Limited Automata and Regular Languages

  • Giovanni Pighizzini
  • Andrea Pisoni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8031)


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.


finite automata formal languages Turing machines regular languages context-free languages descriptional complexity 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Giovanni Pighizzini
    • 1
  • Andrea Pisoni
    • 1
  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoItaly

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