Related papers: Fast Witness Extraction Using a Decision Oracle
In recent years much effort was put into developing polynomial-time conditional lower bounds for algorithms and data structures in both static and dynamic settings. Along these lines we suggest a framework for proving conditional lower…
Entanglement in multipartite systems is a key resource for quantum information and communication protocols, making its verification in complex systems a necessity. Because an exact calculation of arbitrary entanglement probes is impossible,…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
Different mathematical models of recognition processes are known. In the present paper we consider a pattern recognition algorithm as an oracle computation on a Turing machine. Such point of view seems to be useful in pattern recognition as…
We give an efficient algorithm to enumerate all elements of a Pareto front in a multi-objective optimization problem in which the space of values is finite for all objectives. Our algorithm uses a feasibility check for a search space…
Precise test oracles for reactive systems such as critical control systems and communication protocols can be modelled with deterministic finite state machines (FSMs). Among other roles, they serve in evaluating the correctness of systems…
We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x.…
JSON Schema is an important, evolving standard schema language for families of JSON documents. It is based on a complex combination of structural and Boolean assertions, and features negation and recursion. The static analysis of JSON…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…
A generic algorithm is developed to reduce the problem of obtaining linear and nonlinear entanglement witnesses of a given quantum system, to convex optimization problem. This approach is completely general and can be applied for the…
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…
It is a long-standing open question in quantum complexity theory whether the definition of $\textit{non-deterministic}$ quantum computation requires quantum witnesses $(\textsf{QMA})$ or if classical witnesses suffice $(\textsf{QCMA})$. We…
Given a random variable $O \in \mathbb{R}$ and a set of experts $E$, we describe a method for finding a subset of experts $S \subseteq E$ whose aggregated opinion best predicts the outcome of $O$. Therefore, the problem can be regarded as a…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
We provide a general framework to remove short advice by formulating the following computational task for a function $f$: given two oracles at least one of which is honest (i.e. correctly computes $f$ on all inputs) as well as an input, the…
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the…
We study the Witness Set problem, a natural dual to the classical Art Gallery problem. In the Witness Set problem, we are given a polygon $P$ and an integer $k$ as input, and the objective is to determine whether $P$ has a witness set of…
JSON Schema is an evolving standard for the description of families of JSON documents. JSON Schema is a logical language, based on a set of assertions that describe features of the JSON value under analysis and on logical or structural…
A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…