2012/01/26 by Pablo Arrighi, Vincent Nesme, Arrighi, Pablo +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #37B15 #37N20 #68Q80 #B.6.1 #Cellular Automata and Applications #DNA and Biological Computing #Discrete Mathematics (cs.DM) #F.1.1 #FOS: Computer and information sciences #FOS: Physical sciences #Formal Languages and Automata Theory (cs.FL) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #acm:37B15 #acm:37N20 #acm:68Q80 #cs.DM #cs.FL #msc:37B15 #msc:37N20 #msc:68Q80 #quant-ph
paper · pdf · doi:10.48550/arxiv.1201.5529
6 pages, 3 figures, Automata 2011
arxiv created 2012/01/26 · openalex publication_date 2012/01/26 · arxiv updated 2012/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Reversible Cellular Automata (RCA) are a physics-like model of computation consisting of an array of identical cells, evolving in discrete time steps by iterating a global evolution G. Further, G is required to be shift-invariant (it acts the same everywhere), causal (information cannot be transmitted faster than some fixed number of cells per time step), and reversible (it has an inverse which verifies the same requirements). An important, though only recently studied special case is that of Time-symmetric Cellular Automata (TSCA), for which G and its inverse are related via a local operation. In this note we revisit the question of the Block representation of RCA, i.e. we provide a very simple proof of the existence of a reversible circuit description implementing G. This operational, bottom-up description of G turns out to be time-symmetric, suggesting interesting connections with TSCA. Indeed we prove, using a similar technique, that a wide class of them admit an Exact block representation (EBR), i.e. one which does not increase the state space.