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Iterative tree arrays with logarithmic depth. (English) Zbl 0655.68056

An iterative tree array (ITA) is a binay tree-connected systolic network in which each cell is a finite-state machine and the input is provided serially to the root. We present an algorithm for simulating a pushdown stack of size S(n) on an ITA of depth log S(n) in real-time. Some interesting applications are the following:
1) Every linear iterative array operating in (simultaneous) time T(n) and space S(n) can be simulated by an ITA in time T(n) and depth log S(n).
2) S(n)-space bounded on-line TM’s are equivalent to log S(n)-depth bounded ITA’s.
3) log n depth is a necessary and sufficient condition for an ITA to recognize every context-free language.
4) log log n depth is a necessary condition for an ITA to recognize a nonregular set.
5) Every on-line nondeterministic TM with log n-bounded nondeterminism operating in linear time and space can be simulated by an ITA with O(log n) depth in linear time.

MSC:

68Q80 Cellular automata (computational aspects)
68Q45 Formal languages and automata
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