Formal Semantics for Ward & Mellor's TRANSFORMATION SCHEMA's and its Application to Fault-Tolerant Systems

A family of formal semantics is given for the Essential Model of the Transformation Schema of Ward & Mellor using recent techniques developed for defining the semantics of Statecharts by Pnueli and Huizing. A number of ambiguities and inconsistencies in Ward & Mellor's original definition is resolved. The models developed closely resemble those used for synchronous languages. Each model has its own application area, e.g., one fits best for fault-tolerant systems

Absolute metingen der geluidsintensiteit ter bepaling van het minimum audible

In this thesis a method is described of measuring the intensity of sound, more especially of weak sounds, down to energy valus of 10(-10) ergs per cm2 per sec. In the first chapter a number of formulas are mentioned regarding the energetics of sound. A relation is obtained for the radiating power from a vibrating circular plate, clamped at the edge, and compared with the results of other investigators. The literature concerning absolute measurements of the intensity of sound is discussed. ... Zie: Summary

Generalizations of Rice’s Theorem, Applicable to Executable and Non-Executable Formalisms

We formulate and prove two Rice-like theorems that characterize limitations on nameability of properties within a given naming scheme for partial functions. Such a naming scheme can, but need not be, an executable formalism. A programming language is an example of an executable naming scheme, where the program text names the partial function it implements. Halting is an example of a property that is not nameable in that naming scheme. The proofs reveal requirements on the naming scheme to make the characterization work. Universal programming languages satisfy these requirements, but also other formalisms can satisfy them. We present some non-universal programming languages and a non-executable specification language satisfying these requirements. Our theorems have Turing’s well-known Halting Theorem and Rice’s Theorem as special cases, by applying them to a universal programming language or Turing Machines as naming scheme. Thus, our proofs separate the nature of the naming scheme (which can, but need not, coincide with computability) from the diagonal argument. This sheds further light on how far reaching and simple the ‘diagonal ’ argument is in itself.

Preface

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Cooperation-Based Invariants for OO Languages

In general, invariants may depend on the state of other objects. The approach introduced in this paper allows this for objects of mutually visible classes, in a way that supports modular verification. To this end, dependencies are made explicit by cooperation. In particular, invariants expressing non-hierarchical object relations are supported. Furthermore, an inc-set allows a method to specify explicitly that it does not depend on the validity of a certain invariant. This way, it can be called even when that invariant is violated.

Halting still standing - Programs versus specifications

In UTP’06 [4], Hehner claims that the traditional proof of the incomputability of the Halting Function is rather a proof of the inconsistency of its specification. We identify where his argument fails. Hehner claims that assuming a well-defined Halting Function for specifications leads to a contradiction by a very similar argument as assuming a computable Halting Function for programs does. In the case of programs, this argument leads to concluding that the Halting Function is not computable, porting the proof to the case of specifications, it is claimed to allow concluding that the Halting Function is ill-defined. He reasons that if the Halting Function for specifications is ill-defined, then the concept of the Halting Function in general is inconsistent, including the one for programs. We do not challenge this generalization, but rather point out a flaw in his argument for the specification case. We formalize his argument in UTP-style. This enables us to show that there is a subtle tacit assumption being made about the recursive definition that is used to arrive at the contradiction, namely that the defining equation has a solution. We also explain why this does not affect the proof for the program case. Furthermore, we analyze whether recursion in the language Hehner uses is essential for his argument and our refutation. Porting the arguments to a language without recursion shows that the issue of the existence of the contradicting specification remains. We conclude that this line of argument does not challenge the healthiness of the concept of the Halting Function, including its extension to specifications

Formal semantics for Ward and Mellor's transformation schemas and its application to fault tolerant systems

A family of formal semantics is given for the Essential Model of the Transformation Schema of Ward and Mellor1 using recent techniques developed for defining the semantics of Statecharts2 by Pnueli and Huizing. A number of ambiguities and inconsistencies in Ward and Mellor's original definition is resolved. The models developed closely resemble those used for synchronous languages3. Each model has its own application area, e.g. one fits best for fault-tolerant systems