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Separating the Classes of Recursively Enumerable Languages Based on Machine Size

2015
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International Journal of Foundations of Computer Science
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Many years ago it was observed that the r.e. languages form an infinite proper hierarchy RE1 ⊂ RE2 ⊂ · · · based on the size of the Turing machines that accept them. Aside from some basic facts, little seems known about it in general. We examine the position of the finite languages and their complements in the hierarchy. We show that for every finite language L one has L,L ∈ REn for some n ≤ p·(m− log 2 p +1)+1 where m is the length of the longest word in L, c is the cardinality of L, and p =

doi:10.1142/s0129054115500380
fatcat:a3egpgjiwjbn7jvnqhgawogno4