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» On Euclid's algorithm and elementary number theory
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CORR
2008
Springer
129views Education» more  CORR 2008»
13 years 5 months ago
A polytime proof of correctness of the Rabin-Miller algorithm from Fermat's little theorem
Although a deterministic polytime algorithm for primality testing is now known ([4]), the Rabin-Miller randomized test of primality continues being the most efficient and widely u...
Grzegorz Herman, Michael Soltys
TPHOL
2005
IEEE
13 years 11 months ago
A HOL Theory of Euclidean Space
We describe a formalization of the elementary algebra, topology and analysis of finite-dimensional Euclidean space in the HOL Light theorem prover. (Euclidean space is RN with the...
John Harrison
CORR
2004
Springer
176views Education» more  CORR 2004»
13 years 5 months ago
The First-Order Theory of Sets with Cardinality Constraints is Decidable
Data structures often use an integer variable to keep track of the number of elements they store. An invariant of such data structure is that the value of the integer variable is ...
Viktor Kuncak, Martin C. Rinard
CADE
2005
Springer
14 years 5 months ago
An Algorithm for Deciding BAPA: Boolean Algebra with Presburger Arithmetic
We describe an algorithm for deciding the first-order multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmeti...
Viktor Kuncak, Huu Hai Nguyen, Martin C. Rinard
PODS
1997
ACM
124views Database» more  PODS 1997»
13 years 9 months ago
Languages for Relational Databases over Interpreted Structures
We rework parts of the classical relational theory when the underlying domain is a structure with some interpreted operations that can be used in queries. We identify parts of the...
Michael Benedikt, Leonid Libkin