The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A combinatorial problem which is complete in polynomial space
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Some simplified NP-complete problems
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Polynomial complete scheduling problems
SOSP '73 Proceedings of the fourth ACM symposium on Operating system principles
On Some Central Problems in Computational Complexity
On Some Central Problems in Computational Complexity
The Complexity of Resolution Procedures for Theorem Proving in the Propositional Calculus
The Complexity of Resolution Procedures for Theorem Proving in the Propositional Calculus
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A note on #P-completeness of NP-witnessing relations
Information Processing Letters
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If all NP complete sets are isomorphic under deterministic polynomial time mappings (p-isomorphic) then P @@@@ NP and if all PTAPE complete sets are p-isomorphic then P @@@@ PTAPE. We show that all NP complete sets known (in the literature) are indeed p-isomorphic and so are the known PTAPE complete sets. Thus showing that, inspite of the radically different origins and attempted simplification of these sets, all the known NP complete sets are identical but for polynomially time bounded permutations. Furthermore, if all NP complete sets are p-isomorphic then they all must have similar densities and, for example, no language over a single letter alphabet can be NP complete, nor can any sparse language over an arbitrary alphabet be NP complete. We show that complete sets in EXPTIME and EXPTAPE cannot be sparse and therefore they cannot be over a single letter alphabet. Similarly, we show that the hardest context-sensitive languages cannot be sparse. We also relate the existence of sparse complete sets to the existence of simple combinatorial circuits for the corresponding truncated recognition problem of these languages.