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.

Characterizations of Catalytic Membrane Computing Systems

Abstract: We look at 1-region membrane computing systems which only use rules of the form Ca →Cv, where C is a catalyst, a is a noncatalyst, and v is a (possibly null) string of noncatalysts. There are no rules of the form a →v. Thus, we can think of these systems as “purely” catalytic. We consider two types: (1) when the initial configuration contains only one catalyst, and (2) when the initial configuration contains multiple (not necessarily distinct) catalysts. We show that systems of the first type are equivalent to communication-free Petri nets, which are also equivalent to commutative context-free grammars. They define precisely the semilinear sets. This partially answers an open question in [19]. Systems of the second type define exactly the recursively enumerable sets of tuples (i.e., Turing machine computable). We also study an extended model where the rules are of the form q: (p, Ca →Cv) (where q and p are states), i.e., the application of the rules is guided by a finite-state control. For this generalized model, type (1) as well as type (2) with some restriction correspond to vector addition systems.

Matrix Grammars with a Leftmost Restriction

Abstract: The family of languages generated by matrix grammars with context-free (context-free λ -free) core productions and with a leftmost restriction on derivations equals the family of recursively enumerable (context-sensitive) languages.

Degrees of autostability relative to strong constructivizations

Abstract: The spectra of the Turing degrees of autostability of computable models are studied. For almost prime decidable models, it is shown that the autostability spectrum relative to strong constructivizations of such models always contains a certain recursively enumerable Turing degree; moreover, it is shown that for any recursively enumerable Turing degree, there exist prime models in which this degree is the least one in the autostability spectrum relative to strong constructivizations.