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From automatic structures to automatic groups
TLDR
This paper proves that all finitely generated 2-nilpotent groups and Baumslag-Solitar groups B(1,n) are graph automatic, as well as many other metabelian groups. Expand
Recursively enumerable reals and Chaitin Ω numbers
A real α is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay [23] and Chaitin [10] we say that an r.e. real α dominatesExpand
Degree spectra and computable dimensions in algebraic structures
TLDR
This paper shows how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings; rings (with zero-divisors); integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. Expand
Automata theory and its applications
1. Basic Notions.- 1.1 Sets.- 1.2 Sequences and Tuples.- 1.3 Functions, Relations, Operations.- 1.4 Equivalence Relations.- 1.5 Linearly Ordered Sets.- 1.6 Partially Ordered Sets.- 1.7 Graphs.- 1.8Expand
Deciding parity games in quasipolynomial time
TLDR
It is shown that the parity game can be solved in quasipolynomial time and it is proven that coloured Muller games with n nodes and m colours can be decided in time O((mm · n)5); it is also shown that this bound cannot be improved to O((2m · n), for any c, unless FPT = W[1]. Expand
Automatic structures: richness and limitations
TLDR
It is proven that the free Abelian group of infinite rank and many Fraisse limits do not have automatic presentations, and the complexity of the isomorphism problem for the class of all automatic structures is /spl Sigma//sub 1//sup 1/-complete. Expand
Automatic linear orders and trees
TLDR
It is shown that every infinite path in an automatic tree with countably many infinite paths is a regular language. Expand
Computable Models of Theories with Few Models
TLDR
It is shown that there exists an א1-categorical but not א0- categorical theory T such that all the countable models of T except its prime model, have computable presentations. Expand
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