K. Inoue, I. Takanami and A. Nakamura. A note on two-dimensional finite automata. Information Processing Letters, Vol. 7, No. 1, pages 49--52, 1978.  Home/Search   Document Not in Database   Summary   Related Articles

....letter was 1, then the automaton accepts; otherwise it rejects. The families of languages recognized by four way non deterministic and deterministic automata are denoted by L(4NFA) and L(4DFA) respectively. The main results established on these family of languages are given below (cf. 1] and [23]) they show that, despite 4FA s are a very natural generalization of finite automata to two dimensions, they do not maintain most of the important properties that finite automata have for strings. Theorem 4.1 L(4DFA) is strictly included in L(4NFA) Proof: We show that the language L 1 over ....

....and ends outside b 1 ; hence it must accepts also p 2 but the central position of p 2 is a 0. This gives the desired contradiction. 2 Theorem 4.2 L(4DFA) and L(4NFA) are not closed under row and column concatenation and closure operations. The complete proof of the above theorem can be found in [23]. As in the proof of Theorem 4.1, the main idea behind the proof is to use combinatorial arguments to show that some particular languages are not in L(4NFA) For example, to prove the non closure under row concatenation, it is enough to show that the language L 1 described in Example 2.4 cannot be ....

K. Inoue, I. Takanami and A. Nakamura. A note on two-dimensional finite automata. Information Processing Letters, Vol. 7, No. 1, pages 49--52, 1978.

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