Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Achieving while maintaining:A logic of knowing how with intermediate constraints

In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve $\phi$ given $\psi$ while maintaining $\chi$ in-between. It generalizes the logic of goal-directed knowing how proposed by Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete axiomatization of this logic.Comment: appear in Proceedings of ICLA 201

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

The Road to General Intelligence

Humans have always dreamed of automating laborious physical and intellectual tasks, but the latter has proved more elusive than naively suspected. Seven decades of systematic study of Artificial Intelligence have witnessed cycles of hubris and despair. The successful realization of General Intelligence (evidenced by the kind of cross-domain flexibility enjoyed by humans) will spawn an industry worth billions and transform the range of viable automation tasks.The recent notable successes of Machine Learning has lead to conjecture that it might be the appropriate technology for delivering General Intelligence. In this book, we argue that the framework of machine learning is fundamentally at odds with any reasonable notion of intelligence and that essential insights from previous decades of AI research are being forgotten. We claim that a fundamental change in perspective is required, mirroring that which took place in the philosophy of science in the mid 20th century. We propose a framework for General Intelligence, together with a reference architecture that emphasizes the need for anytime bounded rationality and a situated denotational semantics. We given necessary emphasis to compositional reasoning, with the required compositionality being provided via principled symbolic-numeric inference mechanisms based on universal constructions from category theory. • Details the pragmatic requirements for real-world General Intelligence. • Describes how machine learning fails to meet these requirements. • Provides a philosophical basis for the proposed approach. • Provides mathematical detail for a reference architecture. • Describes a research program intended to address issues of concern in contemporary AI. The book includes an extensive bibliography, with ~400 entries covering the history of AI and many related areas of computer science and mathematics.The target audience is the entire gamut of Artificial Intelligence/Machine Learning researchers and industrial practitioners. There are a mixture of descriptive and rigorous sections, according to the nature of the topic. Undergraduate mathematics is in general sufficient. Familiarity with category theory is advantageous for a complete understanding of the more advanced sections, but these may be skipped by the reader who desires an overall picture of the essential concepts This is an open access book

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

Tensor Network methods in many-body physics

Strongly correlated systems exhibit phenomena -- such as high-T_c superconductivity or the fractional quantum Hall effect -- that are not explicable by classical and semi-classical methods. Moreover, due to the exponential scaling of the associated Hilbert space, solving the proposed model Hamiltonians by brute-force numerical methods is bound to fail. Thus, it is important to develop novel numerical and analytical methods that can explain the physics in this regime. Tensor Network states are quantum many-body states that help to overcome some of these difficulties by defining a family of states that depend only on a small number of parameters. Their use is twofold: they are used as variational ansatzes in numerical algorithms as well as providing a framework to represent a large class of exactly solvable models that are believed to represent all possible phases of matter. The present thesis investigates mathematical properties of these states thus deepening the understanding of how and why Tensor Networks are suitable for the description of quantum many-body systems. It is believed that tensor networks can represent ground states of local Hamiltonians, but how good is this representation? This question is of fundamental importance as variational algorithms based on tensor networks can only perform well if any ground state can be approximated efficiently in such a way. While any state can be written as a tensor network state, the number of parameters needed for the description might be too large. This is not the case for one-dimensional systems: only a few parameters are required to have a good approximation of their ground states; that, in turn, allows for numerical algorithms based on tensor networks performing well. The situation in two dimensions is somewhat more complicated, but it is known that ground states of local Hamiltonians can be expressed as tensor networks with sub-exponentially many parameters. In the present thesis, we improve on these existing bounds strengthening the claim that the language of tensor networks is suitable to describe many-body systems. Another central question is how symmetries of the system such as translational invariance, time-reversal symmetry or local unitary symmetry can be reflected in tensor networks. This question is important as systems appearing in nature might intrinsically possess certain symmetries; on one hand, understanding these symmetries simplifies the description of these systems. On the other hand, the presence of symmetries leads to the appearance of novel phases -- symmetry-protected topological (SPT) order, -- and tensor networks provide the right language to classify these phases. In one dimension and for certain classes of two-dimensional tensor networks (states generated by so-called injective tensors) it is well understood how symmetries of the state can be described. A general framework, however, has yet to be developed. In the present thesis, we contribute to the development of the theory in two ways. We first investigate the question for injective tensors, and generalize the existing proof for any geometry including the hyperbolic geometry used in the AdS/CFT correspondence. Second, we introduce a class of tensor network states that include previously known examples of states exhibiting SPT order. We show how symmetries are reflected in these states thus deepening the understanding of SPT order in two dimensions.Stark korrelierte Systeme zeigen Phänomene wie Hochtemperatursupraleitung oder den Quanten-Hall-Effekt, die mit klassischen und semiklassischen Methoden nicht erklärbar sind. Da die Dimension des zugrundeliegenden Hilbertraums exponentiell mit der Größe des Systems wächst, versagen viele der traditionellen Ansätze für derartige Systeme. Es ist daher notwendig, neuartige numerische und analytische Methoden zu entwickeln, die die Physik in diesem Bereich erklären können. Tensor-Netzwerkzustände können diese Schwierigkeiten zum Teil überwinden, indem sie eine Familie von Zuständen definieren, die nur von einer kleinen Anzahl von Parametern abhängen. Diese Zustände tragen auf zwei Arten zur Lösung des Problems bei: Erstens werden sie als Variationsansatz in numerischen Algorithmen verwendet. Zweitens bieten sie einen analytischen Zugang zu einer großen Klasse genau lösbarer Modelle, von denen angenommen wird, dass sie alle möglichen Materiephasen repräsentieren. In der vorliegenden Arbeit werden mathematische Eigenschaften dieser Zustände untersucht, wodurch das Verständnis dafür, wie und warum Tensor-Netzwerke für die Beschreibung von Quantensystemen geeignet sind, vertieft wird. Zunächst widmen wir uns der Frage, inwiefern Tensornetzwerke Grundzustände lokaler Hamiltonians darstellen können. Diese Frage ist von grundlegender Bedeutung, da Variationsalgorithmen, die auf Tensornetzwerken basieren, nur dann akkurate Ergebnisse liefern können, wenn der Grundzustand nicht allzu weit von der zugrundeliegenden variationellen Mannigfaltigkeit entfernt ist. Zwar kann prinzipiell jeder Quantenzustand als Tensornetzwerkstatus beschrieben werden. Jedoch ist die Anzahl der für die Beschreibung erforderlichen Parameter möglicherweise extrem groß. Dies ist bei eindimensionalen Systemen nicht der Fall: Nur wenige Parameter sind erforderlich, um eine gute Näherung ihrer Grundzustände zu erhalten. Aufgrund dieser theoretische Grundlage kann darauf vertraut werden, dass die Ergebnisse der tensornetzwerkbasierten Algorithmen akkurat sind. Die Situation in zwei Dimensionen ist komplizierter, aber es ist bekannt, dass Grundzustände lokaler Hamiltonians als Tensornetzwerke mit subexponentiell vielen Parametern ausgedrückt werden können. In der vorliegenden Arbeit verbessern wir diese bestehenden Grenzen und verstärken die Behauptung, dass Tensornetzwerke geeignet ist, Vielteilchensysteme zu beschreiben. Eine weitere zentrale Frage ist, wie Symmetrien des Systems wie Translationsinvarianz, Zeitumkehrsymmetrie oder lokale Symmetrie in Tensornetzwerken reflektiert werden können. Das Verständnis dieser Symmetrien vereinfacht einerseits die Beschreibung der Systeme, in denen diese Symmetrien auftreten. Auf der anderen Seite führt das Vorhandensein von Symmetrien zum Entstehen neuer Phasen - sogenannter “symmetry protected topological phases” (SPT) -, und Tensornetzwerke liefern die richtige Beschreibung, um diese Phasen zu klassifizieren. In einer Dimension und für bestimmte Klassen von zweidimensionalen Tensornetzwerken (Zustände, die von sogenannten injektiven Tensoren erzeugt werden) ist es gut verstanden, wie Symmetrien des physikalischen System sich in ihrer Beschreibung als Tensornetzwerk widerspiegeln. Ein allgemeiner Rahmen muss jedoch noch entwickelt werden. In der vorliegenden Arbeit tragen wir auf zweierlei Weise zur Weiterentwicklung der Theorie bei. Wir untersuchen zunächst die Frage nach injektiven Tensoren und verallgemeinern den vorhandenen Beweis für jede Geometrie, einschließlich der in der AdS / CFT-Korrespondenz verwendeten hyperbolischen Geometrie. Zweitens führen wir eine Klasse von Tensornetzwerkzuständen ein, die bereits bekannte Beispiele für Zustände mit SPT-Ordnung enthalten. Wir zeigen, wie sich Symmetrien in diesen Zuständen widerspiegeln, wodurch das Verständnis der SPT-Ordnung in zwei Dimensionen vertieft wird