Related papers: A Finite-Automaton Based Stream Cipher As a Quasig…
The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are given.
A quasi-schemoid is a small category with a particular partition of the set of morphisms. We define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. As a homotopy invariant, the homotopy set of…
We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of…
A During last two decades, there has been a prolific growth in the chaos based image encryption algorithms. Up to an extent these algorithms have been able to provide an alternative to exchange large media files (images and videos) over the…
We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is…
A quantum finite-state automaton (QFA) is a theoretical model designed to simulate the evolution of a quantum system with finite memory in response to sequential input strings. We define the language of a QFA as the set of strings that lead…
We prove two characterisations of accessibility of locally finite quasi-transitive connected graphs. First, we prove that any such graph $G$ is accessible if and only if its set of separations of finite order is an ${\rm Aut}(G)$-finitely…
By definition, a group $G$ is quasi-perfect, if $G$ is perfect or the commutator subgroup of $G$ is perfect. In this note we give a description of quasi-perfect Dyer groups by properties of the corresponding Dyer graphs.
Nishioka et al claim in [1], elaborating on their earlier paper [2], that the direct encryption scheme called Y-00 [3,4] is equivalent to a classical non-random additive stream cipher, and thus offers no more security than the latter. In…
As an absolute invariant of smooth conjugacy, the multiplier group described the types of space-time symmetries that the flow has, and for a quasiperiodic flow on the $n$-torus, is the determining factor of the structure of its generalized…
This paper concerns the general problem of classifying the finite deterministic automata that admit a synchronizing (or reset) word. (For our purposes it is irrelevant if the automata has initial or final states.) Our departure point is the…
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the…
The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…
We introduce what --if some kind of group action exists-- is a truly (information theoretically) safe cryptographic communication system: a protocol which provides \emph{zero} information to any passive adversary having full access to the…
A token ring is an arrangement of N processors that take turns engaging in an activity which must be controlled. A token confers the right to engage in the controlled activity. Processors communicate with neighbors in the ring to obtain and…
Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…
For any class $\mathcal{C}$ of bipartite graphs, we define quasi-$\cal C$ to be the class of all graphs $G$ such that every bipartition of $G$ belongs to $\cal C$. This definition is motivated by a generalisation of the switch Markov chain…
We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.
A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a…
Simplified trusted nodes (STNs) are a form of trusted node for quantum key distribution (QKD) networks which do not require running a full QKD stack every instance (i.e., they do not need to run error correction and privacy amplification…