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- Bakhadyr Khoussainov, Anil Nerode
- LCC
- 1994

A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay (unpublished manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, New York, May 1975, 215 pp.) and Chaitin (IBM J. Res. Develop. 21 (1977) 350–359, 496.) we say that an r.e. real dominates an r.e. real if… (More)

- Bakhadyr Khoussainov, André Nies, Sasha Rubin, Frank Stephan
- Proceedings of the 19th Annual IEEE Symposium on…
- 2004

This paper studies the existence of automatic presentations for various algebraic structures. The automatic Boolean algebras are characterised, and it is proven that the free Abelian group of infinite rank and many Fraisse limits do not have automatic presentations. In particular, the countably infinite random graph and the universal partial order do not… (More)

- Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore, Arkadii M. Slinko
- Ann. Pure Appl. Logic
- 2002

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting.… (More)

- Bakhadyr Khoussainov, Sasha Rubin, Frank Stephan
- ACM Trans. Comput. Log.
- 2005

We investigate partial orders that are computable, in a precise sense, by finite automata. Our emphasis is on trees and linear orders. We study the relationship between automatic linear orders and trees in terms of rank functions that are related to Cantor--Bendixson rank. We prove that automatic linear orders and automatic trees have finite rank. As an… (More)

- Bakhadyr Khoussainov, André Nies, Richard A. Shore
- Notre Dame Journal of Formal Logic
- 1997

A real is computable if its left cut, L( ); is computable. If (qi)i is a computable sequence of rationals computably converging to ; then fqig; the corresponding set, is always computable. A computably enumerable (c.e.) real is a real which is the limit of an increasing computable sequence of rationals, and has a left cut which is c.e. We study the Turing… (More)

- Greg Hjorth, Bakhadyr Khoussainov, Antonio Montalbán, André Nies
- 2008 23rd Annual IEEE Symposium on Logic in…
- 2008

We study the classes of Buchi and Rabin automatic structures. For Buchi (Rabin) automatic structures their domains consist of infinite strings (trees), and the basic relations, including the equality relation, and graphs of operations are recognized by Buchi (Rabin) automata. A Buchi (Rabin) automatic structure is injective if different infinite strings… (More)

- Bakhadyr Khoussainov, Sasha Rubin, Frank Stephan
- STACS
- 2004

We show there is a computable linear order with a 02 initial segment that is not isomorphic to any computable linear order.