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It is known that if a Büchi context-free language (BCFL) consists of scattered words, then there is an integer n, depending only on the language, such that the Hausdorff rank of each word in the language is bounded by n. Every BCFL is a Müller context-free language (MCFL). In the first part of the paper, we prove that an MCFL of scattered words is a BCFL… (More)
In this survey we generalize some results on formal tree languages, tree grammars and tree automata by an algebraic treatment using semirings, fixed point theory, formal tree series and matrices. The use of these mathematical constructs makes definitions, constructions, and proofs more satisfactory from an mathematical point of view than the customary ones.… (More)
We provide the basics of a 2-dimensional theory of automata on series-parallel biposets. We define recognizable, regular and rational sets of series-parallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.