Independence of Boolean algebras and forcing

AbstractIf κ⩾ω is a cardinal, a complete Boolean algebra B is called κ-dependent if for each sequence 〈bβ:β<κ〉 of elements of B there exists a partition of the unity, P, such that each p∈P extends bβ or bβ′, for κ-many β∈κ. The connection of this property with cardinal functions, distributivity laws, forcing and collapsing of cardinals is considered

The measure algebra does not always embed

The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(N)/fin. We also discuss the errors in previous results on the embeddability of the measure algebra.Comment: 10 pages 2000/01/24: final version, 11 page

Sekvencijalne topologije na Bulovim algebrama

A priori limit operator>. maps sequence of a set X into a subset of X. There exists maximal topology on X such that for each sequence x there holds >.(x) C limx. The space obtained in such way is always sequential. If a priori limit operator each sequence x which satisfy lim sup x = lim inf x maps into {lim sup x}, then we obtain the sequential topology Ts.  If a priori 'limit operator maps each sequence x into {lim sup x}, we obtain topology denoted by aT. Properties of these topologies, in general, on class of Boolean algebras with condition (Ii) and on class of weakly-distributive b-cc algebras are investigated. Also, the relations between these classes and other classes of Boolean algebras are considered.A priori limit operator A svakom nizu elemenata skupa X dodeljuje neki podskup skupa X. Tada na skupu X postoji maksimalna topologija takva da za svaki niz x vazi A(X) c lim x. Tako dobijen prostor je uvek sekvencijalan. Ako a priori limit operator svakom nizu x koji zadovoljava uslov lim sup x = liminfx dodeljuje skup {limsupx} onda se, na gore opisan nacin, dobija tzv. sekvencijalna topologija Ts. Ako a priori limit operator svakom nizu x dodeljuje {lim sup x}, dobija se topologija oznacena sa OT.  Ispitivane su osobine ovih topologija, generalno, na klasi Bulovih algebri koje zadovoljavaju uslov (Ii) ina klasi slabo-distributivnih i b-cc algebri, kao i odnosi ovih klasa prema drugim klasama Bulovih algebri

Transformational maintenance by reuse of design histories

This thesis provides theory and procedures for modifying software artifacts implemented by a formal transformation process. Installing modifications requires knowing not only what transformations were applied (a derivation history) to construct the artifact, but also why the application sequence ensures that the artifact meets its specification. The derivation history and the justification are collectively called a design history. A Design Maintenance System (DMS), when provided with a formal change called a maintenance delta, revises a design history to guide construction of a new artifact. A DMS can be used to integrate a stream of deltas into a history, providing implementations as a side effect, leading to an incremental-evolution model for software construction.We provide a broadly applicable formal model of transformation systems in which specifications are performance predicates, subsuming the functional specifications which are traditional for transformation systems. Such performance predicates provide vocabulary used in the design history to describe the effect of applying sets of transformations.A nonprocedural, performance-goal-oriented Transformation Control Language (TCL) is defined to control navigation of the design space for a transformation system. Recording the execution of a TCL metaprogram directly provides a design history.A complete classification of, and representation for, the set of possible maintenance deltas is given in terms of the inputs defined by the transformation system model. Such deltas include not only specification changes, but also changes to implementation support technologies. Delta integration procedures for revising derivation histories given functional or support technology deltas are provided, based on rearranging the order of transformations in the design space. Building on these operations, integration procedures that revise the design history for each type of delta are described. An agenda-oriented TCL execution process dovetails smoothly with the integration procedures.Our DMS is compared to a number of other maintenance systems. By using an explicit delta and verified commutativity, our DMS often reuses transformations correctly when others fail

Doctor of Philosophy

dissertationOver the last decade, cyber-physical systems (CPSs) have seen significant applications in many safety-critical areas, such as autonomous automotive systems, automatic pilot avionics, wireless sensor networks, etc. A Cps uses networked embedded computers to monitor and control physical processes. The motivating example for this dissertation is the use of fault- tolerant routing protocol for a Network-on-Chip (NoC) architecture that connects electronic control units (Ecus) to regulate sensors and actuators in a vehicle. With a network allowing Ecus to communicate with each other, it is possible for them to share processing power to improve performance. In addition, networked Ecus enable flexible mapping to physical processes (e.g., sensors, actuators), which increases resilience to Ecu failures by reassigning physical processes to spare Ecus. For the on-chip routing protocol, the ability to tolerate network faults is important for hardware reconfiguration to maintain the normal operation of a system. Adding a fault-tolerance feature in a routing protocol, however, increases its design complexity, making it prone to many functional problems. Formal verification techniques are therefore needed to verify its correctness. This dissertation proposes a link-fault-tolerant, multiflit wormhole routing algorithm, and its formal modeling and verification using two different methodologies. An improvement upon the previously published fault-tolerant routing algorithm, a link-fault routing algorithm is proposed to relax the unrealistic node-fault assumptions of these algorithms, while avoiding deadlock conservatively by appropriately dropping network packets. This routing algorithm, together with its routing architecture, is then modeled in a process-algebra language LNT, and compositional verification techniques are used to verify its key functional properties. As a comparison, it is modeled using channel-level VHDL which is compiled to labeled Petri-nets (LPNs). Algorithms for a partial order reduction method on LPNs are given. An optimal result is obtained from heuristics that trace back on LPNs to find causally related enabled predecessor transitions. Key observations are made from the comparison between these two verification methodologies

Rules and Meaning in Quantum Mechanics

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic.Comment: 150 page

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems