D.L. Milgram, \A region crossing problem for array-bounded automata." Information and Control 31 (1976) 147-152.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....which recognizes it. As for boundary conditions, we have a choice. The DFA can be bounded, in that it must always move back into the block if it detects a ] or unbounded, in which it is allowed to move into the ] s. However, it can be shown that an unbounded DFA can be simulated by a bounded one [39]; if it has n states, it will either return to the block within n steps, or get caught in a loop and wander o to in nity. So these two are equivalent. We then have Proposition. The class of DFA languages properly contains the LLL s. Proof. We rst show containment. We simply de ne a DFA which ....

D.L. Milgram, \A region crossing problem for array-bounded automata." Information and Control 31 (1976) 147-152.

....words, the same set of rectangles can be recognized by a DFA that moves east and south along the edges of the rectangle from the upper left corner to the lower right corner. A similar result was shown for DFAs which are allowed to make excursions into the plane outside the rectangle by Milgram [9]. Lemma 3.1. Let S # N 2 be recognized from the outside by an NFA A. Then there exist positive integers t H and pH , called the horizontal transient and the period, respectively, such that for every w t H and every h (w, h) # S =# (w pH , h) # S where the numbers t H and pH are ....

D.L. Milgram (1976) A region crossing problem for array-bounded automata. Information and Control 31 147--152.

....which recognizes it. As for boundary conditions, we have a choice. The DFA can be bounded, in that it must always move back into the block if it detects a ] or unbounded, in which it is allowed to move into the ] s. However, it can be shown that an unbounded DFA can be simulated by a bounded one [34]; if it has n states, it will either return to the block within n steps, or get caught in a loop and wander off to infinity. So these two are equivalent. We then have Proposition. The class of DFA languages properly contains the LLL s. Proof. We first show containment. We simply define a DFA ....

D.L. Milgram, "A region crossing problem for array-bounded automata." Information and Control 31 (1976) 147--152.

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D.L. Milgram, \A region crossing problem for array-bounded automata." Information and Control 31 (1976) 147-152.

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