Inductive Explorations With Class 2 Systems

The theory of computational complexity is based on the tradeoff between two computational resources, memory space and computer time. This paper investigates the physical counterparts of these resources. Memory space is the number of bits of information required by a computer over the course of a computation. Physically, information is intimately connected with entropy: entropy can be thought of as random bits of information. The physical analogue of the amount of memory space required for a computation, Ф- SPACE, is the difference between the maximum entropy Smax of the computing system and its actual entropy, S.Ф-SPACE = S - Smax is the thermodynamic depth of the computation. Ф-SPACE is the maximum number of bits of memory space available for a physical system to perform computation. In conventional computational complexity theory, computer time is identified as the number of elementary logical operations (AND, OR, NOT, COPY) required to perform the computation. The physical analogue of time computational complexity is simply the time required for the physical computing system to perform the computation. In order to obtain a number that measures the number of physical operations that can be performed by the system over time t, we define Ф-TIME to be proportional to the computation time multiplied by the energy E of the computing system over the course of the computation: Ф-TIME = 2Et/πħ. Here, the proportionality factor 2/πħ is chosen to match the time it takes a computing system with energy E to flip a bit in time t. Ф-TIME is thus the number of bit flips that can take place in an information processing system. In addition, we propose a novel measure of physical complexity that combines these measures. The free energy F = E - TS of a system is the amount of energy that is available to do useful work - as opposed to the energy bound up in the thermal fluctuations of heat. We define the free complexity to be the free energy × time product, 2Ft/πħ required by a physical system to perform a computation. Physical spatial and temporal complexity provide upper bounds on the amount of computation that can be performed by any physical system. We discuss the implications of physical complexity for the computational complexity hierarchy, in particular, we show that in the presence of errors in the computation, Ф-SPACE is proportional Ф-TIME. We apply the resulting theory of physical computational complexity to analyze the computational power of black holes: exactly half of the energy of a black hole is available for physical computation.

This paper is an introduction to the computational complexity theory. I believe that the standard courses in complexity theory make some things much more important than they really are, while things which I find extremely interesting are marginalized. Thus, it can be seen as my subjective view on what is important and interesting in computational complexity, and what is not. We state the basic facts from computational complexity theory using the blackboard computations (one-dimensional cellular automata) as the standard computation model; we argue the benefits of such approach. This article is somewhat based on my series of talks from Warsztaty Logiczne 2014 in Białka Tatrzańska, although these talks covered more topics, such as NL=coNL, and links between BPP and the polynomial hierarchy.

As part of the comprehensive theme of the relationships between dynamic systems and computational theories, a very active area of research has been the relationships between the generic dynamic behavior of Cellular Automata (CA) and their computational abilities. Various investigations have been carried out on the computational power of CA, with concentrated efforts in the study of one-dimensional CA and their computational abilities. One of the approaches is the use of Genetic Algorithms (GA) to look for CA with a predefined computational behavior. A set of parameters which we have previously shown to be effective in helping forecast CA dynamic behavior, are used here as an auxiliary metric to guide the GA search. To this end, we modified selection, mutation and crossover of a GA, so as to incorporate the heuristic, and obtained very effective results in the evolution search for CA that can solve the so-called synchronization task.

The main thesis of this chapter is that a dynamical viewpoint allows us to better understand some important foundational issues of computation theory. Effective procedures are traditionally studied from two different but complementary points of view. The first approach is concerned with individuating those numeric functions that are effectively calculable. This approach reached its systematization with the theory of the recursive functions (Gödel, Church Kleene).This theory is not directly concerned with computing devices or computations. Rather, the effective calculability of a recursive function is guaranteed by the algorithmic nature of its definition. In contrast, the second approach focuses on a family of abstract mechanisms, which are then typically used to compute or recognize numeric functions, sets of numbers, or numbers. These devices can be divided into two broad categories: automata or machines (Turing and Post), and systems of rules for symbol manipulation (Post). The mechanisms that have been studied include: a. Automata or Machines 1. gate-nets and McCulloch-Pitts nets 2. finite automata (Mealy and Moore machines) 3. push-down automata 4. stack automata 5. Turing machines 6. register machines 7. wang machines 8. cellular automata b. Systems of Rules 9. monogenic production systems in general 10. monogenic Post canonical systems 11. monogenic Post normal systems 12. tag systems. I call any device studied by computation theory a computational system. Computation theory is traditionally interested in studying the relations between each type of computational system and the others, and in establishing what class of numeric functions each type can compute. Accordingly one proves two kinds of theorem: (1) that systems of a given type emulate systems of another type (examples: Turing machines emulate register machines and cellular automata; cellular automata emulate Turing machines, etc.), and (2) that a certain type of system is complete relative to the class of the (partial) recursive functions or, in other words, that this type of system can compute all and only the (partial) recursive functions (examples of complete systems: Turing machines, register machines, cellular automata, tag systems, etc.). All different types of computational systems have much in common. Nevertheless, it is not at all clear exactly which properties these mechanisms share.

Background & Context Continuously developing teachers’ knowledge, practice, and professional identity is one of the key standards for effective computer science (CS) teachers. Objective This study aims to understand the landscape of CS teachers in the United States, the professional identity they hold, and how their background and teaching context are associated with their CS teacher identity. Method Using data of 3540 teachers, we performed a two-step cluster analysis to reveal homogeneous subgroups of CS teachers. The relationship between teachers’ backgrounds and their CS teacher identity was also assessed. Findings This study identified four profiles of CS teachers based on their professional identity. . CS teacher identity is strongly associated with teachers’ Computer Science Teachers Association membership, teaching responsibility, teaching experience, and their exposure to CS coursework. Implications More professional support is needed for CS teachers, especially for early-career CS teachers, elementary school teachers, and teachers with multiple responsibilities and little CS background.

Kauffman nets, also known as N-K models, have been studied extensively because their dynamics can be used to model a variety of interesting dynamical processes. This paper investigates the properties of the problem of determining whether or not a given configuration of a Kauffman net has a predecessor. Here it is shown that when the parameter K that governs the number of connections grows as ln(N) , where N is the number of elements, the problem of finding a solution is extremely sensitive to small changes in the problem statement. This result has implications for studies of the physics of random systems and also may have applications for questions in computational complexity theory.

Justice-centered approaches to equitable computer science (CS) education\nframe CS learning as a means for advancing peace, antiracism, and social\njustice rather than war, empire, and corporations. However, most research in\njustice-centered approaches in CS education focus on K-12 learning\nenvironments. In this position paper, we review justice-centered approaches to\nCS education, problematize the lack of justice-centered approaches to CS in\nhigher education in particular, and describe a justice-centered approach for\nundergraduate Data Structures and Algorithms. Our approach emphasizes three\ncomponents: (1) ethics: critiques the sociopolitical values of data structure\nand algorithm design as well as the underlying logics of dominant computing\nculture; (2) identity: draws on culturally responsive-sustaining pedagogies to\nemphasize student identity as rooted in resistance to the dominant computing\nculture; and (3) political vision: ensures the rightful presence of political\nstruggles by reauthoring rights to frame CS learning as a force for social\njustice. Through a case study of this Critical Comparative Data Structures and\nAlgorithms pedagogy, we argue that justice-centered approaches to higher CS\neducation can help all computing students not only learn about the ethical\nimplications of nominally technical concepts, but also develop greater respect\nfor diverse epistemologies, cultures, and experiences surrounding computing\nthat are essential to creating the socially-just worlds we need.\n

In the quest to study and deliver Computer Science (CS) education reform, attention to gate-keeping teacher characteristics is imperative. Broad research in teacher education has demonstrated that teacher dispositions are an important driver of teacher motivation, professional choices, and classroom practices. Identification and measurements of teacher dispositions enables further analysis of how teacher beliefs may support or hinder effective practice in CS instruction, how teacher populations may differ, and how identified dispositions may change with exposure to various CS learning experiences. We analyzed 17 key documents produced by 12 national CS organizations using a grounded theory methodology to identify desirable attitudes and beliefs associated with CS and the CS education reform movement. The documents included standards, corporate research reports, advocacy tools for CS education, and organizational documents of professional associations for CS and CS Education. The analysis yielded several important dispositional targets for description and measurement in the area of teacher attitudes and beliefs. An analysis of 98 coded segments related to dispositions yielded consensus attitudes and beliefs. Professional documents in CS highlight an equity orientation, a teacher growth mindset, and identify key beliefs regarding (career) outcomes and epistemology of CS. It is possible, based on this analysis, to create a profile of a teacher who demonstrates the attitudes and beliefs of a reform-aligned CS teacher, the CS "Champion''. Instrument development along these factors is an important next step towards unlocking the analytical power of teacher attitudes and beliefs.

Computer science is a higher education domain that still show a significant male dominance. Many research studies have highlighted the importance of diversity and gender balance in computer science related areas such as software engineering and system development. However, there is still a well-identified problem that university programmes and courses on computer science fail to attract the female audience. The objective of this study is to investigate the concept of gender-inclusive computer science (CS) education with the aim of broadening participation in CS courses and programs. This is conducted through a literature study, initially focusing on keywords and research areas, and subsequently searching into existing research. The research question that guided the study was: "What concepts can be found in literature to make computer science education more gender-inclusive?". Data were analysed thematically in a two-step analysis process inspired by the grounded theory methods of Open coding and Axial coding. Findings suggest that there is significant room for learning in this field, particularly from Critical CS education studies. The Open coding analysis showed that the findings can be categorised into eight main themes. In the Axial coding the themes were merged, refined, renamed, and centred around the main axial theme of 'Epistemological pluralism'. Other essential themes that all are related to the axial main theme were: 'Design and creativity', 'Bias awareness and ethics', 'Collaboration and communication', 'Self-regulated learning', 'Real-world applications', and 'Role models and mentorship'. The result of this study is presented through a visual model that illustrates essential aspects of inclusive computer science education. The paper also proposes various directions for future research.

This paper explores the potential of virtual education options to fulfill policies designed to broaden participation in computer science (CS) education. Virtual education platforms inherently offer access to a wider range of students than traditional brick-and-mortar schools. Access does not preclude the various socio-economic challenges to engaging these platforms, but this format could be used to mitigate barriers to reaching groups of students that have historically been marginalized in CS courses. In 2019, Georgia passed legislation that requires all middle and high schools to offer CS courses by 2025. The legislation also allowed for virtual courses to satisfy the requirement. While the legislation is intent on broadening participation in CS education, it specifically incorporates a virtual option, making it novel among similar legislative actions across the country. In this context, we examine whether virtual CS courses increase access for marginalized student populations. As such, we explore (1) to what extent do the disparities in CS education found in brick-and-mortar classrooms also appear in virtual settings and (2) to what extent is there an association between modality and rurality on CS course enrollment. Using district enrollment data from 2012 to 2019 for CS courses in Georgia, we calculated the percentage of students in marginalized groups that enrolled in physical courses across the state compared to the percentage enrolled in statewide virtual courses to illuminate existing disparities in enrollment. We conducted this analysis at the district level to highlight variability in representative disparity and the underlying structural differences that might contribute to these disparities. Our analysis provides insight that incorporates the different levels of representative disparity districts have overall. As an early adopter of virtual CS education, the Georgia model provides valuable information for states interested in policies to broaden participation in CS courses.

Teaching formal methods in software construction has often been a concern of several computer science educators. In our opinion, the origin of most of the difficulties in learning formal methods in computer science and software engineering does not lie in computer science courses but in the mathematical background of the students. Moreover, there are numerous obstacles to learning basic concepts noted by both computer science and mathematics educators. To change this situation it is necessary to integrate the work of mathematics and computer science educators. That is, the main focus should be the creation of new educational approachs nourished by two components: a theoretical one (formally introducing discrete mathematics concepts) and an experimental one (implementing those concepts in a suitable programming language). In this paper, using examples from a discrete mathematics course for high school teachers, we describe the main characteristics of our approach.

THE INTERFACE BETWEEN LANGUAGE THEORY AND COMPLEXITY THEORY

Efforts in the United States to broaden the participation of racial and ethnic minorities in K12 computer science (CS) education often focus on the need for children to change themselves to meet the standards and norms of traditional computing education. Less attention has been paid to how CS education itself might change and adapt to cultural contexts and locations that children already participate in and find of value. In this paper, we describe efforts to change the shape and culture of CS education by designing and implementing it in and for a youth boxing gym in an African American community. We report findings from a boxing inspired CS curriculum that was designed in collaboration with boxing coaches, mentors, and academic staff members at the gym. It was piloted over the course of two six-hour workshops with 15 middle and high school age children. We focused on two issues that are relevant to broadening participation and reshaping the culture of CS education: (1) how the curriculum changed children's perceptions of CS and (2) the creative adaptations that children made to the curricular content and materials. An analysis of pre- and post-surveys using a nonparametric test showed significant positive changes in children's responses to the constructs of self-confidence and expression with CS. Vignettes of children appropriating and personalizing technologies from the workshops are used to unpack these findings. We end with a discussion about the implications of these findings for culture-based CS education in both school and community contexts.

Little is known about how K-12 Computer Science (CS) teachers use technology and problem-based learning (PBL) to teach CS content in the context of CS Principles curricula. Significantly, little qualitative research has been conducted in these areas in computer science education, so we lack an in-depth understanding of the complicated realities of CS teachers' experiences. This paper describes the practices and experiences of six teachers' use of technology that was implemented to support PBL in the context of a dual enrollment CS Principles course.

Professor Nikos A. Salingaros, a practicing Urbanist and Architectural Theorist, presents a powerful series of compelling hour-long lectures that apply cutting-edge mathematical techniques to architectural design. This breakthrough lecture series seeks to explain the foundations of architectural form using scientific concepts from hierarchical scaling to memes. Dr. Salingaros has applied the most exciting scientific developments of the past decade, such as fractals, complexity theory, evolutionary biology, and artificial intelligence to produce a series of lectures explaining in great detail the mathematical and scientific basis behind structure, and how structures affect the way in which human beings interact with the built environment. The twelve lectures were integrated to relate topics such as algorithmic processes, cellular automata, Sierpinski carpets, harmony-seeking computations, generative codes, and New Urbanist codes. The lectures were transmitted live via streaming video to participating institutions throughout the world, and have now been made freely available.