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.

Limited automata and regular languages / G. Pighizzini, A. Pisoni - In: Descriptional complexity of formal systems : 15th international workshop, DCFS 2013 : London, Canada, july 22-25, 2013 : proceedings / [a cura di] H. Jürgensen, R. Reis. - Berlin : Springer, 2013. - ISBN 9783642393099. - pp. 253-264 (( Intervento presentato al 15. convegno International Workshop on Descriptional Complexity of Formal Systems tenutosi a London, Ontario, Canada nel 2013.

Limited automata and regular languages

G. Pighizzini
Primo
;
2013

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.
context-free languages; descriptional complexity; finite automata; formal languages; regular languages; Turing machines
Settore INF/01 - Informatica
2013
Book Part (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/221215
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