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Systolic tree acceptors. (English) Zbl 0571.68043
Motivated by VLSI and systolic arrays this paper introduces a new kind of automata as language acceptors: systolic tree acceptors (STA). Like in a tree representing an arithmetical expression an operator or function symbol is associated with each (internal) node of the tree. For convenience the underlying tree is supposed to be infinite, satisfying a regularity and a growth rate condition. The entire input string (augmented with blanks) is fed simultaneously at the smallest level of the tree which contains sufficiently many nodes that it fits. The final decision about acceptance is made at the root of the tree. Regular languages can be accepted by STAs with any underlying tree. Depending on the tree structure certain languages with a suitable exponential growth rate are acceptable too, but all the examples of nonregular context-free languages which were studied are not acceptable with an underlying binary tree structure. If we fix the tree structure, we obtain a language family which is closed under Boolean operations. However, in general the class of STA acceptable languages has weak closure properties. As a normal form of an STA one may require that nodes of the same arity represent identical functions. All these introductory results are presented nicely with mostly informal outlines of proofs which seems to be quite appropriate in this area.
Reviewer: M.Kunze

68Q45 Formal languages and automata
68Q80 Cellular automata (computational aspects)
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
Full Text: EuDML
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