Universality and Almost Decidability
نویسندگان
چکیده
منابع مشابه
Universality and Almost Decidability
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a decidable and generic (i.e. a set of natural density one) set whose intersection with S is decidable. Every decidable set is almost decidable, but the conve...
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Many different definitions of computational universality for various types of dynamical systems have flourished since Turing’s work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our defini...
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Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the definition of the property to include cellular automata with any set of states in Z, and show that they can be always extended to “usual” NCCA with contiguous state...
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ژورنال
عنوان ژورنال: Fundamenta Informaticae
سال: 2015
ISSN: 0169-2968
DOI: 10.3233/fi-2015-1199