Some Results Concerning 2-D On-line Tessellation Acceptors and 2-D Alternating Finite Automata

A two-dimensional nondeterministic on-line tessellation acceptor (2-NOTA) is a special type of real-time two-dimensional nondeterministic cellular automaton in which data flows from the upper-left corner to the lower-right corner. A two-dimensional alternating finite automaton (2-AFA) is an alternating finite automaton with a two-dimensional rectangular input whose input head can move in all four directions on the input. In this paper, we show that 2-NOTA's and 2-AFA's are incomparable. This answers in the negative an open question in [IT89a]. Closure properties of the classes of languages (i.e., sets of two-dimensional patterns) accepted by two-way, three-way, and four-way two-dimensional alternating finite automata and two-dimensional alternating finite automata with only universal states are also obtained which answer several open questions in [IN88].

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