A nontrivial lower bound for an NP problem on automata
SIAM Journal on Computing
Linear Time Algorithms and NP-Complete Problems
SIAM Journal on Computing
Theoretical Computer Science
The Complexity of Planar Counting Problems
SIAM Journal on Computing
Monadic logical definability of nondeterministic linear time
Computational Complexity
Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time
SIAM Journal on Computing
MonadicNLIN and Quantifier-Free Reductions
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
On unique graph 3-colorability and parsimonious reductions in the plane
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
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This paper aims at being a step in the precise classification of the many NP-complete problems which belong to NLIN (nondeterministic linear time complexity on random-access machines), but are seemingly not NLIN-complete. We define the complexity class LIN-LOCAL - the class of problems linearly reducible to problems defined by Boolean local constraints - as well as its planar restriction LIN-PLAN-LOCAL. We show that both "local" classes are rather computationally robust and that SAT and PLAN-SAT are complete in classes LIN-LOCAL and LIN-PLAN-LOCAL, respectively. We prove that some unexpected problems that involve some seemingly global constraints are complete for those classes. E.g., VERTEX-COVER and many similar problems involving cardinality constraints are LIN-LOCAL-complete. Our most striking result is that PLAN-HAMILTON - the planar version of the Hamiltonian problem - is LIN-PLAN-LOCAL and even is LIN-PLAN-LOCAL-complete. Further, since our linear-time reductions also turn out to be parsimonious, they yield new DP-completeness results for UNIQUE-PLAN-HAMILTON and UNIQUE-PLAN-VERTEX-COVER.