Abstract Is the current formulation of multiset theory, which is based on sets and multiplicities of their elements, adequate? We exhibit both mathematical and metamathematical reasons which should cause one to rethink the definition. Some problems with multiset theory in its accepted formulation concern even the basic operations of union, intersection, and complement; others, more deeply rooted, concern Cartesian products, relations, or morphisms. We compare current definitions and conclude that the problems of multiset theory need to be resolved at the fundamental level of sets and mappings (or equivalent constructs) with multiplicities introduced only as a secondary concept. As a consequence, we propose to define multisets as families. A mapping establishes the connection to the familiar theory of multisets. Without losing anything, our proposal is simple and provides for an elegant mathematical theory.

A grammar-based approach to the specification of mathematical notation is proposed. The method is based on a meta-structure using attributed context-free grammars for capturing the meaning of mathematical concepts. The proposal is based on an authoring model which addresses the user needs as a fundamental requirement. It is structured around a scope mechanism allowing the mapping between semantics and syntax to be modified at any time during authoring. This process supports the dynamics of the meaning-to-syntax binding necessary in the authoring of mathematical concepts. Modular grammar fragments characterized by a one-to-one mapping between mathematical concept and grammar representation provide the adequate support for the definition of the various scopes. An incremental update process is defined to modify the grammar fragments which support the changes needed in the authoring process.

In this paper, a new compaction technique based on signature analysis is presented. Rather than comparing the final signature with the expected one after the test is completed, the binary output of the MISA is converted into an alternating binary signal by two simple cover circuits. An error is indicated whenever the alternation of the output signal is disturbed. This technique results in a higher fault coverage, improved fault diagnosis capability, a greater test autonomy in core-based designs, and early fault notification.

The notions of independence and dimension as introduced by Cohn for universal algebras are quite significantly different from the standard ones. This paper compares some of these notions. In particular, necessary and sufficient conditions for spanning and generating to coincide are derived. Moreover, the paper exhibits a new class of algebras which have bases and well-defined dimensions. This class extends that of v * -algebras and is incomparable with the class of v ** -algebras.

No abstract available.

In this work a termination condition for the Arimoto-Blahut algorithm for computing the capacity of a discrete memoryless channel will be discussed which turns out to decrease the number of iterations needed in many cases.