In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of ...

One approach to formally specifying a system is to use a form of extended finite-state machine called a stream X-machine. A stream X-machine is a type of X-machine that describes a system as a finite set of states, each with an internal store, called memory, and a number of transitions between the states. A stream X-machine may be modelled by a finite automaton (the associated finite automaton)...

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.

The partial derivative automaton (Apd) is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptotic...

The central aim of this paper and its projected successors is to prove in detail that stimulus-response theory, or at least a mathematically precise version, can give an account of the learning of many phrase-structure grammars. Section 2 is concerned with standard notions of finite and probabilistic automata. An automaton is defined as a device with a finite number of internal states. Section ...

Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A.Ambainis and R.Freivalds that quantum finite automata with pure states can have exponentially smaller number of states than deterministic finite automata recognizing the same language. There was a never published ”folk theor...

A sequence s(n)n≥0 is called k-automatic if s(n) is a finite-memory function of the base-k digits of n. This means that some computer with only finitely many possible states can compute s(n) for any n by reading the base-k digits of n one at a time (beginning with the least significant digit) and following a transition rule that specifies the next state of the computer as a function of both the...

The visualization has become essential in many application areas. The finite graphs and automata undoubtedly belong to such areas. A problem of a visual image of a directed finite graph has appeared in the study of the road coloring conjecture. Given a finite directed graph, a coloring of its edges turns the graph into finitestate automaton. The visual perception of the structure properties of ...

We exhibit a family {Ln} of finite regular languages such that any 1-way quantum finite automaton (QFA) accepting Ln with probability 1 2 + ǫ (for any constant ǫ > 0) must have 2 Ω(n/ logn) states. On the other hand, each language Ln can be recognized by a deterministic finite automaton (DFA) of size O(n). This is in immediate contrast to the result of [1] which shows that for some regular lang...

The visualization has become essential in many application areas. The finite graphs and automata undoubtedly belong to such areas. A problem of a visual image of a directed finite graph has appeared in the study of the road coloring conjecture. Given a finite directed graph, a coloring of its edges turns the graph into finitestate automaton. The visual perception of the structure properties of ...