Related papers: De Morgan Dual Nominal Quantifiers Modelling Priva…
We study the problem of differentially private (DP) secure multiplication in distributed computing systems, focusing on regimes where perfect privacy and perfect accuracy cannot be simultaneously achieved. Specifically, N nodes…
Differentially private (DP) mechanisms face the challenge of providing accurate results while protecting their inputs: the privacy-utility trade-off. A simple but powerful technique for DP adds noise to sensitivity-bounded query outputs to…
In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
The $\pi$-calculus is the paradigmatical name-passing calculus. While being purely name-passing, it allows the representation of higher-order functions and store. We study how $\pi$-calculus processes can be controlled so that computations…
<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…
Characteristic formulae give a complete logical description of the behaviour of processes modulo some chosen notion of behavioural semantics. They allow one to reduce equivalence or preorder checking to model checking, and are exactly the…
We present two sample-efficient differentially private mean estimators for $d$-dimensional (sub)Gaussian distributions with unknown covariance. Informally, given $n \gtrsim d/\alpha^2$ samples from such a distribution with mean $\mu$ and…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
We characterise disentanglement in smooth generative pushforward models, such as in VAEs and GANs. For a generator/decoder $g:Z\to X$ and factorised prior $p(z)=\prod_i p_i(z_i)$, we define disentanglement as factorisation of the…
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
Model quantization enables efficient deployment of deep neural networks on edge devices through low-bit parameter representation, yet raises critical challenges for implementing machine unlearning (MU) under data privacy regulations.…
We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix…
We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which…
Ritt-Wu's algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for…
We prove near-optimal trade-offs for quantifier depth versus number of variables in first-order logic by exhibiting pairs of $n$-element structures that can be distinguished by a $k$-variable first-order sentence but where every such…
Families of operator identities appeared as a consequence of an existence of finite-dimensional representation of (super) Lie algebras of first-order differential operators and $q$-deformed (quantum) algebras of first-order…
The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…
We specify the operational semantics and bisimulation relations for the finite pi-calculus within a logic that contains the nabla quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the…
We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The…