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- Pierre Fraigniaud, Ivan Rapaport, Ville Salo, Ioan Todinca
- DISC
- 2016

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)

- Ville Salo, Ilkka Törmä
- Fundam. Inform.
- 2013

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)

- Jarkko Kari, Martín Matamala, Ivan Rapaport, Ville Salo
- SIROCCO
- 2015

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)

- Jarkko Kari, Ville Salo
- Algebraic Foundations in Computer Science
- 2011

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)

- Ville Salo
- AUTOMATA & JAC
- 2012

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)

- Ville Salo, Ilkka Törmä
- MFCS
- 2012

We investigate the computational properties of cellular automata on countable (equivalently, zero entropy) sofic shifts with an emphasis on nilpotency, periodicity, and asymptotic behavior. As a tool for proving decidability results, we prove the Starfleet Lemma, which is of independent interest. We present computational results including the decidability… (More)

- Tim Boykett, Jarkko Kari, Ville Salo
- RC
- 2016

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)

- Ville Salo, Ilkka Törmä
- Automata
- 2013

We discuss bipermutive cellular automata from a combinatorial and topological perspective. We prove a type of topological randomizing property for bipermutive CA, show that the commutator of a bipermutive CA is always small and that bipermutive affine CA have only affine CA in their commutator. We show the last result also in the multidimensional case,… (More)

- Ville Salo, Ilkka Törmä
- AUTOMATA & JAC
- 2012

We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of two-dimensional countable subshifts with interesting properties. We present an SFT whose iterated derivatives are maximally… (More)

- Ville Salo, Ilkka Törmä
- Automata
- 2015