Explorations in theoretical computer science for kids (using paper toys)

Aim/Purpose: The purpose of this study is to identify how Advanced level Mathematics and Mathematics course units offered at university level do impact on the academic performance of theoretical Computer Science course units. Background: In Sri Lankan state universities, students have been enrolled only from the Physical Science stream to do a degree program in Computer Science. In addition to that, universities have been offering some course units in Mathematics to provide the required mathematical maturity to Computer Science undergraduates. Despite of this it is observed that the failure rates in fundamental theoretical Computer Science course units are much higher than other course units offered in the general degree program every year. Methodology : Academic records comprised of all 459 undergraduates from three consecutive batches admitted to the degree program in Computer Science from a university were considered for this study. Contribution: This study helps academics in identifying suitable curricula for Mathematics course units to improve students’ performance in theoretical Computer Science courses. Findings: Advanced level Mathematics does not have any significant effect on the academic performance of theoretical Computer Science course units. Even though all Mathematics course units offered were significantly correlated with academic performance of every theoretical Computer Science course unit, only the Discrete Mathematics course unit highly impacted on the academic performance of all three theoretical Computer Science course units. Further this study indicates that the academic performance of female undergraduates is better than males in all theoretical Computer Science and Mathematics course units. Future Research: Identifying other critical success factors contributing to the students’ academic performance of the theoretical Computer Science through empirical studies

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.

The number of computer science (CS) courses has been dramatically expanding in U.S. high schools (HS). In comparison with well-established courses in mathematics and science, little is known about how the decisions made by HS CS teachers regarding how and what to teach impact student performance later in introductory college CS courses. Drawing on a large sample of 2,871 introductory college CS students at 115 U.S. institutions who had taken a CS course in HS, we examined the topic coverage and prevailing instructional methods in the HS course and investigated how these experiences influenced student performance in college CS. Controlling for differences in student background, we find two predictors of higher grades in college CS: greater frequency of coding-related activities in HS (programming, debugging, studying algorithms) and lower frequency of “non-coding” computer use (e.g., data analysis, computer security). Interaction models revealed a more complex story. Coding-related activity more heavily benefited students who did not have coding help available at home. In the 28% of college CS courses in which instructors employed innovative pedagogies, students with higher ACT or SAT mathematics scores had a greater advantage than in traditionally taught courses. Finally, in the innovative college courses, students whose HS CS exams had typically included testing on vocabulary did worse than students whose exams had not included such tests.

At the University of Tennessee at Martin (UTM), freshman computer science majors were being successful in their first quarter in computer science, but many majors were not completing the year sequence (Programming Concepts and Problem Solving I, II, and III). This study describes a freshman studies program that helps increase student retention in the first computer science course.Two populations were used in this study. The first population (Group A) consisted of 25 freshman computer science majors (16 men and 9 women) enrolled Fall Quarter 85 in freshman orientation General Studies GS1000 for one quarter hour credit. The second population (Group B) consisted of 17 freshman computer science majors (12 men and 5 women) enrolled the Fall Quarter 86 in freshman orientation General Studies GS1001 for two quarter hours credit. Both groups were placed in the first course in computer science using the cutting scores ACT English > 17 or 0.78 (ACT English) + 0.49 (UTM Math Placement) > 33. Both Groups A and B had an average ACT English score of 20 and an average UTM Math Placement score of 55. Each quarter during the freshman year, the computer science major enrolls in calculus (4 hrs.), Programming Concepts and Problem Solving (3 hrs.), a laboratory science (4 hrs.), English (3 hrs.), and a humanities course (3 hrs.).Group A was offered a freshman orientation program that involved a pass/fail one quarter hour credit GS1000 which met one hour each day during freshman studies week. Each section consisted of twenty-five heterogeneously grouped students. The course content was review of study skills. Group B was offered a freshman orientation program that involved a pass/fail two quarter hour credit GS1001 which met one hour each day during freshman studies week, plus one hour each week during the first quarter. Each section consisted of only students of a particular major (computer science) and was taught by a faculty member of that department. The topics of this course consisted of a review of study skills, discussions of student problems, special academic speakers, field trips to professional sites, cultural events, meetings with deans and department heads, and a follow-up on study skills. In the meeting before the final exam week, the faculty member dealt specifically with suggestions on preparing for finals.Groups A and B were enrolled in the same first computer science sequence (Programming Concepts and Problem Solving I, II, and III) their freshman year. Both groups had the same instructors, text (Introduction to Computing and Computer Science with Pascal by H. Walker), and course syllabus for this sequence. Both groups carried the same academic course load their freshman year. However, in Group A only 20% (5 out of 25) of the students completed the first computer science sequence with a grade of C or better, while in Group B 41% (7 out of 17) completed the same sequence with a grade of C or better. Student retention is achieved through the students' integration into the academic and social systems of the college by two factors: (1) faculty-student interaction and (2) peer-group interaction. Although the population of this study was small, I believe GS1001 provides one way of increasing student retention in computer science.

The adoption of innovative online teaching tools in Computer Science (CS) courses provides opportunities for data-informed instruction as a regular teaching practice in CS classrooms. In this paper, we present a design study for an interactive visual analytics dashboard, called UserFlow, that supports feedback collection from teaching documents and assists instructors in interpreting feedback and acting on it in a timely manner. The design study is conducted with eight domain experts comprising of four teaching instructors, two learning analytics (LA) experts and two instructional designers. UserFlow offers a set of novel visualization designs for presenting the four interleaving aspects of document engagement (i.e., annotations, document traversal path, reading/focus time and student information). We evaluated UserFlow in an undergraduate computer science course with over 700 students. Our results demonstrate the usefulness and need for such a tool for CS educators to inform teaching approaches and courseware improvement.

In a previous study, we investigated a framework for teaching abstraction in computer science (CS) in the context of an introductory CS course for 7th-grade students. The framework was found effective for developing CS abstraction skills. In this paper, we describe a study that investigated teaching abstraction in CS to 7th-grade students through the perspective of gender. Specifically, we compared the CS abstraction abilities of boys and girls taking the introductory CS course in 7th grade (using the Scratch environment). We also examined the difference in the effect of the teaching strategy on CS abstraction abilities between boys and girls. Our findings show a significant advantage of girls over boys regarding several aspects of CS abstraction. We also found that the framework for teaching CS abstraction, which was already established in our previous study as effective in the context of an introductory course for 7th-grade students, has an enhanced effect in this context when it comes to girls. This enhancement was manifested by a better overall performance by the girls, when comparing boys and girls that took an introductory CS course in which this framework was used. It was also manifested by the girls' deeper and more reliable perception of CS. We conjecture that this framework has the potential to affect girls' self-efficacy, and as a result to create a positive effect by encouraging and motivating girls to pursue CS education beyond this introductory course. That is, this framework has the potential to contribute to solving the issue of underrepresentation of females at the different stages of CS education, or in other words, to widening the CS pipeline for females.

This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS).

In this thesis, we introduce and examine four new temporal logic formalisms that can be used as specification languages for the automated verification of the reliability of hardware and software designs with respect to a desired behavior. The work is organized in two parts. In the first one, we reason about two logics for computations, GCTL* and MCTL*, which are useful to describe a correct execution of monolithic closed systems. In the second one, instead, we focus on two logics for strategies, SL and mATL*, which are useful to formalize several interesting properties about interactive plays in multi-entities systems modeled as multi-agent games. In the “Logics for Computations” part, we first study the immersion of the idea of graded quantifications into the temporal-logic framework. In first order logic, existential and universal quantifiers express the concepts of the existence of at least one individual object satisfying a formula, or that all individual objects satisfy a formula. In other logics, these quantifiers have been generalized to express that, for a given non-negative integer n, at least n or all but n individuals satisfy a particular formula. Here, we consider GCTL, a temporal logic with graded path quantifiers, which allows to describe properties like “there exist at least n different classes of computational fluxes in which a system reaches a predetermined state”, where the classes over paths are computed by means of a predetermined equivalence relation. More precisely, we uniformly extend the classic concept of graded quantifiers from states to paths, through the use of a concept of path equivalence with respect to a given path formula. About this logic, in particular, we study the expressiveness and succinctness relationships with respect to GµCalculus and the complexity of the satisfiability problem, which results to be ExpTime-Complete. This research is partially based on the works [BMM09] “Graded Computation Tree Logic” and [BMM10] “Graded Computation Tree Logic with Binary Coding” published, respectively, in the proceedings of the “IEEE Symposium on Logic in Computer Science, 2009” and “EACSL Annual Conference on Computer Science Logic, 2010”. Preliminary results can be also found in [Mog07]. Furthermore, we consider special quantifiers over substructures, which allow to select, using parametric criteria, small critical parts of a system to be successively verified. In literature, there are some attempts to define a logic that allows to modify the underlying structure under exam and then to verify on it some assigned property. However, as far as we know, none of them is able to select minimal submodels of a given property describing the criteria on which then execute the verification process. Here, we base our work on the search of a new operator that merges the concept of quantifiers on structures with that one derived by a generalization of the concept of pruning. The results of this work, is a class of three different extensions of CTL* with minimal model quantifiers, which we name MCTL*. Regarding these logics, we study several reductions among them, as well as the satisfiability problem that we prove to be highly undecidability, i.e., Σ_1^1-Hard, for two out of the three cases. This research is partially based on the work [MM09] “Branching-Time Temporal Logics with Minimal Model Quantifiers” published in the proceedings of the “International Conference on Developments in Language Theory, 2009”. In the “Logics for Strategies” part, we first study the problem of defining a new specification language through which it is possible to express several important properties of multi-entities systems that are neither expressible using classical monolithic temporal logics, such as CTL*, nor using two-agent-teams temporal logics, such as ATL*. In literature, we can found some proposal of logics that try to achieve this goal, but unfortunately, none of them succeeds completely on all the aspects. Among them, one of the most important attempts is CHP-SL, a logics in which one can use variables over strategies. However, this logic has a deep weakness, since it does not allow to describe games with more than two players and even two-players concurrent games. Here, we introduce SL, a logic with a syntax similar in some aspects to the first order logic, in which the strategies of the agent building the game are treated as first order objects on which we can quantify. This logic generalizes CHP-SL, by allowing the specification of the correct behavior of multi-agent concurrent games. In SL, for example, we are able to express very complex but useful Nash equilibria that are not expressible with CHP-SL. We enlighten that Nash equilibrium is one of the most important concepts in game theory. For the introduced logic, we solve two problems left open in the work on CHP-SL. Precisely, we show that the related model-checking problem is 2ExpTime-Complete, thus not harder of the same problem for several subsumed logics, while we prove that its satisfiability problem is highly undecidable, i.e., Σ_1^1-Hard. This research is partially based on the work [MMV10a] “Reasoning About Strategies” published in the proceedings of the “IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 2010”. Finally, we consider the concept of relentful strategic reasoning, i.e., a formalism that expresses the ability of a strategy to be used not only to achieve a first given goal, but also to change its final goal in dependence of the history of the play. In the context of planning, memoryful quantification, i.e., quantification over computations that does not lose information about the past along the time, is one of the principal way to express the fact that a system is able to achieve a desired result, and shift to a different goal if some event happens. However, this kind of quantification was not considered before in the context of multi-agent planning. Here, we introduce mATL*, a fusion of the classic alternating temporal logic ATL* with memoryful quantification, with the aim of covering the previous idea. About this logics, we prove that, although it is equivalent to ATL*, it is exponentially more succinct. Nevertheless, we prove that both the model-checking and the satisfiability problems remain 2ExpTime-Complete, as for ATL*. This research is partially based on the work [MMV10b] “Relentful Strategic Reasoning in Alternating-Time Temporal Logic” published in the proceedings of the “International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2010”.

Computability is one of the fundamental notions of mathematics and computer science, trying to capture the effective content of mathematics and its applications. Computability Theory explores the frontiers and limits of effectiveness and algorithmic methods. It has its origins in Godel's Incompleteness Theorems and the formalization of computability by Turing and others, which later led to the emergence of computer science as we know it today. Computability Theory is strongly connected to other areas of mathematics and theoretical computer science. The core of this theory is the analysis of relative computability and the induced degrees of unsolvability; its applications are mainly to Kolmogorov complexity and randomness as well as mathematical logic, analysis and algebra. Current research in computability theory stresses these applications and focuses on algorithmic randomness, computable analysis, computable model theory, and reverse mathematics (proof theory). Recent advances in these research directions have revealed some deep interactions not only among these areas but also with the core parts of computability theory. The goal of this Dagstuhl Seminar is to bring together researchers from all parts of computability theory and related areas in order to discuss advances in the individual areas and the interactions among those.

Topological Cones: Foundations for a Domain Theoretical Semantics Combining Probability and Nondeterminism

The correspondence between partial metrics and semivaluations

The pipeline of three introductory computer science courses at our university have low pass rates. As part of our efforts to improve the pass rates in these courses, we examine the students' mathematics preparation and their progress from one course to the next. We find that the minority of students who enter the university with good mathematics preparation are likely to succeed in our introductory computer science courses. For the majority of students, we suggest a series of interventions throughout the pipeline. Prior to taking Computer Science 1, students could gain more experience with problem solving during the Introduction to Computer Science and Introduction to Computer Engineering courses. We suggest adding precalculus as a prerequisite for Computer Science 2. For students who do not earn an A in Computer Science 2, we plan to examine whether taking a class in a second programming language before taking Computer Science 3 will improve performance in Computer Science 3. Our goal is to improve student learning and retention through these efforts, combined with continual innovation in the classroom.

This research shows an audience of fellow computer science teachers that there is benefit in testing college student's scientific reasoning skills and that the students increase their logical thinking skills in computer science classes when they are presented with real world problems, engaged in group activities, and given hands-on experiments.Students' scientific reasoning skills from several different computer science courses are analyzed and tested before and after taking the computer science course to measure their improvement in logical thinking. The higher order thinking skills test results are compared, and the overall class and individual student improvement between the classes that use different teaching strategies are analyzed. Also, the test results are compared with students' ability to perform adequately in a computer science course. This information is valuable to advisors when placing students in computer science courses.In the assessments of students' entering knowledge and evaluations of students' thinking improvement, the students' individual higher order thinking skills as well as their overall level of cognitive development are analyzed. Through the analysis of their individual skills and level of thinking, one can expand conclusions about the students' and teacher's performance over time.

Analytic information theory aims at studying problems of information theory using analytic techniques of computer science and combinatorics. Following Hadamard's and Knuth's precept, we tackle these problems by complex analysis methods such as generating functions, Mellin transform, Fourier series, saddle point method, analytic poissonization and de-poissonization, and singularity analysis. This approach lies at the crossroad of computer science and information theory. In this talk, we concentrate on one facet of information theory (i.e., source coding better known as data compression), namely the redundancy rate problem and types. The redundancy rate problem for a class of sources is the determination of how far the actual code length exceeds the optimal (ideal) code length. The method of types is a powerful technique in information theory, large deviations, and analysis of algorithms. It reduces calculations of the probability of rare events to a combinatorial analysis. Two sequences are of the same type if they have the same empirical distribution. We shall argue that counting types can be accomplished efficiently by enumerating Eulerian paths (Markov types) or binary trees with a given path length (universal types). On the other hand, analysis of the redundancy rate problem for memoryless and Markov sources leads us to tree generating functions (e.g., arising in counting labeled rooted trees) studied extensively in computer science.

The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists.