K. Skodinis, E. Wanke, Emptiness problems of eNCE graph languages, J. of Comp. Syst. Sci. 51 (1995), 472-485. Home/Search Document Details and Download
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Normal Forms for Context-Free Node-Rewriting Hypergraph Grammars - Klempien-Hinrichs (4 citations) (Correct)
....The rst ensures that the rank of a hyperedge cannot decrease during the embedding process, and the second allows to eliminate so called blocking hyperedges, i.e. nonterminal hyperedges which are incident to terminal nodes only. The construction of a non blocking normal form was rst given in [SW95] for con uent eNCE grammars, and reformulated for con uent edNCE grammars in [ER97, Theorem 1.3.21] Let NG = N; T ; P; S) be an hNCE grammar and (R; C) a hypergraph with embedding over N [ T . A connection instruction ( x 1 : xm= y 1 : yn ) 2 C is called link preserving if there is ....
....grammar NG is nonblocking if no terminal sentential form of NG contains a blocking hyperedge. Theorem 3. For every C hNCE grammar NG, an equivalent non blocking C hNCE grammar NG 0 can be constructed. If NG is remote free or link preserving, then so is NG 0 . Proof sketch. Analogously to [SW95,ER97], the idea is to de ne a new alphabet of nonterminal node labels containing the information whether a hypergraph which is derived from a node labelled with such a symbol does or does not contain a blocking hyperedge. The new start symbol is then related to the old one and contains information ....
Konstantin Skodinis and Egon Wanke. Emptiness problems of eNCE graph languages. Journal of Computer and System Sciences, 51:472-485, 1995.
Computing by Graph Transformation - A Survey and Annotated.. - Ehrig, (eds.) (1996) (3 citations) (Correct)
....HR grammars) The complexity of the membership problem of NR graph languages was investigated in, e.g. Bra83, Kau85, RW86, EL89b] The results concerning graph languages of bounded degree were superseded by those of [Lau90] for HR languages. Other complexity issues are studied, e.g. in [Bra88, SW95, SW96, Wan91, Wan94] In [Eng89, EO95] it is shown that the NR graph languages can be characterized by regular tree and string languages. For finite string languages the apex graph languages are obtained. Node replacement in hypergraphs is introduced in [Kle96] yielding hypergraph grammars ....
....common subterms saves space and avoids the repetition of computations. 24 4. 3 Languages Based on Graph Transformation A formalism for rewriting hypergraphs in a controlled manner has been developed by MaggioloSchettini and Winkowski in a series of papers, including [MSW91, WMS92, MSW92, MSW94, MSW95] The formalism is essentially a programming language with rewriting rules playing the role of basic instructions. The programs are built from productions by means of constructors which specify order and modalities of the rewriting steps. When applied to a hypergraph such programs produce ....
K. Skodinis and E. Wanke. Emptiness problems of eNCE graph languages. J. Comp. Syst. Sci., 51:472-485, 1995.
Finite Graph Automata for Linear and Boundary Graph Languages - Brandenburg, Skodinis (2001) (1 citation) Self-citation (Skodinis) (Correct)
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K. Skodinis, E. Wanke, Emptiness problems of eNCE graph languages, J. of Comp. Syst. Sci. 51 (1995), 472-485.
The Bounded Tree-Width Problem of Context-Free Graph Languages - Skodinis (1997) Self-citation (Skodinis) (Correct)
....we denote such graph grammars by edNCE. edNCE and eNCE graph grammars can generate so called blocking edges. These are nonterminal edges incident to two terminal nodes. Dealing with blocking edges is complicated. If the elimination of the blocking edges is possible, it is of high complexity, see [SW95]. In parallel to context free string grammars a graph grammar is called reduced if every label A is reachable from the axiom S and can generate a terminal graph. Using the classical techniques it can be seen that every NCE (C NCE, B NCE, L NCE) graph grammar can be transformed into an equivalent ....
....eNCE (edNCE) graph grammars. The only difference are multiple edges. The proofs are based on the same idea. If the NR graph grammars contain blocking edges the following complexity result can be easily obtained by Lemma 12 and by the emptiness problem of confluent edNCE graph grammars from [SW95]: The bounded tree width problem is DEXPTIME complete for confluent and boundary edNCE and PSPACE complete for linear edNCE graph grammars. Moreover the problem whether or not the language of a given edNCE graph grammar contains complete bipartite subgraphs K n;n of an arbitrarily large size n is ....
K. Skodinis and E. Wanke. Emptiness problems of eNCE graph languages. J. Comput. System Sci., 51:472--485, 1995.
The complexity of the Kn,n-problem for node.. - Konstantin Skodinis Self-citation (Skodinis) (Correct)
....NL is the class of languages recognizable by nondeterministic Turing machines with logarithmic work space. An eNCE graph grammar is reduced if it has no useless productions. The NL completeness results carry over to the case of NCE and edNCE graph grammars. Together with the earlier results from [SW95] this settles the complexity of the bounded K n;n problem for all types of graph grammars. This is summarized in Table 1.1. In the case of blocking graph grammars we have to eliminate blocking edges, which causes a high complexity. Our investigations are motivated by the notion of tree width and ....
....we reduce the GAP problem (graph accessibility problem) to the bounded K n;n problem for reduced L NCE graph grammars. This implies the NL completeness of the bounded K n;n problem for all reduced subclasses of nonblocking node replacement graph grammars. The NL completeness and the results from [SW95] also settle the complexity of the conditions given in Courcelle s Theorem 2.8. In our proofs we will also use some techniques similar to the ones in [SW97] where it has been shown that the bounded degree problem is NL complete for reduced N eNCE graph grammars. Therefore we recall Lemma 3.11 from ....
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K. Skodinis and E. Wanke. Emptiness problems of eNCE graph languages. J. Comput. System Sci., 51(3):472--485, 1995.
Degree Problems for eNCE Graph Grammars - Skodinis, Wanke Self-citation (Skodinis Wanke) (Correct)
....of these graph grammars, the bounded degree problem can be solved in polynomial time. On the other hand, the bounded degree problem is at least as hard as the emptiness problem and thus P complete 3 for N edNCE, N eNCE, NCE, NLC, and hyperedge replacement systems. Moreover, by the results from [SW95], the emptiness problem is undecidable, DEXPTIME hard 4 , and PSPACE hard for general eNCE graph grammars, confluent boundary eNCE graph grammars, and linear eNCE graph grammars, respectively. In this paper we show that the bounded degree problem is undecidable for eNCE graph grammars, ....
....Is there an integer k such that deg(G) k for all graphs G from L(G) Lower bounds for the bounded degree problem can simply be shown using the emptiness problem. The emptiness problem for eNCE graph grammars is the question whether or not the language of a given eNCE graph grammar is empty. In [SW95] the following has been shown: Lemma 3.1 The emptiness problem is undecidable for eNCE graph grammars, DEXPTIMEcomplete for C B eNCE graph grammars, PSPACE complete for L eNCE graph grammars, and P complete for N eNCE graph grammars. The emptiness problem for non blocking eNCE graph grammars is ....
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K. Skodinis and E. Wanke. Emptiness problems of eNCE graph languages. Journal of Computer and System Sciences, 51:472--485, 1995. 19
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