On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

To Some Structural Properties Of ∞-languages

Properties of catenation of sequences of finite (words) and infinite (  lengths are largely studied in formal language theory. These operations are derived from the mechanism how they are accepted or generated by the corresponding devices. Finite automata accept structures containing only words, automata accept only words. Structures containing both words and words (∞ - words) are mostly generated by various types of ∞ - automata(∞- machines). The aim of the paper is to investigate algebraic properties of operations on ∞ - words generated by IGk –automata, where k is to model the depth of memory. It has importance in many applications (shift registers, discrete systems with memory,…). It is shown that resulting algebraic structures are of „pure“ groupoid or partial groupoid type

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time

Complementation and Inclusion of Weighted Automata on Infinite Trees

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally

Complementation and Inclusion of Weighted Automata on Infinite Trees: Revised Version

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation, and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally

Fuzzy finite switchboard automata with complete residuated lattices

The theory of fuzzy finite switchboard automata (FFSA) is introduced by the use of general algebraic structures such as complete residuated lattices in order to enhance the process ability of FFSA. We established the notion of homomorphism, strong homomorphism and reverse homomorphism and shows some of its properties. The subsystem of FFSA is studied and the set of switchboard subsystemforms a complete ℒ -sublattices is shown. The algorithm of FFSA with complete residuated lattices is given and an example is provided