126 research outputs found
Parsing of Adaptive Star Grammars
In a recent paper, adaptive star grammars have been proposed as an
extension of node and hyperedge replacement grammars. A
rule in an adaptive star grammar is actually a rule schema which, via the
so-called cloning operation, yields a potentially infinite number of
concrete rules. Adaptive star grammars are motivated by application areas
such as modeling and refactoring object-oriented programs, and they are more
powerful than node and hyperedge replacement grammars by this mechanism. It
has been shown that the membership problem is decidable for a reasonably
large subclass of adaptive star grammars, however no parser has been
proposed. This paper describes such a parser for this subclass motivated by
the well-known string parser by Cocke, Younger, and
Kasami
Graph-Based Shape Analysis Beyond Context-Freeness
We develop a shape analysis for reasoning about relational properties of data
structures. Both the concrete and the abstract domain are represented by
hypergraphs. The analysis is parameterized by user-supplied indexed graph
grammars to guide concretization and abstraction. This novel extension of
context-free graph grammars is powerful enough to model complex data structures
such as balanced binary trees with parent pointers, while preserving most
desirable properties of context-free graph grammars. One strength of our
analysis is that no artifacts apart from grammars are required from the user;
it thus offers a high degree of automation. We implemented our analysis and
successfully applied it to various programs manipulating AVL trees,
(doubly-linked) lists, and combinations of both
Decidability and Expressiveness of Finitely Representable Recognizable Graph Languages
Recognizable graph languages are a generalization of regular (word) languages to graphs (as well as arbitrary categories). Recently automaton functors were proposed as acceptors of recognizable graph languages. They promise to be a useful tool for the verification of dynamic systems, for example for invariant checking. Since automaton functors may contain an infinite number of finite state sets, one must restrict to finitely representable ones for implementation reasons. In this paper we take into account two such finite representations: primitive recursive automaton functors - in which the automaton functor can be constructed on-the-fly by a primitive recursive function -, and bounded automaton functors - in which the interface size of the graphs (cf. path width) is bounded, so that the automaton functor can be explicitly represented. We show that the language classes of both kinds of automaton functor are closed under boolean operations, and compare the expressiveness of the two paradigms with hyperedge replacement grammars. In addition we show that the emptiness and equivalence problem are decidable for bounded automaton functors, but undecidable for primitive recursive automaton functors
Towards Alternating Automata for Graph Languages
In this paper we introduce alternating automata for languages of arrows of an arbitrary category, and as an instantiation thereof alternating automata for graph languages. We study some of their closure properties and compare them, with respect to expressiveness, to other methods for describing graph languages. We show, by providing several examples, that many graph properties (of graphs of bounded path width) can be naturally expressed as alternating automata
Graph Rewriting with Contextual Refinement
In the standard theory of graph transformation, a rule modifies only subgraphs of constant size and fixed shape. The rules supported by the graph-rewriting tool GrGen are far more expressive: they may modify subgraphs of unbounded size and variable shape. Therefore properties like termination and confluence cannot be analyzed as for the standard case. In order to lift such results, we formalize the outstanding feature of GrGen rules by using plain rules on two levels: schemata} are rules with variables; they are refined with meta-rules, which are based on contextual hyperedge replacement, before they are used for rewriting.We show that every rule based on single pushouts, on neighborhood-controlled embedding, or on variable substitution can be modeled by a schema with appropriate meta-rules. It turns out that the question whether schemata may have overlapping refinements is not decidable
Graph Isomorphism in Quasipolynomial Time Parameterized by Treewidth
We extend Babai's quasipolynomial-time graph isomorphism test (STOC 2016) and
develop a quasipolynomial-time algorithm for the multiple-coset isomorphism
problem. The algorithm for the multiple-coset isomorphism problem allows to
exploit graph decompositions of the given input graphs within Babai's
group-theoretic framework.
We use it to develop a graph isomorphism test that runs in time
where is the number of vertices and is
the minimum treewidth of the given graphs and is
some polynomial in . Our result generalizes Babai's
quasipolynomial-time graph isomorphism test.Comment: 52 pages, 1 figur
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
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