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We introduce a concept of similarity between vertices of directed graphs. Let G A and G B be two directed graphs with, respectively, n A and n B vertices. We define an n B × n A similarity matrix S whose real entry s ij expresses how similar vertex j (in G A) is to vertex i (in G B): we say that s ij is their similarity score. The similarity matrix can be… (More)

The virtual ant introduced by C. Langton has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one dimensional cellular automata and Turing machines, the… (More)

We introduce a concept of similarity between vertices of directed graphs. Let G A and G B be two directed graphs with respectively n A and n B vertices. We define a n B × n A similarity matrix S whose real entry s ij expresses how similar vertex j (in G A) is to vertex i (in G B) : we say that s ij is their similarity score. The similarity matrix can be… (More)

Together with the concept of reversibility, another relevant physical notion is time-symmetry, which expresses that there is no way of distinguishing between backward and forward time directions. This notion, found in physical theories, has been neglected in the area of discrete dynamical systems. Here we formalize it in the context of cellular automata and… (More)

- Anahí Gajardo
- JAC
- 2008