1,913 research outputs found
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
Homology and closure properties of autostackable groups
Autostackability for finitely presented groups is a topological property of
the Cayley graph combined with formal language theoretic restrictions, that
implies solvability of the word problem. The class of autostackable groups is
known to include all asynchronously automatic groups with respect to a
prefix-closed normal form set, and all groups admitting finite complete
rewriting systems. Although groups in the latter two classes all satisfy the
homological finiteness condition , we show that the class of
autostackable groups includes a group that is not of type . We also show
that the class of autostackable groups is closed under graph products and
extensions.Comment: 20 page
Automatic enumeration of regular objects
We describe a framework for systematic enumeration of families combinatorial
structures which possess a certain regularity. More precisely, we describe how
to obtain the differential equations satisfied by their generating series.
These differential equations are then used to determine the initial counting
sequence and for asymptotic analysis. The key tool is the scalar product for
symmetric functions and that this operation preserves D-finiteness.Comment: Corrected for readability; To appear in the Journal of Integer
Sequence
An undecidability result on limits of sparse graphs
Given a set B of finite rooted graphs and a radius r as an input, we prove
that it is undecidable to determine whether there exists a sequence (G_i) of
finite bounded degree graphs such that the rooted r-radius neighbourhood of a
random node of G_i is isomorphic to a rooted graph in B with probability
tending to 1. Our proof implies a similar result for the case where the
sequence (G_i) is replaced by a unimodular random graph.Comment: 6 page
A language theoretic analysis of combings
A group is combable if it can be represented by a language of words
satisfying a fellow traveller property; an automatic group has a synchronous
combing which is a regular language. This paper gives a systematic analysis of
the properties of groups with combings in various formal language classes, and
of the closure properties of the associated classes of groups. It generalises
previous work, in particular of Epstein et al. and Bridson and Gilman.Comment: DVI and Post-Script files only, 21 pages. Submitted to International
Journal of Algebra and Computatio
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