784 research outputs found
Graph automata
AbstractMagmoids satisfying the 15 fundamental equations of graphs, namely graphoids, are introduced. Automata on directed hypergraphs are defined by virtue of a relational graphoid. The closure properties of the so-obtained class are investigated, and a comparison is being made with the class of syntactically recognizable graph languages
Fuzzy graphs: Algebraic structure and syntactic recognition
© Springer Science+Business Media Dordrecht 2013. Directed fuzzy hypergraphs are introduced as a generalization of both crisp directed hypergraphs and directed fuzzy graphs. It is proved that the set of all directed fuzzy hypergraphs can be structured into a magmoid with operations graph composition and disjoint union. In this framework a notion of syntactic recognition inside magmoids is defined. The corresponding class is proved to be closed under boolean operations and inverse mor-phisms of magmoids. Moreover, the language of all strongly connected fuzzy graphs and the language that consists of all fuzzy graphs that have at least one directed path from the begin node to the end node through edges with membership grade 1 are recognizable. Additionally, a useful characterization of recognizability through left derivatives is also achieved
Specifying Graph Languages with Type Graphs
We investigate three formalisms to specify graph languages, i.e. sets of
graphs, based on type graphs. First, we are interested in (pure) type graphs,
where the corresponding language consists of all graphs that can be mapped
homomorphically to a given type graph. In this context, we also study languages
specified by restriction graphs and their relation to type graphs. Second, we
extend this basic approach to a type graph logic and, third, to type graphs
with annotations. We present decidability results and closure properties for
each of the formalisms.Comment: (v2): -Fixed some typos -Added more reference
Recognizable Graph Languages for Checking Invariants
We generalize the order-theoretic variant of the Myhill-Nerode theorem to graph languages, and characterize the recognizable graph languages as the class of languages for which the Myhill-Nerode quasi order is a well quasi order. In the second part of the paper we restrict our attention to graphs of bounded interface size, and use Myhill-Nerode quasi orders to verify that, for such bounded graphs, a recognizable graph property is an invariant of a graph transformation system. A recognizable graph property is a recognizable graph language, given as an automaton functor. Finally, we present an algorithm to approximate the Myhill-Nerode ordering
Deterministic recognizability of picture languages with Wang automata
special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to ApplicationsInternational audienceWe present a model of automaton for picture language recognition, called Wang automaton, which is based on labeled Wang tiles. Wang automata combine features of both online tessellation acceptors and 4-way automata: as in online tessellation acceptors, computation assigns states to each picture position; as in 4-way automata, the input head visits the picture moving from one pixel to an adjacent one, according to some scanning strategy. Wang automata recognize the class REC, i.e. they are equivalent to tiling systems or online tessellation acceptors, and hence strictly more powerful than 4-way automata. We also introduce a natural notion of determinism for Wang automata, and study the resulting class, extending the more traditional approach of diagonal-based determinism, used e. g. by deterministic tiling systems. In particular, we prove that the concept of row (or column) ambiguity defines the class of languages recognized by Wang automata directed by boustrophedonic scanning strategies
Revisiting Membership Problems in Subclasses of Rational Relations
We revisit the membership problem for subclasses of rational relations over
finite and infinite words: Given a relation R in a class C_2, does R belong to
a smaller class C_1? The subclasses of rational relations that we consider are
formed by the deterministic rational relations, synchronous (also called
automatic or regular) relations, and recognizable relations. For almost all
versions of the membership problem, determining the precise complexity or even
decidability has remained an open problem for almost two decades. In this
paper, we provide improved complexity and new decidability results. (i) Testing
whether a synchronous relation over infinite words is recognizable is
NL-complete (PSPACE-complete) if the relation is given by a deterministic
(nondeterministic) omega-automaton. This fully settles the complexity of this
recognizability problem, matching the complexity of the same problem over
finite words. (ii) Testing whether a deterministic rational binary relation is
recognizable is decidable in polynomial time, which improves a previously known
double exponential time upper bound. For relations of higher arity, we present
a randomized exponential time algorithm. (iii) We provide the first algorithm
to decide whether a deterministic rational relation is synchronous. For binary
relations the algorithm even runs in polynomial time
- …