Related papers: A Turing machine simulation by P systems without c…
We prove that the word problem of a finitely generated group $G$ is in NP (solvable in polynomial time by a non-deterministic Turing machine) if and only if this group is a subgroup of a finitely presented group $H$ with polynomial…
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers,…
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…
There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…
The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic"…
By using of analytical multi-logic expresses in conjunction with non-deterministic Turing machine the proposition was proved that algorithm of deterministic Turing counter machine of polynomial time complexity can be decreased to the…
Type systems as a way to control or analyze programs have been largely studied in the context of functional programming languages. Some of those work allow to extract from a typing derivation for a program a complexity bound on this…
This article shows that PSPACE not equal EXP. A simple but novel proof technique has been used to separate these two classes. Whether an arbitrary Turing machine accepts an input when the running time is limited has been computed in this…
The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $\tau$-Conjecture for polynomials implies that…
We state a version of the P=?NP problem for infinite time Turing machines. It is observed that P not= NP for this version.
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
We show that the problem of determining the feasibility of quadratic systems over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$ requires exponential time. This separates P and NP over these fields/rings in the BCSS model of computation.
We define and study a new notion of "robust simulations" between complexity classes which is intermediate between the traditional notions of infinitely-often and almost-everywhere, as well as a corresponding notion of "significant…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…
Testing equivalence was originally defined by De Nicola and Hennessy in a process algebraic setting (CCS) with the aim of defining an equivalence relation between processes being less discriminating than bisimulation and with a natural…