Related papers: A Coq Formalization of Unification Modulo Exclusiv…
XOR oblivious transfer is a universal cryptographic primitive that can be related to linear polynomial evaluation. We firstly introduce some bipartite quantum protocols for XOR oblivious transfer, which are not secure if one party cheats,…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We review some of the features of the ProjectQ software framework and quantify their impact on the resulting circuits. The concise high-level language facilitates implementing even complex algorithms in a very time-efficient manner while,…
The Agora system is a prototypical Wiki for formal mathematics: a web-based system for collaborating on formal mathematics, intended to support informal documentation of formal developments. This system requires a reusable proof editor…
We present a Coq formalization of the Quantified Reflection Calculus with one modality, or $\mathsf{QRC}_1$. This is a decidable, strictly positive, and quantified modal logic previously studied for its applications in proof theory. The…
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…
An open question in quantum complexity theory is whether or not the class $\operatorname{MIP}^{co}$, consisting of languages that can be efficiently verified using interacting provers sharing quantum resources according to the quantum…
In this paper, we show a new tagging scheme for cryptographic protocol messages. Under this tagging, equational theories of operators such as exclusive-or, binary addition etc. are effectively disabled, when terms are unified. We believe…
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
In this paper, we describe the formalization of the axiom of choice and several of its famous equivalent theorems in Morse-Kelley set theory. These theorems include Tukey's lemma, the Hausdorff maximal principle, the maximal principle,…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
Type-flaw attacks and multi-protocol attacks on security protocols have been frequently reported in the literature. Heather et al. and Guttman et al. have proven that these could be prevented by tagging encrypted components with distinct…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…
Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…
Recently, we developed an automated theorem prover for projective incidence geometry. This prover, based on a combinatorial approach using matroids, proceeds by saturation using the matroid rules. It is designed as an independent tool,…
This paper presents experiments on common knowledge logic, conducted with the help of the proof assistant Coq. The main feature of common knowledge logic is the eponymous modality that says that a group of agents shares a knowledge about a…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…