Related papers: Width Hierarchies for Quantum and Classical Ordere…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…
In this paper order estimates for the linear widths of some function classes are obtained; these classes are defined by restrictions on the weighted $L_{p_1}$-norm of the r-th derivative and the weighted $L_{p_0}$-norm of zero derivative.
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Categorical data plays an important part in machine learning research and appears in a variety of applications. Models that can express large classes of real-valued functions on the Boolean cube are useful for problems involving…
Modeling decision-dependent scenario probabilities in stochastic programs is difficult and typically leads to large and highly non-linear MINLPs that are very difficult to solve. In this paper, we develop a new approach to obtain a compact…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
We consider in this paper the possibility of embedding a quantum search algorithm within a classical binary search framework. The result appears promising: taking full advantage of quantum parallelism, we show that it may actually be…
Monadic second order logic (MSO2) plays an important role in parameterized complexity due to the Courcelle's theorem. This theorem states that the problem of checking if a given graph has a property specified by a given MSO2 formula can be…
Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to…
In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform…
Binary Decision Diagrams (BDDs) are instrumental in many electronic design automation (EDA) tasks thanks to their compact representation of Boolean functions. In BDD-based reversible-circuit synthesis, which is critical for quantum…
For the verification of systems using model-checking techniques, symbolic representations based on binary decision diagrams (BDDs) often help to tackle the well-known state-space explosion problem. Symbolic BDD-based representations have…
Given a computable sequence of natural numbers, it is a natural task to find a G\"odel number of a program that generates this sequence. It is easy to see that this problem is neither continuous nor computable. In algorithmic learning…
In this paper, we provide a comprehensive overview of a recent debate over the quantum versus classical solvability of bounded distance decoding (BDD). Specifically, we review the work of Eldar and Hallgren [EH22], [Hal21] demonstrating a…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…