Related papers: Pseudodeterministic Constructions in Subexponentia…
A nondeterministic automaton is history-deterministic if its nondeterminism can be resolved by only considering the prefix of the word read so far. Due to their good compositional properties, history-deterministic automata are useful in…
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 argue that proven exponential upper bounds on runtimes, an established area in classic algorithms, are interesting also in heuristic search and we prove several such results. We show that any of the algorithms randomized local search,…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
For a wide family of formations $\mathfrak{F}$ (which includes Baer-local formations) it is proved that the $ \mathfrak{F}$-hypercenter of a permutation finite group can be computed in polynomial time. In particular, the algorithms for…
Partially Observable Markov Decision Processes (POMDPs) are a natural and general model in reinforcement learning that take into account the agent's uncertainty about its current state. In the literature on POMDPs, it is customary to assume…
Let $g: \{-1,1\}^k \to \{-1,1\}$ be any Boolean function and $q_1,\dots,q_k$ be any degree-2 polynomials over $\{-1,1\}^n.$ We give a \emph{deterministic} algorithm which, given as input explicit descriptions of $g,q_1,\dots,q_k$ and an…
This paper analyzes infinitary nondeterministic computability theory. The main result is D $\ne$ ND $\cap$ coND where D is the class of sets decidable by infinite time Turing machines and ND is the class of sets recognizable by a…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we study similar notions for finite and profinite associative…
We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o-minimal structure. This fact together with the results in a previous paper implies tame dimension theory and…
The distinguishing result of this paper is a $\mathbf{P}$-time enumerable partition of all the potential perfect matchings in a bipartite graph. This partition is a set of equivalence classes induced by the missing edges in the potential…
A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently proposed to solve the problem of large-scale anomaly detection. It is a non-parametric and distribution free kernel method based on the Hilbert space embedding of…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
In this paper, we introduce a certain method to construct polynomials producing many absolute pseudoprimes. By this method, we give new polynomials producing absolute pseudoprimes with any fixed number of prime factors which can be viewed…
We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have…
Semi-random processes involve an adaptive decision-maker, whose goal is to achieve some predetermined objective in an online randomized environment. They have algorithmic implications in various areas of computer science, as well as…
The question whether the Simplex Algorithm admits an efficient pivot rule remains one of the most important open questions in discrete optimization. While many natural, deterministic pivot rules are known to yield exponential running times,…