Turku Centre for Computer Science

About: Turku Centre for Computer Science is a facility organization based out in Turku, Finland. It is known for research contribution in the topics: Decidability & Word (group theory). The organization has 382 authors who have published 1027 publications receiving 19560 citations.

GENERALIZED CONTEXTS AND n-ARY SYNTACTIC SEMIGROUPS OF TREE LANGUAGES

Abstract: A new type of syntactic monoid and semigroup of tree languages is introduced. For each n ≥ 1, we define for any tree language T its n-ary syntactic monoid Mn(T) and its n-ary syntactic semigroup Sn(T) as quotients of the monoid or semigroup, respectively, formed by certain new generalized contexts. For n = 1 these contexts are just the ordinary contexts (or 'special trees') and M1(T) is the syntactic monoid introduced by W. Thomas (1982,1984). Several properties of these monoids and semigroups are proved. For example, it is shown that Mn(T) and Sn(T) are isomorphic to certain monoids and semigroups associated with the minimal tree recognizer of T. Using these syntactic monoids or semigroups, we can associate with any variety of finite monoids or semigroups, respectively, a variety of tree languages. Although there are varieties of tree languages that cannot be obtained this way, we prove that the definite tree languages can be characterized by the syntactic semigroups S2(T), which is not possible using the classical syntactic monoids or semigroups.

A Uniquely Ergodic Cellular Automaton

Abstract: We construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on the self-simulating automaton of Gacs. We also prove related results of dynamical and computational nature, including the undecidability of unique ergodicity, and the undecidability of nilpotency in uniquely ergodic cellular automata.

Geometric Transformations of Language Families: The Power of Symmetry

Abstract: We consider certain isomorphisms between language families. When viewed as a group, the isomorphisms reduce to well-known geometric transformations. We obtain new characterizations for linear, simple matrix, simple contextual and trace languages. Our results make it possible to transfer results concerning languages in one family into results concerning languages in another family.

Distinguishability, Simulation and Universality of Moore Tree Automata

Abstract: We extend the notions of distinguishability of states, simulation and universality of string automata to tree automata of Moore type. In particular, we prove that for each finite class of tree automata satisfying certain conditions, there is a unique minimal universal tree automaton. The transfer from strings to trees brings new aspects but also adds difficulties in generalizing classical Moore results.

On MIDO Space-Time Block Codes

Abstract: In this paper, the need for the construction of multiple input-double output (MIDO) space-time block codes (STBCs) is discussed, concentrating on the case of four transmitters for simplicity. Above the trivial method, i.e. switching off the extra layers in the usual multiple input-multiple output (MIMO) setting, two smarter yet simple MIDO construction methods are proposed. The use of these general methods is then demonstrated by building explicit, sphere decodable codes using two different cyclic division algebras (CDAs). We verify by computer simulations that the newly proposed methods perform extremely well as opposed to the trivial construction.