Linear MIM-Width of Trees

We provide an $O(n \log n)$ algorithm computing the linear maximum induced matching width of a tree and an optimal layout.Comment: 19 pages, 7 figures, full version of WG19 paper of same nam

Exponential time analysis of confluent and boundary eNCE graph languages

. eNCE (edge label neighborhood controlled) graph grammars belong to the most powerful graph rewriting systems with single-node graphs on the left-hand side of the productions. From an algorithmic point of view, confluent and boundary eNCE graph grammars are the most interesting subclasses of eNCE graph grammars. In confluent eNCE graph grammars, the order in which nonterminal nodes are substituted is irrelevant for the resulting graph. In boundary eNCE graph grammars, nonterminal nodes are never adjacent. In this paper, we show that given a confluent or boundary eNCE graph grammar G, the problem whether the language L(G) defined by G is empty, is DEXPTIME-complete. 1 Introduction The theory of graph grammars constitutes a well-motivated and well-developed area within theoretical computer science. The area of graph grammars has grown quite impressively in recent years. This growth was motivated by applications in pattern recognition, software specification and development, V..

Emptiness problems of eNCE graph languages

We consider the complexity of the emptiness problem for various classes of graph languages defined by eNCE (edge label neighborhood controlled embedding) graph grammars. In particular, we show that the emptiness problem is undecidable for general eNCE graph grammars, DEXPTIME-complete for confluent and boundary eNCE graph grammars, PSPACE-complete for linear eNCE graph grammars, NLcomplete for deterministic confluent, deterministic boundary, and deterministic linear eNCE graph grammars. The exponential time algorithm for deciding emptiness of confluent eNCE graph grammars is based on an exponential time transformation of a confluent eNCE graph grammar into a nonblocking confluent eNCE graph grammar generating the same language. 1 Introduction The theory of graph grammars constitutes a well-motivated and well-developed area within theoretical computer science. The area of graph grammars has grown quite impressively in recent years. This growth was motivated by applications in..

Finite graph automata for linear and boundary graph languages

Graph grammars can be regarded as a generalization of context-free grammars from strings to graphs. Over the past 30 years several types of graph grammars have been introduced and a rich theory of graph grammars and their languages has been developed. However, there are no graph automata corresponding to the major classes of graph grammars. There is no duality between generative and recognizing devices, as it is known for the Chomsky hierarchy of formal languages. We introduce graph automata as devices for the recognition of graph languages. A graph automaton consists of a finite state control, a finite set of instructions, and a collection of heads or guards. It traverses and reads an input graph in a systematic way and performs a graph search directed by the instructions. As our main results we show that nite graph automata recognize exactly the set of graph languages generated by linear NCE graph grammars and that alternating finite graph automata recognize exactly the languages of boundary graph grammars. These results can be specialized to hold for connected graph languages and graph languages of bounded degree. We generalize some automata theoretic properties from string to graph automata and re-establish the best possible complexity results of some decision problems in a straightforward manner