183 research outputs found
Polishness of some topologies related to word or tree automata
We prove that the B\"uchi topology and the automatic topology are Polish. We
also show that this cannot be fully extended to the case of a space of infinite
labelled binary trees; in particular the B\"uchi and the Muller topologies are
not Polish in this case.Comment: This paper is an extended version of a paper which appeared in the
proceedings of the 26th EACSL Annual Conference on Computer Science and
Logic, CSL 2017. The main addition with regard to the conference paper
consists in the study of the B\"uchi topology and of the Muller topology in
the case of a space of trees, which now forms Section
Transfinite Lyndon words
In this paper, we extend the notion of Lyndon word to transfinite words. We
prove two main results. We first show that, given a transfinite word, there
exists a unique factorization in Lyndon words that are densely non-increasing,
a relaxation of the condition used in the case of finite words.
In the annex, we prove that the factorization of a rational word has a
special form and that it can be computed from a rational expression describing
the word
Continuity of Functional Transducers: A Profinite Study of Rational Functions
A word-to-word function is continuous for a class of languages~
if its inverse maps _languages to~. This notion
provides a basis for an algebraic study of transducers, and was integral to the
characterization of the sequential transducers computable in some circuit
complexity classes.
Here, we report on the decidability of continuity for functional transducers
and some standard classes of regular languages. To this end, we develop a
robust theory rooted in the standard profinite analysis of regular languages.
Since previous algebraic studies of transducers have focused on the sole
structure of the underlying input automaton, we also compare the two algebraic
approaches. We focus on two questions: When are the automaton structure and the
continuity properties related, and when does continuity propagate to
superclasses
INCREASING CONCENTRATION IN THE U.S. HARD WHEAT MILLING INDUSTRY
This research shows that increased concentration in the U.S. wheat milling industry has not led to noncompetive pricing in upstream or downstream markets. Increased concentration has helped to reduce the marketing margin by $0.65 for every 100 pounds of flour produced. This is about 7% of the average marketing margin.Crop Production/Industries, Industrial Organization,
Algebraic Characterization of FO for Scattered Linear Orderings
We prove that for the class of sets of words indexed by countable scattered linear orderings, there is an equivalence between definability in first-order logic, star-free expressions with marked product, and recognizability by finite aperiodic semigroups which satisfy some additional equation
Ambiguity through the lens of measure theory
In this paper, we consider automata accepting irreducible sofic shifts, that
is, strongly connected automata where each state is initial and final. We
provide a characterization of unambiguity for finite words by means of measure
of sets of infinite sequences labelling two runs. More precisely, we show that
such an automaton is unambiguous, in the sense that no finite word labels two
runs with the same starting state and the same ending state if and only if for
each state, the set of infinite sequences labelling two runs starting from that
state has measure zero
- …