25,156 research outputs found
Weak MSO+U with Path Quantifiers over Infinite Trees
This paper shows that over infinite trees, satisfiability is decidable for
weak monadic second-order logic extended by the unbounding quantifier U and
quantification over infinite paths. The proof is by reduction to emptiness for
a certain automaton model, while emptiness for the automaton model is decided
using profinite trees.Comment: version of an ICALP 2014 paper with appendice
Standard Young Tableaux and Colored Motzkin Paths
In this paper, we propose a notion of colored Motzkin paths and establish a
bijection between the -cell standard Young tableaux (SYT) of bounded height
and the colored Motzkin paths of length . This result not only gives a
lattice path interpretation of the standard Young tableaux but also reveals an
unexpected intrinsic relation between the set of SYTs with at most rows
and the set of SYTs with at most 2d rows.Comment: 21 page
-Colored Graphs - a Review of Sundry Properties
We review the combinatorial, topological, algebraic and metric properties
supported by -colored graphs, with a focus on those that are pertinent
to the study of tensor model theories. We show how to extract a limiting
continuum metric space from this set of graphs and detail properties of this
limit through the calculation of exponents at criticality
A note on the -coefficients of the "tree Eulerian polynomial"
We consider the generating polynomial of the number of rooted trees on the
set counted by the number of descending edges (a parent with
a greater label than a child). This polynomial is an extension of the descent
generating polynomial of the set of permutations of a totally ordered -set,
known as the Eulerian polynomial. We show how this extension shares some of the
properties of the classical one. B. Drake proved that this polynomial factors
completely over the integers. From his product formula it can be concluded that
this polynomial has positive coefficients in the -basis and we show
that a formula for these coefficients can also be derived. We discuss various
combinatorial interpretations of these positive coefficients in terms of
leaf-labeled binary trees and in terms of the Stirling permutations introduced
by Gessel and Stanley. These interpretations are derived from previous results
of the author and Wachs related to the poset of weighted partitions and the
free multibracketed Lie algebra.Comment: 13 pages, 6 figures, Interpretations derived from results in
arXiv:1309.5527 and arXiv:1408.541
Analyzing Timed Systems Using Tree Automata
Timed systems, such as timed automata, are usually analyzed using their
operational semantics on timed words. The classical region abstraction for
timed automata reduces them to (untimed) finite state automata with the same
time-abstract properties, such as state reachability. We propose a new
technique to analyze such timed systems using finite tree automata instead of
finite word automata. The main idea is to consider timed behaviors as graphs
with matching edges capturing timing constraints. When a family of graphs has
bounded tree-width, they can be interpreted in trees and MSO-definable
properties of such graphs can be checked using tree automata. The technique is
quite general and applies to many timed systems. In this paper, as an example,
we develop the technique on timed pushdown systems, which have recently
received considerable attention. Further, we also demonstrate how we can use it
on timed automata and timed multi-stack pushdown systems (with boundedness
restrictions)
Definability equals recognizability for graphs of bounded treewidth
We prove a conjecture of Courcelle, which states that a graph property is
definable in MSO with modular counting predicates on graphs of constant
treewidth if, and only if it is recognizable in the following sense:
constant-width tree decompositions of graphs satisfying the property can be
recognized by tree automata. While the forward implication is a classic fact
known as Courcelle's theorem, the converse direction remained openComment: 21 pages, an extended abstract will appear in the proceedings of LICS
201
- …