Related papers: d-QBF with Few Existential Variables Revisited
The Strong Exponential Time Hypothesis (SETH) is a standard assumption in (fine-grained) parameterized complexity and many tight lower bounds are based on it. We consider a number of reasonable weakenings of the SETH, with sources from (i)…
This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical…
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms…
In the constraint database model, spatial and spatio-temporal data are stored by boolean combinations of polynomial equalities and inequalities over the real numbers. The relational calculus augmented with polynomial constraints is the…
The Local Lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science, yet there are hardly any natural problems known where it provides an asymptotically tight answer. The main theme of our paper is to…
We introduce the $k$-variable-occurrence fragment, which is the set of terms having at most $k$ occurrences of variables. We give a sufficient condition for the decidability of the equational theory of the $k$-variable-occurrence fragment…
We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach…
It has long been known that Feedback Vertex Set can be solved in time $2^{\mathcal{O}(w\log w)}n^{\mathcal{O}(1)}$ on $n$-vertex graphs of treewidth $w$, but it was only recently that this running time was improved to…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
In the \textsc{Maximum Degree Contraction} problem, input is a graph $G$ on $n$ vertices, and integers $k, d$, and the objective is to check whether $G$ can be transformed into a graph of maximum degree at most $d$, using at most $k$ edge…
Wootters [PRL 80, 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed form expression for the EOF of an arbitrary mixed state in…
Many verification and synthesis approaches rely on solving techniques for quantified Boolean formulas (QBF). Consequently, solution witnesses, in the form of Boolean functions, become more and more important as they represent…
Quantified constraints over the reals appear in numerous contexts. Usually existential quantification occurs when some parameter can be chosen by the user of a system, and univeral quantification when the exact value of a parameter is…
In this paper we revisit the deterministic version of the Sparse Fourier Transform problem, which asks to read only a few entries of $x \in \mathbb{C}^n$ and design a recovery algorithm such that the output of the algorithm approximates…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
The backup control barrier function (CBF) was recently proposed as a tractable formulation that guarantees the feasibility of the CBF quadratic programming (QP) via an implicitly defined control invariant set. The control invariant set is…
The \emph{Chow parameters} of a Boolean function $f: \{-1,1\}^n \to \{-1,1\}$ are its $n+1$ degree-0 and degree-1 Fourier coefficients. It has been known since 1961 (Chow, Tannenbaum) that the (exact values of the) Chow parameters of any…
The two-way finite automaton with quantum and classical states (2QCFA), defined by Ambainis and Watrous, is a model of quantum computation whose quantum part is extremely limited; however, as they showed, 2QCFA are surprisingly powerful: a…
The thesis deals with Quantum Algorithms for solving Hard Constrained Optimization Problems. It shows how quantum computers can solve difficult everyday problems such as finding the best schedule for social workers or the path of a robot…
The extended L\"uroth's Theorem says that if the transcendence degree of $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)/\KK$ is 1 then there exists $f \in \KK(\underline{X})$ such that $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)$ is equal to $\KK(f)$. In…