2,964 research outputs found
On the Commutative Equivalence of Context-Free Languages
The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated
A Chomsky-SchĂĽtzenberger-Stanley type characterization of the class of slender context-free languages
Slender context-free languages have a complete algebraic characterization by L. Ilie in [13]. In this paper we give another characterization of this class of languages. In particular, using linear Dyck languages instead of unrestricted ones, we obtain a Chomsky-SchĂĽtzenberger-Stanley type characterization of slender context-free languages
Structural properties of bounded languages with respect to multiplication by a constant
peer reviewedWe consider the preservation of recognizability of a set of integers after multiplication by a constant for numeration systems built over a bounded language. As a corollary we show that any nonnegative integer can be written as a sum of binomial coefficients with some prescribed properties
Unusual algorithms for lexicographical enumeration
Using well-known results, we consider algorithms for finding minimal words of given length n in regular and context-free languages. We also show algorithms enumerating the words of given length n of regular and contextfree languages in lexicographical order
Splittings and automorphisms of relatively hyperbolic groups
We study automorphisms of a relatively hyperbolic group G. When G is
one-ended, we describe Out(G) using a preferred JSJ tree over subgroups that
are virtually cyclic or parabolic. In particular, when G is toral relatively
hyperbolic, Out(G) is virtually built out of mapping class groups and subgroups
of GL_n(Z) fixing certain basis elements. When more general parabolic groups
are allowed, these subgroups of GL_n(Z) have to be replaced by McCool groups:
automorphisms of parabolic groups acting trivially (i.e. by conjugation) on
certain subgroups. Given a malnormal quasiconvex subgroup P of a hyperbolic
group G, we view G as hyperbolic relative to P and we apply the previous
analysis to describe the group Out(P to G) of automorphisms of P that extend to
G: it is virtually a McCool group. If Out(P to G) is infinite, then P is a
vertex group in a splitting of G. If P is torsion-free, then Out(P to G) is of
type VF, in particular finitely presented. We also determine when Out(G) is
infinite, for G relatively hyperbolic. The interesting case is when G is
infinitely-ended and has torsion. When G is hyperbolic, we show that Out(G) is
infinite if and only if G splits over a maximal virtually cyclic subgroup with
infinite center. In general we show that infiniteness of Out(G) comes from the
existence of a splitting with infinitely many twists, or having a vertex group
that is maximal parabolic with infinitely many automorphisms acting trivially
on incident edge groups.Comment: Minor modifications. To appear in Geometry Groups and Dynamic
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