SIGACT news complexity theory column 63

This thesis presents some contributions in additive combinatorics and arithmetic Ramsey theory. More specifically, it deals with the interaction between combinatorics, number theory and additive combinatorics. This area saw a great improvement with the Szemerédi Regularity Lemma and some of the results that followed. The Regularity Lemma and its consequences have become a widely used tool in graph theory, combinatorics and number theory. Furthermore, its language and point of view has deeply changed the face of additive number theory, a fact universally acknowledged by the Abel award given to Szemerédi in 2012. One of the main reasons for the prize has been Szemerédi's theorem, a result regarding the existence of arbitrarily long arithmetic progressions in dense sets of the integers, the proof of which uses the Regularity Lemma in a key step. One of the earlier consequences of the Regularity Lemma was the Removal Lemma for graphs that was used by Ruzsa and Szemerédi to show Roth theorem, regarding the existence of 3-term arithmetic progressions in dense sets of the integers, in a combinatorial way. The Removal Lemma states that in any graph K with few copies of a subgraph, say a triangle, we can remove few edges from K so that the result contains no copy of the subgraph. This has become a key tool in the applications of the so-called Regularity Method, which has extensive literature in combinatorics, graph theory, number theory and computer science. In 2005 Green introduced a regularity lemma for Abelian groups as well as an algebraic removal lemma. The removal lemma for groups states that, for a given finite Abelian group G, if there are o(|G|^3) solution to x+y+z+t=0 with the variables taking values in S, a subset of G, then we can remove o(|G|) elements from S to make the set S solution-free. The main contributions of this work corresponds to extensions of the removal lemma for groups to either more general contexts, like non-necessary Abelian finite groups, or to linear systems of equations for finite Abelian groups. The main goal is to give a comprehensive and more general framework for many results in additive number theory like Szemerédi Theorem. In particular, we show that the removal lemma for groups by Green can be extended to non-necessary Abelian finite groups. Moreover, we prove a removal lemma for linear systems on finite fields: for every e>0 there exists a d>0 such that if A is a (k x m) linear system of equations with coefficients in a finite field F and the number of solutions to Ax=b, where each variable takes values from a subset Si in F is less than d times |F| raised to m-k, then by removing less than e|F| elements in each Si we can make the resulting sets solution-free, thus solving a conjecture by Green to that respect. Even more, if A is an integer linear system, G is a finite Abelian group, and the determinantal of A and |G| are coprime, then a similar statement holds. Let us mention that the last result allows us to characterize those linear systems where any set S with size proportional to G has a nontrivial solution in S, provided |G| is large enough. This extends the validity of Szmerédi's theorem to finite Abelian groups. These extensions of the removal lemma have been used in arithmetic Ramsey theory to obtain counting results for the number of monochromatic solutions of linear systems. The main result from a work by Frankl, Graham and Rödl in '88 states that the number of monochromatic solutions of regular systems in integer intervals is in fact a positive proportion of the total number of solutions. We give analogous results for solutions in Abelian groups with bounded exponent, for which the main tool in the torsion-free case cannot be applied. Density versions of these counting results are also obtained, in this case with a full characterization.

This chapter describes four interdisciplinary fields originated and defined by Ashu M. G. Solo in 2011 called political engineering, public policy engineering, computational politics, and computational public policy. Political engineering is the application of engineering, computer science, mathematics, or natural science to solving problems in politics. Computational politics is the application of computer science or mathematics to solving problems in politics. Political engineering and computational politics include, but are not limited to, principles and methods for political decision-making, analysis, modeling, optimization, forecasting, simulation, and expression. Public policy engineering is the application of engineering, computer science, mathematics, or natural science to solving problems in public policy. Computational public policy is the application of computer science or mathematics to solving problems in public policy. Public policy engineering and computational public policy include, but are not limited to, principles and methods for public policy formulation, decision-making, analysis, modeling, optimization, forecasting, and simulation. The chapter describes the scope of research and development in these fields, provides examples of research and development in these fields, and provides possible university curricula for academic programs in these fields.

The purpose of the study is to assess the application of Computer science in the fractional distillation of petroleum. The study sought to: Determine the merit of using Computer science in fractional distillation of petroleum. Evaluate the cost effectiveness to the application of Computer science in fractional distillation of petroleum to the welfare of citizens. Determine if Computer science can help in controlling the natural effects of fractional distillation of petroleum on the environment. Computer science has gained wider application in so many areas of human endeavor ranging from the homes to more scientific and industrial applications, hence its application of Computer science in fractional distillation of petroleum cannot be overemphasized. Irrespective of the benefits of the application of Computer science in fractional distillation of petroleum as a whole, it has become pertinent to ask how effective and efficient its application of Computer science in fractional distillation of petroleum has been. This research work tries to investigate how effective the application of Computer science in fractional distillation of petroleum. The project exertion covered statement of the problem, purpose of the study, research questions/hypotheses were formulated to enable the researcher find out facts about the study, highlighted in division one. Subdivision two was based on the literature review of this study. The study covers the research methodology which guided the study, the next stage was based on the presentation of data and its’ analysis as well as the discussion of findings. The final stage of the research was concerned with the conclusion as well as recommendations and suggestions for further studies

One significant tool for addressing the concerns associated with the use of one of the applications in computer science is the law. Numerous laws and rules governing the use of computer science are designed to safeguard users, customers, and society at large. Law uses norms created by governmental and social institutions to control behavior. Programming is used to explore digital information in computer science. Computers got more potent and smaller as they evolved through generations, utilizing various technologies such as integrated circuits. Cyber law regulates online behavior and deals with matters pertaining to intellectual property, privacy, domain names, and other legal concerns. A few of the many concerns that the law must address in order to mitigate the electronic crimes are protecting privacy and security, upholding justice, limiting civil and criminal liability, ensuring safety, and controlling the application of AI in the workplace. Guidelines that people and organizations have to follow when utilizing computer science applications, making sure that these requirements are met in full. Additionally, as companies must commit to recording AI usage procedures and making clear the use of data and algorithms, the regulation fosters accountability and openness. By doing this, the possibility of prejudice and mistakes when utilizing AI is decreased. This survey provides a self-contained introduction to cybercrimes and types of cybercrimes. We also present ways to combat cybercrime and limit its spread.

Arithmetic properties for sparse sequence of integers and its application in number theory, additive combinatorics and ergodic theory In this project we investigate dynamical and form {⌊𝑛𝑐⌋}, for 1<c<2 as large as possible, arithmetic statistics of sequences of the as well as the statistics of the intersection of these sequences with the primes.

Diagrams in general, and graphs in particular, are commonplace for researchers of science. Up to 70% of the papers presented in every Computer Science conference use specialised diagrams or graphs for clarification of ideas and also for demonstrations. Graph theory is a discipline in itself, constantly growing inside Discrete Mathematics. New specialised graph editors are a must for different applications. Examples of such applications in computer science are Petri nets, Pert diagrams, binary trees, Entity Relationship Diagrams, Class diagrams for OO-design, State charts, finite automaton, etc. However, diagrams are used not only in computer science; they are also used in other broad areas such as electrical engineering, chemistry and architecture, of which examples are electrical circuits, chemical reaction chains, molecular models and pipes. Such diagrams or graphs have their own grammar, i.e. their own lexica and their own editing rules. A grammar for binary trees is trivial, but the inner structure of the grammar of a molecular chain could be rather complicated.

A general problem in Extremal Combinatorics asks about the maximum size of a collection of finite objects satisfying certain restrictions, and an ideal solution to it presents to you the objects which attain the maximum size. In several problems, it is the case that any large set satisfying the given property must be similar to one of the few extremal examples. Such stability results give us a complete understanding of the problem, and also make the result more flexible to be applied as a tool in other mathematical problems. Stability results in additive combinatorics and graph theory constitute the main topic of this thesis, in which we solve a question of Erdös and Sarközy on sums of integers, and reprove a conjecture of Posa and Seymour on powers of hamiltonian cycles. Along the way we prove stronger structural statements that have as a corollary the optimal solution to these problems. We also introduce a counting technique and two graph theory tools which we believe to be of great interest in their own right. Namely the Shifting Method, the Connecting Lemma, and a robust version of the classic Erdos-Stone Simonovits theorem.

With the proliferation of computing technologies and an ongoing trend of introducing digital and blended learning aspects into higher education, innovative approaches to teaching complex topics like artificial intelligence (AI) have emerged. Of particular interest is the use of game-based learning approaches. According to problem-based learning theory, providing students with an interactive problem and encouraging them to independently find solutions promotes deeper understanding and skill acquisition. Thus, game-based approaches offer an engaging way for students to explore challenging concepts. However, despite the growing use of game-based methods in fields like economics, their application in computer science - especially in teaching game AI - remains under-explored.Understanding AI is increasingly critical for game development, as modern games emulate human-like behaviour in areas such as decision-making, character routines, and adaptive strategies. While many mechanisms and approaches of agent-level decision-making and planning are well understood, their application in video games poses unique challenges, such as accommodating unpredictable player interactions and ensuring performance efficiency without degrading the player experience. While strategy games like StarCraft or multiplayer online battle arenas like DotA 2 have been of interest as proving grounds for advanced AI training methods, their use in education has been limited due to their high complexity and associated learning curve.This work proposes the development of a novel interactive application to fill this niche. Taking inspiration from city building and management games, the application simulates the campus of the University of Applied Sciences Mittweida, where students are given control of agents acting as archetypal roles of students. The agents' goal is the acquisition of knowledge, an abstract resource gained by participating in courses, requiring the agent to navigate the campus. Students interact with the system through an API that provides information on the state of the simulation and allows issuing commands to specific agents. For example, agents who continuously acquire knowledge over a prolonged period do so at decreasing efficiency. To remedy this, a student implements a routine checking the learning efficiency of all agents, commanding "tired" agents to take a break. Alternatively, the student could train a machine learning algorithm to do the same task, albeit more adaptive. Additionally, the application enables dynamic changes to the environment at runtime, such as adding or removing courses or buildings, simulating player-driven alterations to the game world. By designing decision-making algorithms for these agents, students gain hands-on experience with fundamental AI concepts, i.e. decision trees, bridging the gap between theoretical knowledge and practical application.To evaluate the effectiveness of the application, a comparative study with undergraduate students is planned. Over the course of two semesters, two groups of students will be taught the basics of game AI - one using traditional teaching methods (primarily lectures), the other using a game-based method incorporating the new application. The learning progress of both groups will be monitored using assignments, with students being given a sample project and tasked to develop a game AI solution, i.e. for a non-player character in a first-person shooter.

This paper reviews applications in computer science that decision theorists have addressed for years, discusses the requirements posed by these applications that place great strain on decision theory/social science methods, and explores applications in the social and decision sciences of newer decision-theoretic methods developed with computer science applications in mind. The paper deals with the relation between computer science and decision-theoretic methods of consensus, with the relation between computer science and game theory and decisions, and with “algorithmic decision theory.”

This paper describes a programming system used in the teaching of two Computer Science courses at The Pennsylvania State University (7). The courses are; an upper level undergraduate-beginning graduate level course in graph theory, and a graduate level course in the theory of graphs and networks. As can be ascertained from the description of these courses they are not primarily what would normally be called programming courses. However, since they are computer science courses they do stress the computational aspects of graph and network theory and analysis. Past experiences have indicated that if a computational problem of any reasonable complexity is assigned in class the majority of the students focus an inordinate amount of their energies to the programming problems, and consequently fail to grasp the significant features of the theoretical problems involved. In addition, since graph and network theory encompasses not only computer science, but engineering and physical, and to a lesser extent, the social sciences, many of these students would be unduly burdened by writing many rather complex programs. On the other hand, teaching the computational aspects of graph theory without doing some programming is equally ludicrous. Thus, a default type solution of assigning two or three problems from a narrow set of problems was rapidly becoming an undesirable solution to this dilema. It was at this point that the concept of a dynamically growing programming system, as described in this paper, began to formulate itself.

This workshop in real and harmonic analysis surveyed recent investigations in areas including geometric measure theory and restriction theory, multiple ergodic averages, local smoothing estimates, Schrödinger and Hörmander-type oscillatory integral operators, multilinear estimates and analysis on the Hamming cube. In particular, the workshop emphasized the recent solutions of two longstanding problems: the Kakeya phenomenon in dimension three, and almost everywhere convergence of long time averages associated to multiple commuting measure-preserving transformations. The methods presented during the workshop have yielded applications in ergodic theory, number theory, and computer science.

It is generally accepted that a course in discrete structures such as Course B3 in Curriculum 68 recommendations [1] is an important part of a Computer Science program. In many institutions a Discrete Structures course is offered in the Computer Science Department although it overlaps courses in the Mathematics Department [2,3,4]. In smaller schools the size of the student body and staff limitations make such a solution impractical. At Augusta College we have met the objective of early exposure to discrete mathematics with applications in computer science by offering a two-hour computer science course as a co-requisite to a three-hour mathematics course. While this approach is a compromise it does appear to have some merit.

Games provide mathematical models for interaction. Numerous tasks in computer science can be formulated in game-theoretic terms. This fresh and intuitive way of thinking through complex issues reveals underlying algorithmic questions and clarifies the relationships between different domains. This collection of lectures, by specialists in the field, provides an excellent introduction to various aspects of game theory relevant for applications in computer science that concern program design, synthesis, verification, testing and design of multi-agent or distributed systems. Originally devised for a Spring School organised by the GAMES Networking Programme in 2009, these lectures have since been revised and expanded, and range from tutorials concerning fundamental notions and methods to more advanced presentations of current research topics. This volume is a valuable guide to current research on game-based methods in computer science for undergraduate and graduate students. It will also interest researchers working in mathematical logic, computer science and game theory.

Artificial intelligence (AI) is a rapidly evolving field that has seen tremendous growth in recent years. In this chapter, the authors provide an overview of current trends in AI and their applications in computer science. They also discuss the future directions of AI research and their potential impact on the field of computer science. They start by introducing the basic concepts of AI and its various subfields. Then, they present an overview of current trends in AI research, including machine learning, natural language processing, computer vision, and robotics. The authors discuss how these trends are applied in computer science, such as autonomous vehicles, fraud detection, and personalized medicine. Finally, they discuss the future directions of AI research, including the development of more explainable AI systems, the integration of AI with other emerging technologies, and the ethical considerations of AI.

It is generally accepted that a course in discrete structures such as Course B3 in Curriculum 68 recommendations [1] is an important part of a Computer Science program. In many institutions a Discrete Structures course is offered in the Computer Science Department although it overlaps courses in the Mathematics Department [2,3,4]. In smaller schools the size of the student body and staff limitations make such a solution impractical. At Augusta College we have met the objective of early exposure to discrete mathematics with applications in computer science by offering a two-hour computer science course as a co-requisite to a three-hour mathematics course. While this approach is a compromise it does appear to have some merit.