2,126 research outputs found
Monadic Second-Order Logic with Arbitrary Monadic Predicates
We study Monadic Second-Order Logic (MSO) over finite words, extended with
(non-uniform arbitrary) monadic predicates. We show that it defines a class of
languages that has algebraic, automata-theoretic and machine-independent
characterizations. We consider the regularity question: given a language in
this class, when is it regular? To answer this, we show a substitution property
and the existence of a syntactical predicate.
We give three applications. The first two are to give very simple proofs that
the Straubing Conjecture holds for all fragments of MSO with monadic
predicates, and that the Crane Beach Conjecture holds for MSO with monadic
predicates. The third is to show that it is decidable whether a language
defined by an MSO formula with morphic predicates is regular.Comment: Conference version: MFCS'14, Mathematical Foundations of Computer
Science Journal version: ToCL'17, Transactions on Computational Logi
Asymptotic properties of free monoid morphisms
Motivated by applications in the theory of numeration systems and
recognizable sets of integers, this paper deals with morphic words when erasing
morphisms are taken into account. Cobham showed that if an infinite word is the image of a fixed point of a morphism under another
morphism , then there exist a non-erasing morphism and a coding
such that .
Based on the Perron theorem about asymptotic properties of powers of
non-negative matrices, our main contribution is an in-depth study of the growth
type of iterated morphisms when one replaces erasing morphisms with non-erasing
ones. We also explicitly provide an algorithm computing and
from and .Comment: 25 page
Unambiguous 1-Uniform Morphisms
A morphism h is unambiguous with respect to a word w if there is no other
morphism g that maps w to the same image as h. In the present paper we study
the question of whether, for any given word, there exists an unambiguous
1-uniform morphism, i.e., a morphism that maps every letter in the word to an
image of length 1.Comment: In Proceedings WORDS 2011, arXiv:1108.341
Morphic and principal-ideal group rings
We observe that the class of left and right artinian left and right morphic
rings agrees with the class of artinian principal ideal rings. For an
artinian principal ideal ring and a group, we characterize when is a
principal ideal ring; for finite groups , this characterizes when is a
left and right morphic ring. This extends work of Passman, Sehgal and Fisher in
the case when is a field, and work of Chen, Li, and Zhou on morphic group
rings.Comment: 21 page
A remarkable sequence related to and
We prove that five ways to define entry A086377 in the On-Line Encyclopedia
of Integer Sequences do lead to the same integer sequence
Decidability of the HD0L ultimate periodicity problem
In this paper we prove the decidability of the HD0L ultimate periodicity
problem
Infinite genus surfaces and irrational polygonal billiards
We prove that the natural invariant surface associated with the billiard game
on an irrational polygonal table is homeomorphic to the Loch Ness monster, that
is, the only orientable infinite genus topological real surface with exactly
one end.Comment: 15 pages, 18 figure
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