Related papers: A Proof for P =? NP Problem
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
In this work, we prove the NP-completeness of two variants of tokenisation, defined as the problem of compressing a dataset to at most $\delta$ symbols by either finding a vocabulary directly (direct tokenisation), or selecting a sequence…
We prove that persuasion is an NP-complete problem.
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…
Reachability and LTL model-checking problems for flat counter systems are known to be decidable but whereas the reachability problem can be shown in NP, the best known complexity upper bound for the latter problem is made of a tower of…
The following problem is considered. A Turing machine $M$, that accepts a string of fixed length $t$ as input, runs for a time not exceeding a fixed value $n$ and is guaranteed to produce a binary output, is given. It's required to find a…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems…
Neural Turing Machines (NTMs) are an instance of Memory Augmented Neural Networks, a new class of recurrent neural networks which decouple computation from memory by introducing an external memory unit. NTMs have demonstrated superior…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.
The construction of a universal static quantum computer actually provides another proof of the NP-hardness of spin-glass problems.
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
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…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
We present the MEoP problem that decides the existence of solutions to certain modular equations over prime numbers and show how this separates the complexity class NP from its subclass P
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
The order preserving pattern matching (OPPM) problem is, given a pattern string $p$ and a text string $t$, find all substrings of $t$ which have the same relative orders as $p$. In this paper, we consider two variants of the OPPM problem…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…