TY - GEN

T1 - Relationship between density and deterministic complexity of MP-complete languages

AU - Berman, Piotr

N1 - Publisher Copyright:
© 1978, Springer-Verlag.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1978

Y1 - 1978

N2 - Let Σ be an arbitrary alphabet. denotes ɛ∪Σ∪..∪Σn. We say that a function t, t: is f-sparse iff card for every natural n. The main theorem of this paper establishes that if CLIQUE has some f-sparse translation into another set, which is calculable by a deterministic Turing machine in time bounded by f, then all the sets belonging to NP are calculable in time bounded by a function polynomially related to f. The proof is constructive and shows the way of constructing a proper algorithm. The simplest and most significant corollary says that if there is an NP-complete language over a single letter alphabet, then P=NP.

AB - Let Σ be an arbitrary alphabet. denotes ɛ∪Σ∪..∪Σn. We say that a function t, t: is f-sparse iff card for every natural n. The main theorem of this paper establishes that if CLIQUE has some f-sparse translation into another set, which is calculable by a deterministic Turing machine in time bounded by f, then all the sets belonging to NP are calculable in time bounded by a function polynomially related to f. The proof is constructive and shows the way of constructing a proper algorithm. The simplest and most significant corollary says that if there is an NP-complete language over a single letter alphabet, then P=NP.

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U2 - 10.1007/3-540-08860-1_6

DO - 10.1007/3-540-08860-1_6

M3 - Conference contribution

AN - SCOPUS:85034603266

SN - 9783540088608

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 63

EP - 71

BT - Automata, Languages and Programming - 5th Colloquium

A2 - Bohm, Corrado

A2 - Ausiello, Giorgio

PB - Springer Verlag

T2 - 5th International Colloquium on Automata, Languages and Programming, ICALP 1978

Y2 - 17 July 1978 through 21 July 1978

ER -