1,456 research outputs found
Patterns theory and geodesic automatic structure for a class of groups
We introduce a theory of "patterns" in order to study geodesics in a certain
class of group presentations. Using patterns we show that there does not exist
a geodesic automatic structure for certain group presentations, and that
certain group presentations are almost convex.Comment: Appeared in 2003. I am putting all my past papers on arxi
State Complexity of Reversals of Deterministic Finite Automata with Output
We investigate the worst-case state complexity of reversals of deterministic
finite automata with output (DFAOs). In these automata, each state is assigned
some output value, rather than simply being labelled final or non-final. This
directly generalizes the well-studied problem of determining the worst-case
state complexity of reversals of ordinary deterministic finite automata. If a
DFAO has states and possible output values, there is a known upper
bound of for the state complexity of reversal. We show this bound can be
reached with a ternary input alphabet. We conjecture it cannot be reached with
a binary input alphabet except when , and give a lower bound for the
case . We prove that the state complexity of reversal depends
solely on the transition monoid of the DFAO and the mapping that assigns output
values to states.Comment: 18 pages, 3 tables. Added missing affiliation/funding informatio
The Gremlin Graph Traversal Machine and Language
Gremlin is a graph traversal machine and language designed, developed, and
distributed by the Apache TinkerPop project. Gremlin, as a graph traversal
machine, is composed of three interacting components: a graph , a traversal
, and a set of traversers . The traversers move about the graph
according to the instructions specified in the traversal, where the result of
the computation is the ultimate locations of all halted traversers. A Gremlin
machine can be executed over any supporting graph computing system such as an
OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph
traversal language, is a functional language implemented in the user's native
programming language and is used to define the of a Gremlin machine.
This article provides a mathematical description of Gremlin and details its
automaton and functional properties. These properties enable Gremlin to
naturally support imperative and declarative querying, host language
agnosticism, user-defined domain specific languages, an extensible
compiler/optimizer, single- and multi-machine execution models, hybrid depth-
and breadth-first evaluation, as well as the existence of a Universal Gremlin
Machine and its respective entailments.Comment: To appear in the Proceedings of the 2015 ACM Database Programming
Languages Conferenc
Testing the Equivalence of Regular Languages
The minimal deterministic finite automaton is generally used to determine
regular languages equality. Antimirov and Mosses proposed a rewrite system for
deciding regular expressions equivalence of which Almeida et al. presented an
improved variant. Hopcroft and Karp proposed an almost linear algorithm for
testing the equivalence of two deterministic finite automata that avoids
minimisation. In this paper we improve the best-case running time, present an
extension of this algorithm to non-deterministic finite automata, and establish
a relationship between this algorithm and the one proposed in Almeida et al. We
also present some experimental comparative results. All these algorithms are
closely related with the recent coalgebraic approach to automata proposed by
Rutten
Monotone Grid Drawings of Planar Graphs
A monotone drawing of a planar graph is a planar straight-line drawing of
where a monotone path exists between every pair of vertices of in some
direction. Recently monotone drawings of planar graphs have been proposed as a
new standard for visualizing graphs. A monotone drawing of a planar graph is a
monotone grid drawing if every vertex in the drawing is drawn on a grid point.
In this paper we study monotone grid drawings of planar graphs in a variable
embedding setting. We show that every connected planar graph of vertices
has a monotone grid drawing on a grid of size , and such a
drawing can be found in O(n) time
The finite tiling problem is undecidable in the hyperbolic plane
In this paper, we consider the finite tiling problem which was proved
undecidable in the Euclidean plane by Jarkko Kari in 1994. Here, we prove that
the same problem for the hyperbolic plane is also undecidable
Building the Minimal Automaton of A*X in Linear Time, When X Is of Bounded Cardinality
International audienceWe present an algorithm for constructing the minimal automaton recognizing A∗X, where the pattern X is a set of m (that is a fixed integer) non-empty words over a finite alphabet A whose sum of lengths is n. This algorithm, inspired by Brzozowski's minimization algorithm, uses sparse lists to achieve a linear time complexity with respect to n
On groups and counter automata
We study finitely generated groups whose word problems are accepted by
counter automata. We show that a group has word problem accepted by a blind
n-counter automaton in the sense of Greibach if and only if it is virtually
free abelian of rank n; this result, which answers a question of Gilman, is in
a very precise sense an abelian analogue of the Muller-Schupp theorem. More
generally, if G is a virtually abelian group then every group with word problem
recognised by a G-automaton is virtually abelian with growth class bounded
above by the growth class of G. We consider also other types of counter
automata.Comment: 18 page
Inverse monoids and immersions of 2-complexes
It is well known that under mild conditions on a connected topological space
, connected covers of may be classified via conjugacy
classes of subgroups of the fundamental group of . In this paper,
we extend these results to the study of immersions into 2-dimensional
CW-complexes. An immersion between
CW-complexes is a cellular map such that each point has a
neighborhood that is mapped homeomorphically onto by . In order
to classify immersions into a 2-dimensional CW-complex , we need to
replace the fundamental group of by an appropriate inverse monoid.
We show how conjugacy classes of the closed inverse submonoids of this inverse
monoid may be used to classify connected immersions into the complex
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