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Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification…
The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid sys- tems; however, state-of-the-art theorem provers require ex- tensive manual intervention. Furthermore, there is often a…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
Given a list of N numbers, the maximum can be computed in N iterations. During these N iterations, the maximum gets updated on average as many times as the Nth harmonic number. We first use this fact to approximate the Nth harmonic number…
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Theorem proving is one of the oldest applications which require heuristics to prune the search space. Invertible proof procedures has been the major tool. In this paper, we present a novel and powerful heuristic called $nongshim$ which can…
Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order $2^n$ is needed, and this can be done exactly.…
Many security- and performance-critical domains, such as cryptography, rely on low-level verification to minimize the trusted computing surface and allow code to be written directly in assembly. However, verifying assembly code against a…
The behavior of physical systems is typically modeled using differential equations which are too complex to solve analytically. In practical problems, these equations are discretized on a computational domain, and numerical solutions are…
This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time…