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## Yohei Fujinaka

In this thesis, a new subclass of term rewriting systems (TRSs), layered transducing TRSs (LT-TRSs) is defined and its recognizability preserving property is discussed.

A set of ground terms (tree language) T is recognizable if there exists a tree automaton which accepts T. A TRS R effectively preserves recognizability (EPR) if for any recognizable tree language L, the set of terms obtained by rewriting terms in L by R is also recognizable and a tree automaton which accepts it can be effectively constructed.

EPR-TRS has good mathematical properties, e.g., reachability, joinability and local confluence are decidable for EPR-TRSs. Unfortunately it is undecidable whether a given TRS belongs to EPR-TRS or not.

Therefore decidable subclasses of EPR-TRS have been proposed. These subclasses put a rather strong constraint on the syntax of the right-hand side of a rewrite rule. The class of LT-TRSs contains some EPR-TRSs, e.g., { f(x) -> f(g(x)) } which do not belong to any of the known decidable subclasses of EPR-TRSs. Bottom-up linear tree transducer, which is a well-known computation model in the tree language theory, is a special case of LT-TRS.

In this thesis, two sufficient conditions for an LT-TRS to be an EPR-TRS are presented.
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