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Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…

We provide full certifications of two versions of merge sort of arrays in the verification-aware programming language Dafny. We start by considering schemas for applying the divide-and-conquer or partition method of solution to…

This paper develops verification methodology for quantum programs, and the contribution of the paper is two-fold: 1. Sharir, Pnueli and Hart [SIAM J. Comput. 13(1984)292-314] presented a general method for proving properties of…

We introduce the notion of identity coercions between non-indexed and indexed variants of inductive datatypes, such as lists and vectors. An identity coercion translates one type to another such that the coercion function definitionally…

Increasingly demanding performance requirements for dynamical systems motivates the adoption of nonlinear and adaptive control techniques. One challenge is the nonlinearity of the resulting closed-loop system complicates verification that…

To derive a program for a given specification R means to find an artifact P that satisfies two conditions: P is executable in some programming language; and P is correct with respect to R. Refinement-based program derivation achieves this…

This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…

Invariance to geometric transformations is a highly desirable property of automatic classifiers in many image recognition tasks. Nevertheless, it is unclear to which extent state-of-the-art classifiers are invariant to basic transformations…

Fully Programmable Valve Array (FPVA) has emerged as a new architecture for the next-generation flow-based microfluidic biochips. This 2D-array consists of regularly-arranged valves, which can be dynamically configured by users to realize…

Automated tests play an important role in software evolution because they can rapidly detect faults introduced during changes. In practice, code-coverage metrics are often used as criteria to evaluate the effectiveness of test suites with…

Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…

Analyzing and reasoning about safety properties of software systems becomes an especially challenging task for programs with complex flow and, in particular, with loops or recursion. For such programs one needs additional information, for…

We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…

There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops), where questions regarding the runtime and the size…

This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum…

In this paper we propose a linear variable screening method for computer experiments when the number of input variables is larger than the number of runs. This method uses a linear model to model the nonlinear data, and screens the…

Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…

The compactness lemma in programming language theory states that any recursive function can be simulated by a finite unrolling of the function. One important use case it has is in the logical relations proof technique for proving properties…

We propose a sound and complete proof rule ProbTA for quantitative analysis of violation probability of probabilistic programs. Our approach extends the technique of trace abstraction with probability in the control-flow randomness style,…