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Nonnegativity certificates can be used to obtain tight dual bounds for polynomial optimization problems. Hierarchies of certificate-based relaxations ensure convergence to the global optimum, but higher levels of such hierarchies can become…
A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically,…
We propose a new parameter called proofdoor in an attempt to explain the efficiency of CDCL SAT solvers over formulas derived from circuit (esp., arithmetic) verification applications. Informally, given an unsatisfiable CNF formula F over n…
Variational inequalities are a broad formalism that encompasses a vast number of applications. Motivated by applications in machine learning and beyond, stochastic methods are of great importance. In this paper we consider the problem of…
Quantum Error Correction (QEC) is essential for fault-tolerant quantum copmutation, and its implementation is a very sophisticated process involving both quantum and classical hardware. Formulating and verifying the decomposition of logical…
The Verified Software Toolchain (VST) is a system for proving correctness of C programs using separation logic. By connecting to the verified compiler CompCert, it produces the strongest possible guarantees of correctness for real C code…
Certifying neural network robustness against adversarial examples is challenging, as formal guarantees often require solving non-convex problems. Hence, incomplete verifiers are widely used because they scale efficiently and substantially…
In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach. Our…
With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature…
We present Xenon, a solver-aided method for formally verifying that Verilog hardware executes in constant-time. Xenon scales to realistic hardware designs by drastically reducing the effort needed to localize the root cause of verification…
In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
Arrays are ubiquitous in the context of software verification. However, effective reasoning over arrays is still rare in CP, as local reasoning is dramatically ill-conditioned for constraints over arrays. In this paper, we propose an…
This paper studies mean-risk portfolio optimization models using the conditional value-at-risk (CVaR) as a risk measure. We also employ a cardinality constraint for limiting the number of invested assets. Solving such a…
Software vulnerability detection can be formulated as a binary classification problem that determines whether a given code snippet contains security defects. Existing multimodal methods typically fuse Natural Code Sequence (NCS)…
Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…
Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs…
The design of Systems on Chips (SoCs) is becoming more and more complex due to technological advancements. Missed bugs can cause drastic failures in safety-critical environments leading to the endangerment of lives. To overcome these…
Programming languages and techniques based on logic and constraints, such as the Constraint Handling Rules (CHR), can support many common programming tasks that can be expressed in the form of a search for feasible or optimal solutions.…
Modern software engineering trends towards Cloud-native software development by international teams of developers. Cloud-based version management services, such as GitHub, are used for the source code and other artifacts created during the…