In this paper, we introduce a computational mode of a tree transducer called a bi-stage transducer and study its properties. We consider a mapping on trees realized by composition of any sequence of top-down transducers and bottom-up transducers, and call such a mapping a multi-phase tree transformation. We think a multi-phase tree transformation is sufficiently powerful. It is shown that in the case of rank-preserving transducers, a multi-phase tree transformation is realized by a bi-stage transducer.

In this paper, a recognition algorithm for the class of tree languages generated by linear, monadic context-free tree grammars (LM-CFTGs) is proposed. LM-CFTGs define an important class of tree languages because LM-CFTGs are weakly equivalent to tree adjoining grammars (TAGs). The algorithm uses the CKY algorithm as a subprogram and recognizes whether an input tree can be derived from a given LM-CFTG in O(n4) time, where n is the number of nodes of the input tree.

This paper presents the analogical conception of Chomsky normal form and Greibach normal form for linear, monadic context-free tree grammars (LM-CFTGs). LM-CFTGs generate the same class of languages as four well-known mildly context-sensitive grammars. It will be shown that any LM-CFTG can be transformed into equivalent ones in both normal forms. As Chomsky normal form and Greibach normal form for context-free grammars (CFGs) play a very important role in the study of formal properties of CFGs, it is expected that the Chomsky-like normal form and the Greibach-like normal form for LM-CFTGs will provide deeper analyses of the class of languages generated by mildly context-sensitive grammars.

This paper proposes graph linear notations and an extension of them with regular expressions. Graph linear notations are a set of strings to represent labeled general graphs. They are extended with regular expressions to represent sets of graphs by specifying chosen parts for selections and repetitions of certain induced subgraphs. Methods for the conversion between graph linear notations and labeled general graphs are shown. The NP-completeness of the membership problem for graph regular expressions is proved.

In this paper, we study the minimum spanning tree problem with label selection, that is, the problem of finding a minimum spanning tree of a vertex-labeled graph where the weight of each edge may vary depending on the selection of labels of vertices at both ends. The problem is especially important as the application to mathematical OCR. It is shown that the problem is NP-hard. However, for the application to mathematical OCR, it is sufficient to deal with only graphs with small tree-width. In this paper, a linear-time algorithm for series-parallel graphs is presented. Since the minimum spanning tree problem with label selection is closely related to the generalized minimum spanning tree problem, their relation is discussed.

In this paper, we study deterministic linear pushdown tree automata (deterministic L-PDTAs) and some variations. Since recognition of an input tree by a deterministic L-PDTA can be done in linear time, deterministic L-PDTAs are applicable to many kinds of applications. A strict hierarchy will be shown among the classes of tree languages defined by a variety of deterministic L-PDTAs. It will be also shown that deterministic L-PDTAs are weakly equivalent to nondeterministic L-PDTAs.