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Full-Text Articles in Set Theory
Toward Completeness Theorem For Guarded Kleene Algebra With Tests, Hung Pham
Toward Completeness Theorem For Guarded Kleene Algebra With Tests, Hung Pham
Honors Theses
Code refactoring is a fundamental practice in software engineering, in which a program is restructured without changing the actions it performs and the results it produces. To carry out refactoring with confidence, one requires a formal method for verifying that two programs are equivalent. Guarded Kleene Algebra with Tests (GKAT) provides such a framework, an algebraic system designed to reason about a natural class of programs, namely those in which every branch and loop is governed by a Boolean condition, such as if–else and while statements. Central to GKAT is a finite set of algebraic axioms for deriving program equivalences. …
Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum
Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum
Honors Theses
This paper considers the problem of determining which of the 56092 groups of order 256 contain (256; 120; 56; 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 Z4 Z2 . This construction method was able to produce difference sets in 643 of the 649 unsolved groups with the correct normal subgroup. These constructions elimated approximately 90% of the open cases, leaving 81 remaining unsolved groups.