Constructible functions in cellular automata and their applications to hierarchy results

Authors:
Chuzo Iwamoto;Tomonobu Hatsuyama;Kenichi Morita;Katsunobu Imai
Affiliations:
Hiroshima Univ., Higashi-Hiroshima, Japan;Hiroshima Univ., Higashi-Hiroshima, Japan;Hiroshima Univ., Higashi-Hiroshima, Japan;Hiroshima Univ., Higashi-Hiroshima, Japan
Venue:
Theoretical Computer Science
Year:
2002

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Abstract

We investigate time-constructible functions in one-dimensional cellular automata (CA). It is shown that (i) if a function t(n) is computable by an O(t(n)n)-time Turing machine, then t(n) is time constructible by CA and (ii) if two functions are time constructible by CA, then the sum, product, and exponential functions of them are time constructible by CA. As an application, it is shown that if t1(n) and t2(n) are time constructible functions such that limnt1(n)/t2(n)=0 and t1(n)n, then there is a language which can be recognized by a CA in t2(n) time but not by any CA in t1(n) time.