8 research outputs found
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where is the game quantifier. We
first give a detailed exposition of this result. Next, using an embedding of
the Wadge hierarchy of non self-dual Borel subsets of the Cantor space
into the class , and the notions of Wadge degree
and Veblen function, we argue that this upper bound on the topological
complexity of regular tree languages is much better than the usual
28th International Symposium on Temporal Representation and Reasoning (TIME 2021)
The 28th International Symposium on Temporal Representation and Reasoning (TIME 2021) was planned to take place in Klagenfurt, Austria, but had to move to an online conference due to the insecurities and restrictions caused by the pandemic. Since its frst edition in 1994, TIME Symposium is quite unique in the panorama of the scientifc conferences as its main goal is to bring together researchers from distinct research areas involving the management and representation of temporal data as well as the reasoning about temporal aspects of information. Moreover, TIME Symposium aims to bridge theoretical and applied research, as well as to serve as an interdisciplinary forum for exchange among researchers from the areas of artifcial intelligence, database management, logic and verifcation, and beyond
The addition of temporal neighborhood makes the logic of prefixes and sub-intervals EXPSPACE-complete
A classic result by Stockmeyer gives a non-elementary lower bound to the
emptiness problem for star-free generalized regular expressions. This result is
intimately connected to the satisfiability problem for interval temporal logic,
notably for formulas that make use of the so-called chop operator. Such an
operator can indeed be interpreted as the inverse of the concatenation
operation on regular languages, and this correspondence enables reductions
between non-emptiness of star-free generalized regular expressions and
satisfiability of formulas of the interval temporal logic of chop under the
homogeneity assumption. In this paper, we study the complexity of the
satisfiability problem for suitable weakenings of the chop interval temporal
logic, that can be equivalently viewed as fragments of Halpern and Shoham
interval logic. We first consider the logic featuring
modalities , for \emph{begins}, corresponding to the prefix relation on
pairs of intervals, and , for \emph{during}, corresponding to the infix
relation. The homogeneous models of naturally correspond to
languages defined by restricted forms of regular expressions, that use union,
complementation, and the inverses of the prefix and infix relations. Such a
fragment has been recently shown to be PSPACE-complete . In this paper, we
study the extension with the temporal neighborhood modality
(corresponding to the Allen relation \emph{Meets}), and prove that it
increases both its expressiveness and complexity. In particular, we show that
the resulting logic is EXPSPACE-complete.Comment: arXiv admin note: substantial text overlap with arXiv:2109.0832