Abstract: Limited automata are one-tape Turing machines that are allowed to rewrite the content of any tape cell only in the first d visits, for a fixed constant d. In the case d = 1, namely, when a rewriting is possible only during the first visit to a cell, these models have the same power of finite state automata. We prove state upper and lower bounds for the conversion of 1-limited automata into finite state automata. In particular, we prove a double exponential state gap between nondeterministic 1-limited automata and one-way deterministic finite automata. The gap reduces to single exponential in the case of deterministic 1-limited automata. This also implies an exponential state gap between nondeterministic and deterministic 1-limited automata. Another consequence is that 1-limited automata can have less states than equivalent two-way nondeterministic finite automata. We show that this is true even if we restrict to the case of the one-letter input alphabet. For each d ≥ 2, d-limited automata are known to characterize the class of context-free languages. Using the Chomsky-Schützenberger representation for context-free languages, we present a new conversion from context-free languages into 2-limited automata.
Publication Year: 2013
Publication Date: 2013-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 2
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