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We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. We show that, for every connected 4-node graph H , testing whether a(More)
We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable SFT whose iterated derivatives are maximally complex from the computational point of view, constructions of countable(More)
We study the message size complexity of recognizing, under the broadcast congested clique model, whether a fixed graph H appears in a given graph G as a minor, as a subgraph or as an induced subgraph. The n nodes of the input graph G are the players, and each player only knows the identities of its immediate neighbors. We are mostly interested in the(More)
Picture walking automata were introduced by M. Blum and C. Hewitt in 1967 as a generalization of one-dimensional two-way finite automata to recognize pictures, or two-dimensional words. Several variants have been investigated since then, including deterministic, nondeterministic and alternating transition rules; four-, threeand two-way movements; singleand(More)
One of the most interesting aspects in the theory of cellular automata is the study of different types of nilpotency, that is, different ways in which a cellular automaton can force a particular symbol (usually called 0) to appear frequently in all its spacetime diagrams. The simplest such notion, called simply ‘nilpotency’, is that the cellular automaton c(More)
It is well-known that the Toffoli gate and the negation gate together yield a universal gate set, in the sense that every permutation of {0, 1}n can be implemented as a composition of these gates. Since every bit operation that does not use all of the bits performs an even permutation, we need to use at least one auxiliary bit to perform every permutation,(More)