fixed set of atomic propositions and an underlying SMT solver) in the form of the given template and exploits the(More)
dReach is a bounded reachability analysis tool for nonlinear hybrid systems. It encodes reachability problems of hybrid systems to first-order formulas over real numbers, which are solved by delta-decision procedures in the SMT solver dReal. In this way, dReach is able to handle a wide range of highly nonlinear hybrid systems. It has scaled well on various(More)
We advance the state-of-the-art in verifying periodic programs – a commonly used form of real-time software that consists of a set of asynchronous tasks running periodically and being scheduled preemptively based on their priorities. We focus on an approach based on sequentialization (generating an equivalent sequential program) of a time-bounded periodic(More)
Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous(More)
Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous(More)
This article, based on Doh, Kim, and Schmidt's "abstract parsing" technique, presents an abstract interpretation for statically checking the syntax of generated code in two-staged programs. Abstract parsing is a static analysis technique for checking the syntax of generated strings. We adopt this technique for two-staged programming languages and formulate(More)