Garden of Eden and specification

Abduction, unpredictability and Garden of Eden

Exact Enumeration of Garden of Eden Partitions

We give two proofs for a formula that counts the number of partitions of n that have rank −2 or less (which we call Garden of Eden partitions). These partitions arise naturally in analyzing the game Bulgarian solitaire, summarized in Section 1. Section 2 presents a generating function argument for the formula based on Dyson’s original paper where the rank of a partition is defined. Section 3 gi...

The Garden of Eden theorem: old and new

We review topics in the theory of cellular automata and dynamical systems that are related to the Moore-Myhill Garden of Eden theorem.

Linear Cellular Automata and the Garden-of-Eden

Suppose each of the squares of an n x n chessboard is equipped with an indicator light and a button. If the button of a square is pressed, the light of that square will change from off to on and vice versa; the same happens to the lights of all the edge-adjacent squares. Initially all lights are off. Now, consider the following question: is it possible to press a sequence of buttons in such a w...

Kolmogorov Complexity and the Garden of Eden Theorem

Suppose τ is a cellular automaton over an amenable group and a finite alphabet. Celebrated Garden of Eden theorem states, that pre-injectivity of τ is equivalent to non-existence of Garden of Eden configuration. In this paper we will prove, that imposing some mild restrictions , we could add another equivalent assertion: non-existence of Garden of Eden configuration is equivalent to preservatio...