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The views and conclusions contained in this document are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the sponsoring institutions, the U.S. Government, or any other entity. Abstract Many problems in formal verification of digital hardware circuits and(More)
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)
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)
By combining algorithmic learning, decision procedures, and predicate abstraction, we present an automated technique for finding loop invariants in propositional formulae. Given invariant approximations derived from pre-and post-conditions, our new technique exploits the flexibility in invariants by a simple randomized mechanism. The proposed technique is(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)
Programs that interact with the file system are a classical challenge for automated software testing. A common approach to handling this problem is to insert an abstraction layer between the application and the file system. However, even with a well-defined abstraction layer, the burden on the software developer or tester is still high: they have to(More)
We present a novel approach for solving the probabilistic bounded reachability problem of hybrid systems with parameter uncertainty. Standard approaches to this problem require numerical solutions for large optimization problems, and become unfeasible for systems involving nonlinear dynamics over the reals. Our approach combines randomized sampling of(More)
We present the framework of δ-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving δ-decision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbations. We prove that the verification problems become much(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)