We first observe that NP-completeness immediately follows forCNFSAT and SAT since 3SAT ≤p CNFSAT ≤p SAT . Note that 3SAT ⊂ CNFSAT ⊂ SAT . The reduction in each case is almost the identity (though of course it can’t be since the sets are different). The only issue is that we have to modify satisfiable formulas that are not in 3CNF. For the 3SAT ≤p CNFSAT reduction we simply map any input that is...

Given a set H of binary vectors of length n, is there a cyclic listing of H so that every two successive vectors differ in a single coordinate? The problem of existence of such a listing, which is called a cyclic Gray code of H, is known to be NP-complete in general. The goal of this paper is therefore to specify boundaries between its intractability and polynomial decidability. For that purpos...

The notion of NP-completeness has cut across many elds and has provided a means of identifying deep and unexpected commonalities. Problems from areas as diverse as combinatorics, logic, and operations research turn out to be NP-complete and thus computationally equivalent in the sense discussed in the next paragraph. PSPACE-completeness, NEXP-completeness, and completeness for other complexity ...

We prove that if for some ǫ > 0, NP contains a set that is DTIME(2n ǫ )-bi-immune, then NP contains a set that is 2-Turing complete for NP (hence 3-truth-table complete) but not 1-truth-table complete for NP. Thus this hypothesis implies a strong separation of completeness notions for NP. Lutz and Mayordomo [LM96] and Ambos-Spies and Bentzien [ASB00] previously obtained the same consequence usi...

We consider two types of folding applied to equilateral plane graph linkages. First, under continuous folding motions, we show how to reconfigure any linear equilateral tree (lying on a line) into a canonical configuration. By contrast, such reconfiguration is known to be impossible for linear (nonequilateral) trees and for (nonlinear) equilateral trees. Second, under instantaneous folding moti...

Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of determining whether there exists a joint strategy where each player has an expected payoff of at least r is NP-complete as a function of the number of nodes in the ...