A finitary axiomatization of the algebra of regular events involving only equations and equational implications that is sound for all interpretations over Kleene algebras is given. Axioms for Kleene algebra are presented, and some basic consequences are derived. Matrices over a Kleene algebra are considered. The notion of an automaton over an arbitrary Kleen algebra is defined and used to derive the classical results of the theory of finite automata as a result of the axioms. The completeness of the axioms for the algebra of regular events is treated. Open problems are indicated. >

A completeness theorem for Kleene algebras and the algebra of regular events

This is a survey paper on various topics concerning self-similar groups and branch groups with a focus on those notions and problems that are related to a 3-generated torsion 2 group of intermediate growth G, constructed by the author in 1980, and its generalizations Gω, ω ∈ {0, 1, 2}ℕ.

Solved and Unsolved Problems Around One Group

The paper represents the first part of a series of
 papers on realization theory of switched systems. Part I presents realization theory of linear switched systems,
 Part II presents realization theory of bilinear switched systems.
 More precisely, in Part I necessary and sufficient conditions
 are formulated for a family of input-output maps to be
 realizable by a linear switched system and a characterization
 of minimal realizations is presented. The paper treats two types of switched systems.
 The first one is when all switching sequences are allowed. The second one is when only a subset of switching sequences is
 admissible, but within this restricted set the switching times are arbitrary.
 The paper uses the theory of formal power series to derive
 the results on realization theory.

/pdf/realization-theory-for-linear-and-bilinear-switched-systems-3tl8w7f325.pdf

Realization theory for linear and bilinear switched systems: A formal power series approach - Part I: Realization theory of linear switched systems

The thesis address the realization problem for hybrid control systems. It develops realization theory for a number of classes of hybrid systems.

Realization theory of hybrid systems

The paper develops realization theory for linear hybrid systems, i.e., hybrid systems in continuous-time without guards whose continuous dynamics is determined by linear control systems and whose discrete dynamics is determined by a finite-state automaton. We will formulate necessary and sufficient conditions for the existence of a realization. We will show that minimality is equivalent to observability and span-reachability, and that minimal systems are isomorphic. In turn, observability and span-reachability can be characterized by rank conditions.

Realization Theory for Linear Hybrid Systems

Algebraic theory of automata

“The Archive” brings you selections from the Bulletin’s history to give you perspective on the history of currents in the field. In this edition, we bring you a piece from CSSR Bulletin (1991: 20.2) by the late Ira H. Peak, Jr. (d. 1915), an ethicist who worked at a number of North American universities throughout his career. While teaching at the University of Missouri—Columbia, Peak experimented with what he described as “the Evaluation Menu,” a pedagogical framework for empowering students to participate in the whole of the learning experience—even its grading.

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Algebraic theory of automata

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