Related papers: Approximate NFA Universality and Related Problems …
The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
This paper studies the fixed budget formulation of the Ranking and Selection (R&S) problem with independent normal samples, where the goal is to investigate different algorithms' convergence rate in terms of their resulting probability of…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
Probabilistic omega-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word can be defined in different ways: by requiring…
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…
Causality has gained popularity in recent years. It has helped improve the performance, reliability, and interpretability of machine learning models. However, recent literature on explainable artificial intelligence (XAI) has faced…
An infinite permutation $\alpha$ is a linear ordering of $\mathbb N$. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this…
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we…
Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class…
A real number \alpha is called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to \alpha. The randomness of a recursively enumerable real \alpha can be characterized in various…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…