Related papers: Sound approximate and asymptotic probabilistic bis…

Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…

In this MSc thesis I consider the asymptotic behaviour of the symmetric error in composite hypothesis testing. In the classical case, when the null and alternative hypothesis are finite sets of states, the best achievable symmetric error…

When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…

We consider here asymptotic models that describe the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with uneven bottoms. The…

We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…

The completeness of the quasinormal modes of the wave equation with Poeschl-Teller potential is investigated. A main result is that after a large enough time $t_0$, the solutions of this equation corresponding to $C^{\infty}$-data with…

In this paper, we study analytical approximate solutions of the second-order homogeneous differential equations with the existence of only two turning points (but without poles), by using the uniform asymptotic approximation (UAA) method.…

We present a logic that extends CTL (Computation Tree Logic) with operators that express synchronization properties. A property is synchronized in a system if it holds in all paths of a certain length. The new logic is obtained by using the…

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla…

The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a characterization of…

The P\"ochl-Teller effective potential mimics an asymptotically de Sitter black hole bounded by an event horizon and a cosmological one. Owing to the benefit of being analytically soluble, the asymptotic quasinormal modes in the modified…

We give a sufficient condition under which every finite-satisfiable formula of a given PCTL fragment has a model with at most doubly exponential number of states (consequently, the finite satisfiability problem for the fragment is in…

Let $f: T\to \{ 0,1 \}$ be a Boolean function on the Boolean half-slice, $T$, \ie elements of $\{0,1\}^n$ with Hamming weight $n/2$. We show that if $f(x)+f(y)=f(x+y)$ holds with probability $\frac{1+\delta}{2}$ over a uniform pair $(x,y)$…

Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…

This paper examines the asymptotic convergence properties of Lipschitz interpolation methods within the context of bounded stochastic noise. In the first part of the paper, we establish probabilistic consistency guarantees of the classical…

Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, in order to characterise open bisimilarity, we move to the setting of intuitionistic modal logics. The intuitionistic modal logic…

We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor…

We show that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality can be demonstrated in a certain kind of Bell experiment for all bipartite entangled states. Our protocol allows local filtering measurements and involves shared…

We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our…

This paper presents a formal characterisation of safety and liveness properties \`a la Alpern and Schneider for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is…