Related papers: A "Proof" of $P\neq NP$

The purpose of this paper was to give an algebraic analog of Poincare duality. But there is a mistake in the proof of the main theorem. It will be corrected as soon as possible.

In narrative synthesis of evidence, it can be the case that the only quantitative measures available concerning the efficacy of an intervention is the direction of the effect, i.e. whether it is positive or negative. In such situations, the…

The "paradox" arises in the Two Envelopes Paradox from the incorrect formulation of the argument. The infomation given is misused and therefore the results are incorrect for the question asked. The key is to be clear on what question we are…

In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].

There is a serious mistake in the proof.

We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…

This paper is the second in a series of planned papers which provide first bijective proofs of alternating sign matrix results. Based on the main result from the first paper, we construct a bijective proof of the enumeration formula for…

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…

In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…

The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…

In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.

The purpose of this note is to attach a name to a natural class of combinatorial problems and to point out that this class includes many important special cases. We also show that a simple problem of placing nonoverlapping labels on a…

Although whether P equals NP is an important, open problem in computer science, and although Jaeger's 2008 paper, "Solving the P/NP Problem Under Intrinsic Uncertainty" (arXiv:0811.0463) presents an attempt at tackling the problem by…

Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of…

The note clarifies a gap in the proof of the minimum distance for Projective Reed-Muller Codes. The gap was identified by S.Ghorpade and R.Ludhani in a recent article. Here the original thoughts are explained and the gap closed.

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

One advantage of paraconsistent logic is that it can deal with inconsistencies without making the system trivial. However, unlike classical propositional calculus, its deductive system is limited, and the meaning of paraconsistent negation…