A general time-varying estimation and control problem

This paper solves two problems raised in [HSK]. The first is a uniform norm time-varying linear estimation problem and the second is a general time-varying linear control problem.     

An Abstract Decision Procedure for Satisfiability in the Theory of Recursive Data Types

The theory of recursive data types is a valuable modeling tool for software verification. In the past, decision procedures have been proposed for both the full theory and its universal fragment. However, previous work has been limited in various ways. In this paper, we present a general algorithm for the universal fragment. The algorithm is presented declaratively as a set of abstract rules which are terminating, sound, and complete. We show how other algorithms can be realized as strategies within our general framework. Finally, we propose a new strategy and give experimental results showing that it performs well in practice.     

On a new class of finite dimensional estimation algebras

We introduce a new class of solvable finite dimensional estimation algebras that contains both the linear and the Bene cases. The condition for finite dimensionality is expressed in terms of two matrices. They play an important role in understanding the structure of estimation algebras.     

Formal Performance Modelling and Evaluation of an Adaptive Mechanism for Packetised Audio over the Internet

A case study is presented which concerns the design of an adaptive mechanism for packetised audio for use over the Internet. During the design process, the audio mechanism was modelled with the stochastically timed process algebra EMPA and analysed via simulation by the EMPA based software tool TwoTowers in order to predict the percentage of packets that are received in time for being played out. The predicted performance figures obtained from the algebraic model illustrated in advance the adequacy of the approach adopted in the design of the audio playout delay control mechanism. Based on these performance figures, it was possible to implement and develop the complete mechanism without incurring additional costs due to the late discovery of unexpected errors or inefficiency. Performance results obtained from experiments conducted on the field confirmed the predictive simulative results. Received March 1997 / Accepted in revised form July 1998     

A generalized Ufnarovski graph

An important tool for studying standard finitely presented algebras is the Ufnarovski graph. In this paper we extend the use of the Ufnarovski graph to automaton algebras, introducing the generalized Ufnarovski graph. As an application, we show how this construction can be used to test Noetherianity of automaton algebras.     

Interpretability of first-order linear temporal logics in fork algebras

In this paper we prove theorems on the interpretability of the first-order temporal logics LTL and TL into Fork Algebras. This result is part of a research project on the interpretability of logics in Fork Algebras, and has important applications towards the relational specification of properties of systems within the Ar_gentum tool.     

Equitone Predicate Algebras and Their Applications

Predicates that preserve their values on a larger (extended) body of data are called equitone. An algebra of such predicates is constructed, a system of its generators is specified, and a complete system of transformations of identities is defined. The results obtained are used for construction and investigation of complete classes of compositions of various types and levels of abstractions that are used in logics of partial predicates.     

Nested semantics over finite trees are equationally hard

This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based.     

Peirce algebras

We present a two-sorted algebra, called aPeirce algebra, of relations and sets interacting with each other. In a Peirce algebra, sets can combine with each other as in a Boolean algebra, relations can combine with each other as in a relation algebra, and in addition we have both a set-forming operator on relations (the Peirce product of Boolean modules) and a relation-forming operator on sets (a cylindrification operation). Two applications of Peirce algebras are given. The first points out that Peirce algebras provide a natural algebraic framework for modelling certain programming constructs. The second shows that the so-calledterminological logics arising in knowledge representation have evolved a semantics best described as a calculus of relations interacting with sets.     

Transformational reducibility and synthesis of algorithms and programs of symbolic processing

This paper deals with the algebra of algorithmics in the context of developing modern means of transformation and synthesis of algorithms and programs in object-oriented environments. This report was first presented by the author in English at the conference ECI-2005 (Kosice, Slovakia). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 165–173, September–October 2006.