The module isomorphism problem reconsidered

The Module Isomorphism Problem Reconsidered

Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and Magma, at least in regard to computations with groups and algebras. By contrast, the fundamental ...

The Graph Isomorphism Problem

The graph isomorphism problem can be easily stated: check to see if two graphs that look di erently are actually the same. The problem occupies a rare position in the world of complexity theory, it is clearly in NP but is not known to be in P and it is not known to be NP-complete. Many sub-disciplines of mathematics, such as topology theory and group theory, can be brought to bear on the proble...

The Boolean Isomorphism Problem

We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the veriier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bsho...

The College Admissions Problem Reconsidered

This paper revisits the college admissions problem and studies the efficiency, incentive, and monotonicity for colleges. We show that max-min criterion that is stronger than substitutability, together with the quota-saturability that requires having enough acceptable applicants, guarantees weak Pareto efficiency and strategy-proofness for colleges under the colleges-proposing deferred acceptanc...

The Monty Hall Problem, Reconsidered