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We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language. This richer formalism comes at the price of higher computational…
Problems in program analysis can be solved by developing novel program semantics and deriving abstractions conventionally. For over thirty years, higher-order program analysis has been sold as a hard problem. Its solutions have required…
Answer Set Programming (ASP) is a prominent problem-modeling and solving framework, whose solutions are called answer sets. Epistemic logic programs (ELP) extend ASP to reason about all or some answer sets. Solutions to an ELP can be seen…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
To broaden participation, competitive programming contests may include beginner-level problems that do not require knowledge of advanced Computer Science concepts (e.g., algorithms and data structures). However, since most participants have…
The termination problem for affine programs over the integers was left open in\cite{Braverman}. For more that a decade, it has been considered and cited as a challenging open problem. To the best of our knowledge, we present here the most…
Answer set programming (ASP) with disjunction offers a powerful tool for declaratively representing and solving hard problems. Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise and…
In recent years, deep learning has made tremendous progress in a number of fields that were previously out of reach for artificial intelligence. The successes in these problems has led researchers to consider the possibilities for…
Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the…
Programming has been an important skill for researchers and practitioners in computer science and other related areas. To learn basic programing skills, a long-time systematic training is usually required for beginners. According to a…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
Elementary net systems (ENS) are the most fundamental class of Petri nets. Their synthesis problem has important applications in the design of digital hardware and commercial processes. Given a labeled transition system (TS) $A$,…
Few-shot named entity recognition (NER) systems recognize entities using a few labeled training examples. The general pipeline consists of a span detector to identify entity spans in text and an entity-type classifier to assign types to…
Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an…
The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…
Programming is about automation in a wide variety of domains. Developing itself is one of those. As a side-effect, progress in automated coding may make people less willing to learn computer programming. This could become an issue, if the…
The problem of open-set recognition is considered. While previous approaches only consider this problem in the context of large-scale classifier training, we seek a unified solution for this and the low-shot classification setting. It is…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…