Topic
Recursively enumerable language
About: Recursively enumerable language is a research topic. Over the lifetime, 1508 publications have been published within this topic receiving 32382 citations.
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18 citations
TL;DR: In this article, it was shown that the problem of determining whether a pair of abstract simplicial complexes C and A isomorphic to A(C) is not decidable, i.e., it is recursively enumerable, but not necessarily decidable.
Abstract: An abstract simplicial complex is a finite family of subsets of a finite set, closed under subsets. Every abstract simplicial complex C naturally determines a Bratteli diagram and a stable AF-algebra A(C). Consider the following problem: INPUT: a pair of abstract simplicial complexes C and C'; QUESTION: is A(C) isomorphic to A(C')? We show that this problem is Godel incomplete, i.e., it is recursively enumerable but not decidable. This result is in sharp contrast with the recent decidability result by Bratteli, Jorgensen, Kim and Roush, for the isomorphism problem of stable AF-algebras arising from the iteration of the same positive integer matrix. For the proof we use a combinatorial variant of the De Concini-Procesi theorem for toric varieties, together with the Baker-Beynon duality theory for lattice-ordered abelian groups, Markov's undecidability result, and Elliott's classification theory for AF-algebras.
18 citations
TL;DR: It is shown that, if a, b are recursively enumerable degrees such that 0 a a ∪ b = 0', then there exists a recursically enumerable degree c such that c a and c ∪b = 0'.
18 citations
TL;DR: It is shown that all recursively enumerable languages may be denoted by flow expressions, which contradicts A.C. Shaw's conjecture that the formal descriptive power of flow expressions lies somewhat below context-sensitive grammers.
Abstract: Recently, A.C. Shaw introduced a new class of expressions called flow expressions, and conjectured that the formal descriptive power of flow expressions lies somewhat below context-sensitive grammers. In this paper, we give a negative answer for his conjecture, that is, we show that all recursively enumerable languages may be denoted by flow expressions.
18 citations
TL;DR: Families of subshifts corresponding to context-free, context-sensitive, and recursively enumerable languages are introduced and their closure properties under forward and backward cellular automaton images studied.
18 citations