Showing papers by "Juris Hartmanis published in 1976"

On isomorphisms and density of NP and other complete sets

Abstract: @ 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.

Independence results in computer science

Abstract: In this note we show that instances of problems which appear naturally in computer science cannot be answered in formalized set theory. We show, for example, that some relativized versions of the famous P = NP problem cannot be answered in formalized set theory, that explicit algorithms can be given whose running time is independent of the axioms of set theory, and that one can exhibit a specific context-free grammar G for which it cannot be proven in set theory that L(G) = Σ* or L(G) ≠ Σ*.