Group sequential hypothesis tests with variable group sizes: optimal design and performance evaluation

In this paper, we propose a computer-oriented method of construction of optimal group sequential hypothesis tests with variable group sizes. In particular, for independent and identically distributed observations we obtain the form of optimal group sequential tests which turn to be a particular case of sequentially planned probability ratio tests (SPPRTs, Schmitz, 1993) . Formulas are given for computing the numerical characteristics of general SPPRTs, like error probabilities, average sampling cost, etc. A numerical method of designing the optimal tests and evaluation of the performance characteristics is proposed, and computer algorithms of its implementation are developed. For a particular case of sampling from a Bernoulli population, the proposed method is implemented in R programming language, the code is available in a public GitHub repository. The proposed method is compared numerically with other known sampling plans.Comment: 17 pages, 3 figures, 1 tabl

A System for Deduction-based Formal Verification of Workflow-oriented Software Models

The work concerns formal verification of workflow-oriented software models using deductive approach. The formal correctness of a model's behaviour is considered. Manually building logical specifications, which are considered as a set of temporal logic formulas, seems to be the significant obstacle for an inexperienced user when applying the deductive approach. A system, and its architecture, for the deduction-based verification of workflow-oriented models is proposed. The process of inference is based on the semantic tableaux method which has some advantages when compared to traditional deduction strategies. The algorithm for an automatic generation of logical specifications is proposed. The generation procedure is based on the predefined workflow patterns for BPMN, which is a standard and dominant notation for the modeling of business processes. The main idea for the approach is to consider patterns, defined in terms of temporal logic,as a kind of (logical) primitives which enable the transformation of models to temporal logic formulas constituting a logical specification. Automation of the generation process is crucial for bridging the gap between intuitiveness of the deductive reasoning and the difficulty of its practical application in the case when logical specifications are built manually. This approach has gone some way towards supporting, hopefully enhancing our understanding of, the deduction-based formal verification of workflow-oriented models.Comment: International Journal of Applied Mathematics and Computer Scienc

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks

Permission-Based Separation Logic for Multithreaded Java Programs

This paper presents a program logic for reasoning about multithreaded Java-like programs with dynamic thread creation, thread joining and reentrant object monitors. The logic is based on concurrent separation logic. It is the first detailed adaptation of concurrent separation logic to a multithreaded Java-like language. The program logic associates a unique static access permission with each heap location, ensuring exclusive write accesses and ruling out data races. Concurrent reads are supported through fractional permissions. Permissions can be transferred between threads upon thread starting, thread joining, initial monitor entrancies and final monitor exits. In order to distinguish between initial monitor entrancies and monitor reentrancies, auxiliary variables keep track of multisets of currently held monitors. Data abstraction and behavioral subtyping are facilitated through abstract predicates, which are also used to represent monitor invariants, preconditions for thread starting and postconditions for thread joining. Value-parametrized types allow to conveniently capture common strong global invariants, like static object ownership relations. The program logic is presented for a model language with Java-like classes and interfaces, the soundness of the program logic is proven, and a number of illustrative examples are presented

WIRIS OM tools: a semantic formula editor

With the increasing reliance on computers for the automatic processing of information a new method is needed for editing mathematical formulae. We are used to WYSIWYG editors that produce beautiful presentations of formulae and store the typesetting primitives rather than the meaning of the formulas. However, new services such as database searching or calculation web-services work best if they have access to the semantic information behind a formula. This can only be done with a new generation of formula editors. In this paper we present WIRIS OM Tools [17], a semantic oriented formula editor which addresses these concerns. It is based on the OpenMath language and a suitable transformation process between OpenMath and MathML ex- pressions. Additionally, this approach adds new features for the users such as error, type and syntax checking. The editor is currently being used in the LeActiveMath and WebALT projects

A Modal Logic for Subject-Oriented Spatial Reasoning

We present a modal logic for representing and reasoning about space seen from the subject\u27s perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete