Interactive computations in algorithmic algebras

A conception of interactive computations is developed on the basis of the algebraic-logical approach.Translated from Kibernetika, No. 1, pp. 13–20, January–February, 1990.     

Independence of axiom system of basic algebras

We prove that the axiom system of basic algebras as given in Chajda and Emanovsky (Discuss Math Gen Algebra Appl 24:31–42, 2004) is not independent. The axiom (BA3) can be deleted and the remaining axioms are shown to be independent. The case when the axiom of double negation is deleted is also treated. This work is supported by the Research Project MSM6198959214 by Czech Government.     

On some classes of algorithmic algebras

Two classes of algorithmic algebras are studied: S^*-algebras, which are a direct generalization of S-algebras (algebras with closed conditions), and Markov systems of algorithmic algebras (a stochastic version of algorithmic algebras).Translated from Kibernetika, No. 3, pp. 100–104, May–June 1990.     

Glushkov algorithmic algebras and system modeling

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 106–116, May–June, 1993.     

On the algorithmic complexity of associative algebras

The complexity L(A) of a finite dimensional associative algebra A is the number of non-scalar multiplications/divisions of an optimal algorithm to compute the product of two elements of the algebra. We show

$\text{L(A) ? 2ddim A?t}$

, where t is the number of maximal two-sided ideals of A.     

Multilevel block design of discrete devices using algorithmic algebras

Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 42–52, March–April, 1995.     

Development systems with finite axiom sets

In this paper the notion of a developmental system without interactions is generalized to include a finite number of axioms (rather than one). It is shown that whereas this generalization considerably increases the class of languages generated, the main properties of the larger class of languages are basically the same as those of the smaller class.     

Developmental systems with finite axiom sets Part II. systems with interactions

In this paper the notion of a developmental system with interactions is generalized to include a finite number of (rather than one) axioms. It is shown that whereas this generalization considerably enlarges the class of languages generated, the main properties of the larger class of languages are basically the same as those of the smaller class     

PHAVer: algorithmic verification of hybrid systems past HyTech

In 1995, HyTech broke new ground as a potentially powerful tool for verifying hybrid systems. But due to practical and systematic limitations it is only applicable to relatively simple systems. We address the main problems of HyTech with PHAVer, a new tool for the exact verification of safety properties of hybrid systems with piecewise constant bounds on the derivatives, so-called linear hybrid automata. Affine dynamics are handled by on-the-fly overapproximation and partitioning of the state space based on user-provided constraints and the dynamics of the system. PHAVer features exact arithmetic in a robust implementation that, based on the Parma Polyhedra Library, supports arbitrarily large numbers. To force termination and manage the complexity of the polyhedral computations, we propose methods to conservatively limit the number of bits and constraints of polyhedra. Experimental results for a navigation benchmark and a tunnel diode circuit demonstrate the effectiveness of the approach. A preliminary version of this paper appeared in the Proceedings of Hybrid Systems: Computation and Control (HSCC 2005), Lecture Notes in Computer Science 3414, Springer-Verlag, 2005, pp. 258–273.     

Process algebras for systems diagnosis

In this paper we propose a new characterization of model-based diagnosis based on process algebras, a framework which is widely used in several areas of computer science. We show that process algebras provide a powerful modelling language which allows us to capture, in an uniform way, different types of models of physical systems, including models of time-varying and dynamic behavior. Then we provide a characterization of diagnosis which is equivalent to the “classical” abductive one. This suggests new interesting opportunities for research on relations between model-based reasoning and process algebras.