Related papers: Computability vs. Nondeterministic and P vs. NP
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
Kallampally and Tewari showed in 2016 that there can be a trade-off between determinism and time in space-bounded computations. This they did by describing an unambiguous non-deterministic algorithm to solve Directed Graph Reachability that…
Assuming a cloning oracle, satisfiability, which is an NP complete problem, is shown to belong to $BPP^C$ and $BQP^C$ (depending on the ability of the oracle C to clone either a binary random variable or a qubit). The same result is…
The NP-complete problem of the travelling salesman (TSP) is considered in the framework of quantum adiabatic computation (QAC). We first derive a remarkable lower bound for the computation time for adiabatic algorithms in general as a…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
The present work proves that P=NP. The proof, presented in this work, is a constructive one: the program of a polynomial time deterministic multi-tape Turing machine M_ExistsAcceptingPath, that determines if there exists an accepting…
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running…
In this PhD thesis the ancient question of determinism ('Does every event have a cause ?') will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic:…
We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…
The question whether P equals NP revolves around the discrepancy between active production and mere verification by Turing machines. In this paper, we examine the analogous problem for finite transducers and automata. Every nondeterministic…
We discuss the accuracy of the attribution commonly given to Turing's 1936 paper "On computable numbers..." for the computable undecidability of the halting problem, coming eventually to a nuanced conclusion.
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
We introduce a method based on Conformal Prediction (CP) to quantify the uncertainty of full ranking algorithms. We focus on a specific scenario where $n+m$ items are to be ranked by some ``black box'' algorithm. It is assumed that the…
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…
The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the…
Quantum theory is widely regarded as fundamentally indeterministic, yet classical frameworks can also exhibit indeterminism once infinite information is abandoned. At the same time, relativity is usually taken to forbid superluminal…