Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis
TLDR
If there is a sparse NP-complete set under polynomial-time many-one reductions, then P = NP, and it is shown that if there is one, then the polynometric-time hierarchy collapses to Δ2P.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1982-10-01 and is currently open access. It has received 295 citations till now. The article focuses on the topics: Hierarchy (mathematics) & Polynomial.read more
Citations
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Book
Structural Complexity I
TL;DR: This volume is written for undergraduate students who have taken a first course in Formal Language Theory and presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory.
Book ChapterDOI
A catalog of complexity classes
TL;DR: This chapter discusses the concepts needed for defining the complexity classes, a set of problems of related resource-based complexity that can be solved by an abstract machine M using O(f(n) of resource R, where n is the size of the input.
Book
Introduction to the theory of complexity
TL;DR: 1. Mathematical Preliminaries, Elements of Computability Theory, and Space-Complexity Classes: Algorithms and Complexity Classes.
Journal ArticleDOI
Infeasibility of instance compression and succinct PCPs for NP
Lance Fortnow,Rahul Santhanam +1 more
TL;DR: There is no reduction from OR-SAT to any set A where the length of the output is bounded by a polynomial in n, unless NP@?coNP/poly, and the Polynomial-Time Hierarchy collapses.
Journal ArticleDOI
Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity
TL;DR: It is shown that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete.
References
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Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Journal ArticleDOI
The complexity of computing the permanent
TL;DR: It is shown that the permanent function of (0, 1)-matrices is a complete problem for the class of counting problems associated with nondeterministic polynomial time computations.