SOME OPEN QUESTIONS AND RECENT RESULTS ON TREE TRANSDUCERS AND TREE LANGUAGES

Publisher Summary The theory of tree automata and tree grammars investigates computation on structured objects and the structure of computation. In both cases, the structure is represented by a tree. The tree language theory uses the methods and results of formal language theory, which is supported by algebraic methods. Since the beginning of tree language theory in 1965, the theory has grown and proved its usefulness in areas such as program scheme theory, theory of syntax-directed translation, and formal language theory itself. This chapter discusses open questions and recent results on tree transducers and tree languages and discusses possible directions of research. It describes the position of tree language theory with respect to theoretical computer science and formal language theory. An important task of theoretical computer science is to formalize and investigate the control structures and data structures used by the programmers to describe their algorithms. Insight into the formal power of such programming constructs and their trade-offs may lead to a better understanding of the nature of computation.

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