1,214 research outputs found
Hyper-Minimization for Deterministic Weighted Tree Automata
Hyper-minimization is a state reduction technique that allows a finite change
in the semantics. The theory for hyper-minimization of deterministic weighted
tree automata is provided. The presence of weights slightly complicates the
situation in comparison to the unweighted case. In addition, the first
hyper-minimization algorithm for deterministic weighted tree automata, weighted
over commutative semifields, is provided together with some implementation
remarks that enable an efficient implementation. In fact, the same run-time O(m
log n) as in the unweighted case is obtained, where m is the size of the
deterministic weighted tree automaton and n is its number of states.Comment: In Proceedings AFL 2014, arXiv:1405.527
Completing Queries: Rewriting of IncompleteWeb Queries under Schema Constraints
Reactive Web systems, Web services, and Web-based publish/
subscribe systems communicate events as XML messages, and in
many cases require composite event detection: it is not sufficient to react
to single event messages, but events have to be considered in relation to
other events that are received over time.
Emphasizing language design and formal semantics, we describe the
rule-based query language XChangeEQ for detecting composite events.
XChangeEQ is designed to completely cover and integrate the four complementary
querying dimensions: event data, event composition, temporal
relationships, and event accumulation. Semantics are provided as
model and fixpoint theories; while this is an established approach for rule
languages, it has not been applied for event queries before
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can
represent abstract simplicial complexes of any dimension and allows efficient
implementation of a large range of basic operations on simplicial complexes. In
this paper, we show how to optimally compress the Simplex Tree while retaining
its functionalities. In addition, we propose two new data structures called the
Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the
compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List
under various settings.Comment: An extended abstract appeared in the proceedings of SoCG 201
Minimization and Canonization of GFG Transition-Based Automata
While many applications of automata in formal methods can use
nondeterministic automata, some applications, most notably synthesis, need
deterministic or good-for-games(GFG) automata. The latter are nondeterministic
automata that can resolve their nondeterministic choices in a way that only
depends on the past. The minimization problem for deterministic B\"uchi and
co-B\"uchi word automata is NP-complete. In particular, no canonical minimal
deterministic automaton exists, and a language may have different minimal
deterministic automata. We describe a polynomial minimization algorithm for GFG
co-B\"uchi word automata with transition-based acceptance. Thus, a run is
accepting if it traverses a set of designated transitions only
finitely often. Our algorithm is based on a sequence of transformations we
apply to the automaton, on top of which a minimal quotient automaton is
defined. We use our minimization algorithm to show canonicity for
transition-based GFG co-B\"uchi word automata: all minimal automata have
isomorphic safe components (namely components obtained by restricting the
transitions to these not in ) and once we saturate the automata with
-transitions, we get full isomorphism.Comment: 28 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:2009.1088
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simplicial complexes. In this paper, we show how to optimally compress the Simplex Tree while retaining its functionalities. In addition, we propose two new data structures called Maximal Simplex Tree (MxST) and Simplex Array List (SAL). We analyze the compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List under various settings
Computations by fly-automata beyond monadic second-order logic
We present logically based methods for constructing XP and FPT graph
algorithms, parametrized by tree-width or clique-width. We will use
fly-automata introduced in a previous article. They make possible to check
properties that are not monadic second-order expressible because their states
may include counters, so that their sets of states may be infinite. We equip
these automata with output functions, so that they can compute values
associated with terms or graphs. Rather than new algorithmic results we present
tools for constructing easily certain dynamic programming algorithms by
combining predefined automata for basic functions and properties.Comment: Accepted for publication in Theoretical Computer Scienc
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