The first example of a non-residually finite group in the classes finitely presented small-cancelation groups, automatic and $\\operatorname{CAT}(0)$ groups was constructed by Wise as fundamental complete square complex (CSC for short) with twelve squares. At same time, Janzen proved that CSCs at most three, five or seven squares have residually group. smallest open cases were four directed $\\...

It is inevitable for networks to be invaded during operation. The intrusion tolerance technology comes into being enable provide the necessary network services. This paper introduces an automatic learning mechanism of system update security strategy, and derives finite automaton model from existing model. proposed was quantified by Markov theory compute stable probability each state. calculated...

Physical universality of a cellular automaton was defined by Janzing in 2010 as the ability to implement an arbitrary transformation of spatial patterns. In 2014, Schaeffer gave a construction of a two-dimensional physically universal cellular automaton. We construct a one-dimensional version of the automaton.

We introduce a new tool, called the orbit automaton, that describes the action of an automaton group G on the subtrees corresponding to the orbits of G on levels of the tree. The connection between G and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work.

We present a language Ln which is recognizable by a probabilistic finite automaton (PFA) with probability 1− ǫ for all ǫ > 0 with O(logn) states, with a deterministic finite automaton (DFA) with O(n) states, but a quantum finite automaton (QFA) needs at least 2 log n) states.