Institution profile

SOKEN, Inc.

Industry researchasia · jp
Official website
Research library6linked papers
Opportunities0open roles
Selected work

Representative Papers

One-Sided-Error Parameterized Reductions for the Minimum Distance and Shortest Vector Problems

Aug 14, 2026

This study addresses the longstanding challenge of establishing deterministic reductions and parameterized approximation hardness for the Minimum Distance Problem (MDP) and Shortest Vector Problem (SVP). We propose a one-sided error randomized reduction framework that leverages OR-function constructions and achieves conditional derandomization under circuit lower bound assumptions. Our results establish both NP-hardness and W[1]-hardness for MDP and SVP under constant-factor approximations. These findings bridge critical gaps in deterministic and parameterized complexity theory, providing novel theoretical foundations for understanding the computational nature of these fundamental lattice problems.

0 citationsRead paper

On the Complexity of Locally Dense Lattices

Aug 14, 2026

This study addresses the decision complexity and definitional equivalence of locally dense lattices by introducing the LDL P decision problem and analyzing it through the polynomial hierarchy. We prove that this problem is Σ₂^P-complete under the infinity norm when p ≥ log₂3. Furthermore, we establish the equivalence between two prevailing definitions via deterministic polynomial-time reductions. By precisely characterizing the computational complexity class of locally dense lattice recognition and unifying classical definitions, this work provides a rigorous theoretical foundation for future research in lattice-based complexity theory and related domains.

0 citationsRead paper
Recent publications

Latest Papers

One-Sided-Error Parameterized Reductions for the Minimum Distance and Shortest Vector Problems

Aug 14, 2026

This study addresses the longstanding challenge of establishing deterministic reductions and parameterized approximation hardness for the Minimum Distance Problem (MDP) and Shortest Vector Problem (SVP). We propose a one-sided error randomized reduction framework that leverages OR-function constructions and achieves conditional derandomization under circuit lower bound assumptions. Our results establish both NP-hardness and W[1]-hardness for MDP and SVP under constant-factor approximations. These findings bridge critical gaps in deterministic and parameterized complexity theory, providing novel theoretical foundations for understanding the computational nature of these fundamental lattice problems.

0 citationsRead paper

On the Complexity of Locally Dense Lattices

Aug 14, 2026

This study addresses the decision complexity and definitional equivalence of locally dense lattices by introducing the LDL P decision problem and analyzing it through the polynomial hierarchy. We prove that this problem is Σ₂^P-complete under the infinity norm when p ≥ log₂3. Furthermore, we establish the equivalence between two prevailing definitions via deterministic polynomial-time reductions. By precisely characterizing the computational complexity class of locally dense lattice recognition and unifying classical definitions, this work provides a rigorous theoretical foundation for future research in lattice-based complexity theory and related domains.

0 citationsRead paper