Related papers: A class of examples demonstrating that P is differ…
Extensions of the Kochen-Specker theorem use quantum logics whose classical interpretation suggests a true-implies-value indefiniteness property. This can be interpreted as an indication that any view of a quantum state beyond a single…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
Contextuality, the impossibility of assigning a single random variable to represent the outcomes of the same measurement procedure under different experimental conditions, is a central aspect of quantum mechanics. Thus defined, it appears…
We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…
Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…
Hidden variables theories for quantum mechanics are usually assumed to satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an…
In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems, showed that all these problems are either in P or NP-complete, and gave a…
We present a definition of the class NP in combinatorial context as the set of languages of structures defined by finitely many forbidden lifted substructures. We apply this to special syntactically defined subclasses and show how they…
We show that the problem of deciding positivity of Kronecker coefficients is NP-hard. Previously, this problem was conjectured to be in P, just as for the Littlewood-Richardson coefficients. Our result establishes in a formal way that…
Mixtures of coherent states are commonly regarded as classical. Here we show that there is a quantum advantage in discriminating between coherent states in a mixture, implying the presence of quantum properties in the mixture, which are…
We study a model where two opposing provers debate over the membership status of a given string in a language, trying to convince a weak verifier whose coins are visible to all. We show that the incorporation of just two qubits to an…
A new class UF of problems is introduced, strictly included in the class NP, which arises in the analysis of the time verifying the intermediate results of computations. The implications of the introduction of this class are considered.…
In this paper, I first establish -- via methods other than the Gottesman-Knill theorem -- the existence of an infinite set of instances of simulating a quantum circuit to decide a decision problem that can be simulated classically. I then…
The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…
We prove an explicit finite-sample version of the Borel--Cantelli lemma under $m$-dependence. Given any $m$-dependent sequence of events $(A_k)_{1\leq k\leq N}$, we show that \[ \mathbb{P}\Bigl(\bigcup_{k=1}^N A_k\Bigr) \ge 1 -…
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…
The Kochen-Specker theorem is a basic and fundamental 50 year old non-existence result affecting the foundations of quantum mechanix, strongly implying the lack of any meaningful notion of "quantum realism", and typically leading to…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
Two theorems about the P versus NP problem be proved in this article (1) There exists a language $L$, that the statement $L \in \textbf{P}$ is independent of ZFC. (2) There exists a language $L \in \textbf{NP}$, for any polynomial time…