A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Tarski's influence on computer science

The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the method of elimination of quantifiers, the semantics of formal languages, modeltheoretic preservation theorems, and algebraic logic; various connections of each with computer science are taken up

A general theory of action languages

We present a general theory of action-based languages as a paradigm, for the description, of those computational systems which include elements of concurrency and networking, and extend this approach to describe dist.ributed systems and also t,o describe the interaction of a system, with an environment. As part of this approach we introduce the Action Language as a common model for the class of nondeterministic concurrent programming languages and define its intensional and interaction semantics in terrors of continuous transformation of environment behavior. This semantics i.s specialized for programs with stores, and extended to describe distributed computations

Algebraic verification of hybrid systems in Isabelle/HOL

The thesis describes an open modular semantic framework for the verification of hybrid systems in a general-purpose proof assistant. We follow this approach to create the first algebraic based verification components for hybrid systems in Isabelle/HOL. The framework benefits from various design choices. Firstly, an algebra for programs such as Kleene algebras with tests or modal Kleene algebras captures the verification condition generation by providing rules for each programming construct. Intermediate relational or state transformer semantics instantiated to a concrete model of the program store allow the framework to handle assignments and ordinary differential equations (ODEs). The verification rules for ODEs require user-provided solutions, differential invariants or analytical descriptions of the continuous dynamics of the system. The construction is a shallow embedding which makes the approach quickly extensible and modular. Taking advantage of these features, we derive differential Hoare logic (dH), a minimalistic logic for the verification of hybrid systems, and the differential refinement calculus (dR) for their stepwise construction. Yet the approach is not limited to these formalisms. We also present a hybrid weakest liberal precondition calculus based on predicate transformers which subsumes powerful deductive verification approaches like differential dynamic logic. The framework is also compositional: we combine it with lenses to vary the model of the program store. We also support it with a formalisation of affine and linear systems of ordinary differential equations in Isabelle/HOL. This integration simplifies various certifications that the proof assistant requires such as guarantees of existence and uniqueness of the corresponding solutions. Verification examples illustrate the approach at work. Formalisations of our solutions to problems of the international friendly competition ARCH2020, where our components participated, further evidence their effectiveness. Finally, a larger case study certifying an invariant for a PID controller of the roll angle in a quadcopter’s flight complements these verifications

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

Remarks on the order-theoretical and algebraic properties of quantum structures

This thesis is concerned with the analysis of common features and distinguishing traits of algebraic structures arising in the sharp as well as in the unsharp approaches to quan- tum theory both from an order-theoretical and an algebraic perspective. Firstly, we recall basic notions of order theory and universal algebra. Furthermore, we introduce fundamental concepts and facts concerning the algebraic structures we deal with, from orthomodular lattices to e↵ect algebras, MV algebras and their non-commutative gener- alizations. Finally, we present Basic algebras as a general framework in which (lattice) quantum structures can be studied from an universal algebraic perspective. Taking advantage of the categorical (term-)equivalence between Basic algebras and Lukasiewicz near semirings, in Chapter 3 we provide a structure theory for the lat- ter in order to highlight that, if turned into near-semirings, orthomodular lattices, MV algebras and Basic algebras determine ideals amenable of a common simple description. As a consequence, we provide a rather general Cantor-Bernstein Theorem for involutive left-residuable near semirings. In Chapter 4, we show that lattice pseudoe↵ect algebras, i.e. non-commutative gener- alizations of lattice e↵ect algebras can be represented as near semirings. One one side, this result allows the arithmetical treatment of pseudoe↵ect algebras as total structures; on the other, it shows that near semirings framework can be really seen as the common “ground” on which (commutative and non commutative) quantum structures can be studied and compared. In Chapter 5 we show that modular paraorthomodular lattices can be represented as semiring-like structures by first converting them into (left-) residuated structures. To this aim, we show that any modular bonded lattice A with antitone involution satisfying a strengthened form of regularity can be turned into a left-residuated groupoid. This condition turns out to be a sucient and necessary for a Kleene lattice to be equipped with a Boolean-like material implication. Finally, in order to highlight order theoretical peculiarities of orthomodular quantum structures, in Chapter 6 we weaken the notion of orthomodularity for posets by introduc- ing the concept of the generalized orthomodularity property (GO-property) expressed in terms of LU-operators. This seemingly mild generalization of orthomodular posets and its order theoretical analysis yields rather strong applications to e↵ect algebras, and orthomodular structures. Also, for several classes of orthoalgebras, the GO-property yields a completely order-theoretical characterization of the coherence law and, in turn, of proper orthoalgebras

Multiply-Recursive Upper Bounds with Higman's Lemma

We develop a new analysis for the length of controlled bad sequences in well-quasi-orderings based on Higman's Lemma. This leads to tight multiply-recursive upper bounds that readily apply to several verification algorithms for well-structured systems

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

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.