Algebraic Theory of Bounded One-dimensional Cellular Automata
نویسندگان
چکیده
A formal mathematical presentation of various algebraic properties of rule 90 elementary one-dimensional cellular automata (CA) with null boundary conditions is given. The CA global rule transition matrix is given and its characteristic polynomial is formally obtained. Mathematical relationships between the CA register lengths and the orders of the corresponding group or semigroup algebraic structures are derived.
منابع مشابه
SOME HYPER K-ALGEBRAIC STRUCTURES INDUCED BY MAX-MIN GENERAL FUZZY AUTOMATA
We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...
متن کاملEfficient exhaustive listings of reversible one dimensional cellular automata
This paper looks at an algebraic formulation of one dimensional cellular automata. Using the formulation, certain properties become apparent and connections to combinatorial structures and graph theory become clear. Strong results about uniqueness and isomorphism allows us to outline eeective algorithms for the generation of exhaustive lists of reversible one dimensional cellular automata, and ...
متن کاملAlgebraic Characterizations of Unitary Linear Quantum Cellular Automata
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the quantum cellular automata’s computational power. The configurations we consider have finite but unbounded size.
متن کاملOn Decidability Properties of One-Dimensional Cellular Automata
In a recent paper Sutner proved that the first-order theory of the phase-space SA = (Q ,−→) of a one-dimensional cellular automaton A whose configurations are elements of Q, for a finite set of states Q, and where −→ is the “next configuration relation”, is decidable [Sut09]. He asked whether this result could be extended to a more expressive logic. We prove in this paper that this is actuallly...
متن کاملBounded Languages Meet Cellular Automata with Sparse Communication
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell communication by bounding the number of allowed uses of the links between cells. Moreover, we consider the devices as acceptors for bounded languages in order to ex...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Complex Systems
دوره 3 شماره
صفحات -
تاریخ انتشار 1989