Learning by game-building

The theory of computer science is based around universal Turing machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of classical UTMs. For the most important class of problem in computer science, non-deterministic polynomial complete problems, non-deterministic UTMs (NUTMs) are theoretically exponentially faster than both classical UTMs and quantum mechanical UTMs (QUTMs). However, no attempt has previously been made to build an NUTM, and their construction has been regarded as impossible. Here, we demonstrate the first physical design of an NUTM. This design is based on Thue string rewriting systems, and thereby avoids the limitations of most previous DNA computing schemes: all the computation is local (simple edits to strings) so there is no need for communication, and there is no need to order operations. The design exploits DNA's ability to replicate to execute an exponential number of computational paths in P time. Each Thue rewriting step is embodied in a DNA edit implemented using a novel combination of polymerase chain reactions and site-directed mutagenesis. We demonstrate that the design works using both computational modelling and in vitro molecular biology experimentation: the design is thermodynamically favourable, microprogramming can be used to encode arbitrary Thue rules, all classes of Thue rule can be implemented, and non-deterministic rule implementation. In an NUTM, the resource limitation is space, which contrasts with classical UTMs and QUTMs where it is time. This fundamental difference enables an NUTM to trade space for time, which is significant for both theoretical computer science and physics. It is also of practical importance, for to quote Richard Feynman ‘there's plenty of room at the bottom’. This means that a desktop DNA NUTM could potentially utilize more processors than all the electronic computers in the world combined, and thereby outperform the world's current fastest supercomputer, while consuming a tiny fraction of its energy.

Turing's present-day and all-time relevance arises from the timelessness of the issues he tackled, and the innovative light he shed upon them. Turing first defined the algorithmic limits of computability, when determined via effective mechanism, and showed the generality of his definition by proving its equivalence to other general, but less algorithmic, non-mechanical, more abstract formulations of computability. In truth, his originality much impressed Gödel, for the simplicity of the mechanism invoked—what we nowadays call a Turing Machine (or program)—and for the proof of existence of a Universal Turing Machine (what we call digital computer)—which can demonstrably mimic any other Turing Machine, i.e. execute any program. Indeed, Turing Machines simply rely on having a finite-state automaton (like a vending machine), and an unbound paper tape made of discrete squares (like a paper roll), with at most one rewritable symbol on each square. Turing also first implicitly introduced the perspective of ‘functionalism'—though he did not use the word, it was introduced later by Putnam, inspired by Turing's work—by showing that what counts is the realizability of functions, independently of the hardware that embodies them. And that realizability is afforded by the very simplicity of his devised mechanism, what he then called A-machines (but now bear his name), which rely solely on the manipulation of symbols—as discrete as the fingers of one hand—wherein both data and instructions are represented with symbols, both being subject to manipulation. The twain, data as well as instructions, are stored in memory, where instructions double as data and as rules for acting—the stored program idea. No one to this day has invented a computational mechanical process with such general properties, which cannot be theoretically approximated with arbitrary precision by some Turing Machine, wherein interactions are to be captured by Turing's innovative concept of oracle. In these days of discrete-time quantization, computational biological processes, and proof of ever expanding universe—the automata and the tape—the Turing Machine reigns supreme. Moreover, universal functionalism—another Turing essence—is what enables the inevitable bringing together of the ghosts in the several embodied machines (silicon-based, biological, extra-terrestrial or otherwise) to promote their symbiotic epistemic co-evolution, since they partake of the same theoretic functionalism. Turing is truly and forever among us.

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

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

No abstract available.

Technological sovereignty, broadly defined as a nation’s capacity to create and employ critical technologies, is of growing importance to national security and economic well-being. Russia is vividly aware of the necessity and thus embarks on the challenging path to achieve technological sovereignty. This paper addresses the specific significance of educating generations of specialists for the overall endeavor. It explores the current state of the Russian education system and the apparent lack of experts in vital technological domains. In addition to engineering schools, supplementary skills in computer science, data analysis, and project management are covered. This is followed by guidelines for reform and policy recommendations to acquire and maintain talent, as well as instilling an ethos of discipline-specific continuing education. The paper concludes with the ultimate prerequisite for success, a multi-faceted strategy centered on technological sovereignty, reliant on long-term educational reform to enable Russia’s path towards technological sovereignty.

Finite State Automata (FSA) serve as a fundamental mathematical model of computation, commonly explored in computer science degree programs. Traditionally, FSA are represented through state diagrams or tables, which, in educational settings necessitating assistive technologies, pose accessibility challenges, particularly for Visually Impaired People (VIP). This work is part of a broader initiative focused on creating tools for inclusive access to scientific information. Its main goal is to explore the effectiveness of a dialogue system (DS) as an alternative method for conveying FSA information to VIP, aiming to enhance their comprehension and user experience. To achieve this, a rule-based DS tailored for facilitating FSA access, with a primary focus on VIP as end users, was developed. The research involved an A/B test comparing participants’ comprehension of FSA using the rule-based DS versus standard tabular representations. Statistical analysis was also carried out to evaluate the performance differences between the two methods. The findings indicate that communication through the DS significantly outperforms the tabular representation, establishing it as a viable and effective alternative for both VIP and non-VIP. Although VIP participants displayed slightly varying performance depending on the questions, their feedback favoured the DS for its ease of use and overall user satisfaction. Additionally, the study analysed the capabilities and limitations of popular Large Language Models (LLMs) in describing graphical structures like FSA. Despite their general effectiveness in language tasks, LLMs proved inadequate for accurately and consistently describing FSA, highlighting the need for more controlled and explainable DS approaches in educational contexts.

The paper describe the possibility of using visualization in education of theoretical computer science. Abstract computational models are used frequently in theoretical computer science. We have developed an animations that visualize a concrete examples this models (finite automata, push down automata, turing machine) that helps the learner to better understand principles of this models. We use these small learning objects in e-learning course in web based environment, LMS Moodle. The work with the visualization object of computational models will enable students to comprehend the theory of computing and it will be also used to check and assess their knowledge.

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).

Finite state automata are of fundamental importance in theory as well as applications in computer science. This dissertation presents several parallel algorithms for processing of them, including minimizing the number of states for a given finite state automaton, finding homing sequences for a given finite state automaton, converting a regular expression into an $\\varepsilon$-free nondeterministic finite automaton. Implementation of some algorithms, as well as their experimental results, are also given. For minimization of deterministic finite automata, we present a parallel algorithm and discuss its implementation on a practical parallel machine using data parallel and message passing paradigms. Its time complexity on a p processor EREW PRAM $(p\\le n)$ for inputs of size n is $O({n\\log\\sp2n\\over p}+\\log n\\ \\log p)$ uniformly on almost all instances. The work done by our algorithm is thus within a factor of $O(\\log n)$ of the best known sequential algorithm. The space used by our algorithm is linear in the input size. The actual resource requirements of our implementations are consistent with these estimates. For finding homing sequences of deterministic finite automata, we present both deterministic and randomized algorithms. Two randomized algorithms of time complexity $O(log\\sp2n)$ are given. One of the randomized algorithms produces a homing sequence of length $O(n\\ log\\sp2n)$ for almost all DFA's with n states. The deterministic algorithm is based on a well known sequential algorithm. The implementation of the deterministic parallel algorithm shows that it can handle randomly generated instances with millions of states, and all DFA's with thousands of states using currently available parallel machines. Finally, we present an efficient parallel algorithm for converting a regular expression into an $\\varepsilon$-free nondeterministic finite automaton. The resulting automaton is natural representation of a regular expression and has some important and practical uses in the document processing area. The time complexity of the algorithm is $O(\\log n)$ and the number of processors used is $O(n\\sp2).$

The non-linear invariance principle of Mossel, O'Donnell and Oleszkiewicz establishes that if f(x1, ..., xn) is a multilinear low-degree polynomial with low influences then the distribution of f(B1, ..., Bn) is close (in various senses) to the distribution of f(G1, ..., Gn), where Bi ∈R {-1, 1} are independent Bernoulli random variables and Gi ~ N(0, 1) are independent standard Gaussians. The invariance principle has seen many application in theoretical computer science, including the Majority is Stablest conjecture, which shows that the Goemans--Williamson algorithm for MAXCUT is optimal under the Unique Games Conjecture. More generally, MOO's invariance principle works for any two vectors of hypercontractive random variables (X1, ..., Xn), (Y1, ..., Yn) such that (i) Matching moments: Xi and Yi have matching first and second moments, (ii) Independence: the variables X1, ..., Xn are independent, as are Y1, ..., Yn. The independence condition is crucial to the proof of the theorem, yet in some cases we would like to use distributions (X1, ..., Xn) in which the individual coordinates are not independent. A common example is the uniform distribution on the slice ([EQUATION]) which consists of all vectors (x1, ..., xn) ∈ {0, 1}n with Hamming weight k. The slice shows up in theoretical computer science (hardness amplification, direct sum testing), extremal combinatorics (Erdos--Ko--Rado theorems) and coding theory (in the guise of the Johnson association scheme). Our main result is an invariance principle in which (X1, ..., Xn) is the uniform distribution on a slice ([EQUATION]) and (Y1, ..., Yn) consists either of n independent Ber(p) random variables, or of n independent N(p, p(1 - p)) random variables. As applications, we prove a version of Majority is Stablest for functions on the slice, a version of Bourgain's tail theorem, a version of the Kindler--Safra structural theorem, and a stability version of the t-intersecting Erdos--Ko--Rado theorem, combining techniques of Wilson and Friedgut. Our proof relies on a combination of ideas from analysis and probability, algebra and combinatorics. In particular, we make essential use of recent work of the first author which describes an explicit Fourier basis for the slice.

Telemail, an electronic mail system for the Univac 1110, was designed and implemented by the Academic Computer Center at the University of Wisconsin with support from Edunet. At present, there are approximately two hundred users including several organized groups: Educom staff and university liasons; Theory-Net researchers in theoretical computer science; a USDA sponsored research project; and a group of experts on mental retardation services/materials/literature. Most participants in the above groups access Telemail via Telenet, a commercial packet switching network. In addition, the system is used by computer center staff and researchers at the university.The Theory-Net project, sponsored by NSF, involves the use of Telemail by a group of about thirty researchers in theoretical computer science at fifteen universities. The goal is to assess the value of an electronic mail system in facilitating interaction (and thereby research productivity) in a small research community. To date a number of Joint research projects have made use of the system. In addition, the 1978 Sigact Symposium Program Committee communicated via Telemail, The next phase of the project involves a substantial increase in the number of participants. Individuals from small schools having only one or two researchers in theoretical computer science will be given high priority.

The papers in this volume were presented at the 5th Innovations in Theoretical Computer Science (ITCS 2014) conference, sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT). The conference was held in Princeton, New Jersey, USA, January 11--14, 2014. ITCS (previously known as ICS) seeks to promote research that carries a strong conceptual message, for instance, introducing a new concept or model, opening a new line of inquiry within traditional or cross-interdisciplinary areas, or introducing new techniques or new applications of known techniques). The call for papers welcomed all submissions, whether aligned with current theory of computation research directions or deviating from them. Altogether 116 submissions were received worldwide. Of these the program committee selected 48 papers. The accepted papers cover a wide range of topics in theoretical computer science, including algorithms, complexity, cryptography, learning, data privacy, quantum, physical and biological computing and relations between computing and social sciences. In addition to the selected papers the committee invited Professor Peter Winkler of Dartmouth to give an evening talk and we are grateful for his acceptance. Another evening was devoted to "Graduating Bits" - short talks by recent graduates. The program committee consisted of 24 members (plus the chair): Deeparnab Chakrabarty (Microsoft Research India), Timothy Chan (University of Waterloo), Costis Daskalakis (MIT), Yuval Emek (ETH and Technion), Kousha Etessami (University of Edinburgh), Yuval Filmus (University of Toronto and Simons Institute, Berkeley), Arpita Ghosh (Cornell University), Monika Henzinger (University of Vienna), Sandy Irani (University of California Irvine), Michael nKearns (University of Pennsylvania), Lap Chi Lau (The Chinese University of Hong Kong), Nati Linial (Hebrew University of Jerusalem), Kobbi Nissim (Ben-Gurion University), Rasmus Pagh (IT University of Copenhagen), Shubhangi Saraf (Rutgers University), Ola Svensson (EPFL), Vinod Vaikuntanathan (University of Toronto and MIT), Jan Vondrak (IBM Almaden Research Center), Manfred Warmuth (University of California, Santa Cruz), Daniel Wichs (Northeastern University), Udi Wieder (Microsoft Research SVC), Ryan Williams (Stanford University), Ronald de Wolf (CWI and University of Amsterdam), David Xiao (CNRS and Université Paris 7). I wish to express my admiration for their hard work of reading, evaluating and debating the merits of the submissions. The many individuals who assisted the reviewing process as subreviewers and extended the expertise of the committee deserve acknowledgments as well.

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.