منابع مشابه
Undecidability and Beyond
We discuss the structure of the recursively enumerable sets under three reducibilities: Turing, truth-table and weak truth-table. Weak truth-table reducibility requires that the questions asked of the oracle be eeectively bounded. Truth-table reducibility also demands such a bound on the the length of the computations. We survey what is known about the algebraic structure and the complexity of ...
متن کاملIncompleteness and Undecidability
Every theory we will consider will be in a language that has a name ṅ for each n ∈ ω. For example, the name for 2 ∈ ω in the language LΩ of arithmetic is the term “1 + 1”. The results stated will only apply to countable languages. This requirement is implicit in the hypothesis of the existence of an enumeration of all formulas with one free variable, for example. We also assume that formulas an...
متن کاملUndecidability and Finite Automata
Using a novel rewriting problem, we show that two natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to prove the undecidability of a related problem about k-automatic sets of rational numbers.
متن کاملRecursion Theory and Undecidability
In the second half of the class, we will explore limits on computation. These are questions of the form “What types of things can be computed at all?” “What types of things can be computed efficiently?” “How fast can problem XYZ be solved?” We already saw some positive examples in class: problems we could solve, and solve efficiently. For instance, we saw that we can sort n numbers in time O(n ...
متن کاملUndecidability and Concatenation
We consider the problem stated by Andrzej Grzegorczyk in “Undecidability without arithmetization” (Studia Logica 79(2005)) whether certain weak theory of concatenation is essentially undecidable. We give a positive answer for this problem.
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ژورنال
عنوان ژورنال: New Literary History
سال: 1981
ISSN: 0028-6087
DOI: 10.2307/468668