It was proved earlier by A. Ambainis and R. Freivalds that the quantum finite automata with pure states can have exponentially smaller number of states than the deterministic finite automata recognizing the same language. There is a never published “folk theorem” claiming that the quantum finite automata with mixed states are no more than super-exponentially concise than the deterministic finit...

We study expansive invertible onesided cellular automata (i.e., expansive automorphisms of onesided full shifts) and find severe dynamical and arithmetic constraints which provide partial answers to questions raised by M. Nasu [N2]. We employ the images and bilateral dimension groups, measure multipliers, and constructive combinatorial characterizations for two classes of cellular automata.

We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy automata and to the decidability of freeness for semigroups generated by two-letter invertible-reversible Mealy automata.

In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-called time-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.

We investigate the language classes recognized by group automata over matrix groups. We present a summary of the results obtained so far together with a number of new results. We look at the computational power of time-bounded group automata where the group under consideration has polynomial growth.

In this paper,we introduce a new verifiable multi-use multi-secretsharing scheme based on automata and one-way hash function. The scheme has theadversary fuzzy structure and satisfy the following properties:1) The dealer can change the participants and the adversary fuzzy structure without refreshing any participants' real-shadow. 2) The scheme is based on the inversion of weakly invertible fin...

Abstract Stateless ordered restart-delete automata (stl-ORD-automata) are studied. These obtained from the stateless restarting (stl-ORWW-automata) by introducing an additional operation, which, based on surrounding context, deletes a single letter. While stl-ORWW-automata accept regular languages, we show that swift stl-ORD-automata yield characterization for class of context-free languages. H...

Many decision problems concerning cellular automata are known to be decidable in the case of algebraic automata, that is, when state set has an structure and automaton acts as a morphism. The most studied cases include finite fields, commutative rings groups. In this paper, we provide methods generalize these results broader group where is (possibly non-commutative) group. configuration space n...

Valence automata are a generalization of various models of automata with storage. Here, each edge carries, in addition to an input word, an element of a monoid. A computation is considered valid if multiplying the monoid elements on the visited edges yields the identity element. By choosing suitable monoids, a variety of automata models can be obtained as special valence automata. This work is ...