Logical Description of Context-free Graph Languages (original) (raw)
Related papers
Regular Description of Context-free Graph Languages
Journal of Computer and System Sciences, 1996
A set of (labeled) graphs can be de ned by a regular tree language and one regular string language for each possible edge label, as follows. For each tree t from the regular tree language the graph gr(t) has the same nodes as t (with the same labels), and there is an edge with label from node x to node y if the string of labels of the nodes on the shortest path from x to y in t belongs to the regular string language for. Slightly generalizing this de nition scheme, we allow gr(t) to have only those nodes of t that have certain labels, and we allow a relabeling of these nodes. It is shown that in this way exactly the class of C-edNCE graph languages (generated by C-edNCE graph grammars) is obtained, one of the largest known classes of context-free graph languages.
Graph grammars and tree transducers
Lecture Notes in Computer Science
Regular tree grammars can be used to generate graphs, by generating expressions that denote graphs. Top-down and bottom-up tree transducers are a tool for proving properties of such graph generating tree grammars. graph languages: the HR-context-free and the VR-context-free graph languages. We give some simple examples.
Context-free graph languages of bounded degree are generated by apex graph grammars
Acta Informatica, 1994
The apex graph grammars generate precisely the context-free graph languages of bounded degree, independently of whether one considers hyperedge replacement systems or (boundary or confluent) NLC or edNCE graph grammars. The main feature of apex graph grammars is that nodes cannot be "passed" from nonterminal to nonterminal. The proof is based on a normal form result for arbitrary hyperedge replacement systems that forbids "passing chains". This generalizes Greibach Normal Form.
Expressiveness and complexity of graph logic
Information and Computation, 2007
We investigate the complexity and expressive power of the spatial logic for querying graphs introduced by Cardelli, Gardner and Ghelli (ICALP 2002). We show that the model-checking complexity of versions of this logic with and without recursion is PSPACE-complete. In terms of expressive power, the version without recursion is a fragment of the monadic second-order logic of graphs and we show that it can express complete problems at every level of the polynomial hierarchy. We also show that it can define all regular languages, when interpretation is restricted to strings. The expressive power of the logic with recursion is much greater as it can express properties that are PSPACE-complete and therefore unlikely to be definable in second-order logic. ´ edgeµ where, -is a set of vertices, a set of edges and a set of labels. These sets are all finite and mutually disjoint. Moreover, and , where is a fixed infinite set of names and a fixed infinite set of labels (names do not actually name anything, they are just the universe of constants from which elements of the graph are drawn).
On Some Closure Properties of nc-eNCE Graph Grammars
arXiv (Cornell University), 2023
In the study of automata and grammars, closure properties of the associated languages have been studied extensively. In particular, closure properties of various types of graph grammars have been examined in (
Graph grammars and operational semantics
Theoretical Computer Science, 1982
Transformations of graphlike expressions are called correct if they preserve a given functional semantics of the expressions. Combining the algebraic theories of graph grammars (cf.
Finite graph automata for linear and boundary graph languages
Theoretical Computer Science, 2005
Graph grammars can be regarded as a generalization of context-free grammars from strings to graphs. Over the past 30 years a rich theory of graph grammars and their languages has been developed. However, there are no graph automata. There is no duality between generative and recognizing devices, as it is known for the Chomsky hierarchy of formal languages.
Let us first start with a brief discussion of the very fundamental definitions of the theory of formal languages (standard references are the books of Lewis & Papadimitriou, 1998, and Hopcroft et al., 2001). An alphabet Σ is a (finite or countably infinite) set of symbols. A string over this alphabet is any finite sequence of symbols. Typically, a string w over Σ will be written as w= α1α2··· αk, for some α1, α2,..., αk∈ Σ. The string without any symbols is called empty string and it is denoted by ε. We denote by {w} the set of symbols contained in the ...
Graph Automata for Linear Graph Languages
Tagt, 1994
We introduce graph automata as devices for the recognition of linear graph languages. A graph automaton is the canonical extension of a nite state automaton recognizing a set of connected labeled graphs. It consists of a nite state control and a collection of heads, which search the input graph. In a move the graph automaton reads a new subgraph, checks some consistency conditions, changes states and moves some of its heads beyond the read subgraph. It proceeds such that the set of currently visited edges is an edge-separator between the visited and the yet undiscovered part of the input graph. Hence, the graph automaton realizes a graph searching strategy. Our main result states that nite graph automata recognize exactly the set of graph languages generated by connected linear NCE graph grammars.