Audit NP-hardness proofs and polynomial-time reductions for decision problems.
npx skills add https://github.com/Arcadi4/nerdy --skill np-completeness
Please help me install this Agent Skill. Skill: np-completeness Source: https://github.com/Arcadi4/nerdy/tree/main/clrs/np-completeness Command: npx skills add https://github.com/Arcadi4/nerdy --skill np-completeness
This skill helps researchers and students formally verify NP-hardness and NP-completeness by guiding the creation of polynomial-time reductions, defining decision languages, and validating certificate-based NP-membership.
Outline a complete NP-completeness analysis for a target problem by selecting a known NP-complete source, constructing a polynomial-time reduction, and proving membership and hardness.
High-intent search queries and answers about installing and using this skill.
To prove NP-completeness, construct a polynomial-time reduction from a known NP-complete problem like SAT or CLIQUE to your target decision problem, verifying both forward and reverse directions along with polynomial construction bounds.
Defining a decision language for an NP-hardness proof requires specifying the problem's input encoding and certificate verification process to establish NP-membership before proving NP-hardness through polynomial-time reductions.
Yes, you can verify reductions from classic template problems including VERTEX-COVER, SUBSET-SUM, CIRCUIT-SAT, and HAM-CYCLE by checking encoding size arguments, reduction composition, and certificate-based NP-membership.
Classify a problem as in P, NP, NP-hard, or NP-complete by verifying certificate-based NP-membership and constructing polynomial-time reductions from canonical NP-complete problems to establish NP-hardness within theoretical computer science contexts.
Limitations include the necessity to strictly enforce definitions of decision languages, verify encoding size, ensure both forward and reverse reduction directions, and maintain polynomial construction bounds for the target problem.
bnebFormulate polynomial-time reductions with Lean 4 correctness proof templates.
rysweetAnalyze computational problems for feasibility, scalability, and fundamental limits.
CodingThrustAnalyze reduction graph topology for orphan problems and NP-hardness proof chains.
scooter-lacroixAnalyze series convergence using ratio, root, and comparison tests.
