Journal ArticleDOI
The Decision Problem for Exponential Diophantine Equations
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This article is published in Journal of Symbolic Logic.The article was published on 1970-03-01. It has received 247 citations till now. The article focuses on the topics: Diophantine equation & Diophantine set.read more
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Existential arithmetization of Diophantine equations
TL;DR: The new method leads to a much simpler construction of a universal Diophantine equation and to the existential arithmetization of Turing machines, register machines, and partial recursive functions.
Journal ArticleDOI
Inferring answers to queries
William Gasarch,Andrew Lee +1 more
TL;DR: This work proposes a new line of research which examines the question of inferring the answers to queries, and shows that any separation that holds between these inference types also holds between the corresponding query inference types.
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Balance problems for integer circuits
TL;DR: The work shows that the balance problem for { ∖, ⋅ } -circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be Undecidable.
Elliptic curves over Q(i)
TL;DR: In this paper, some extensions of the classical theory along with some examples illustrating the results are presented along with the results of a study of the diophantine equation v2 = 2 u4 − 1.