Related papers: Verifying whether One-Tape Non-Deterministic Turin…
The P versus NP problem asks whether every language verifiable in polynomial time can also be decided in deterministic polynomial time. In this paper, we present a constructive proof that P = NP by introducing a universal, graph-based…
We show that for all functions $t(n) \geq n$, every multitape Turing machine running in time $t$ can be simulated in space only $O(\sqrt{t \log t})$. This is a substantial improvement over Hopcroft, Paul, and Valiant's simulation of time…
This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way…
The traveling tournament problem (TTP) is to minimize the total traveling distance of all teams in a double round-robin tournament. In this paper, we focus on TTP-2, in which each team plays at most two consecutive home games and at most…
We prove in this paper that there is a language $L_s$ accepted by some nondeterministic Turing machine that runs within time $O(n^k)$ for any positive integer $k\in\mathbb{N}_1$ but not by any ${\rm co}\mathcal{NP}$ machines. Then we…
The deterministic membership problem for timed automata asks whether the timed language recognised by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. We show that the problem is decidable when the…
Schindler recently addressed two versions of the question P $\stackrel{?}{=}$ NP for Turing machines running in transfinite ordinal time. These versions differ in their definition of input length. The corresponding complexity classes are…
We study a generalized version of reversal bounded Turing machines where, apart from several tapes on which the number of head reversals is bounded by r(n), there are several further tapes on which head reversals remain unrestricted, but…
The power of real-time Turing machines using sublinear space is investigated. In contrast to a claim appearing in the literature, such machines can accept non-regular languages, even if working in deterministic mode. While maintaining a…
The \textsc{Co-Path Packing} (resp., \textsc{Co-Path Set}) problem asks whether a given graph can be edited to a collection of induced paths by deleting at most $k$ vertices (resp., $k$ edges). Both are fundamental problems with significant…
In various models of one-way pushdown automata, the explicit use of two designated endmarkers on a read-once input tape has proven to be extremely useful for making a conscious, final decision on the acceptance/rejection of each input word…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
We introduce and investigate forgetting 1-limited automata, which are single-tape Turing machines that, when visiting a cell for the first time, replace the input symbol in it by a fixed symbol, so forgetting the original contents. These…
We consider how changes in transfinite machine architecture can sometimes alter substantially their capabilities. We approach the subject by answering three open problems touching on: firstly differing halting time considerations for…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
We examine some variants of computation with closed timelike curves (CTCs), where various restrictions are imposed on the memory of the computer, and the information carrying capacity and range of the CTC. We give full characterizations of…
We consider computations of a Turing machine subjected to noise. In every step, the action (the new state and the new content of the observed cell, the direction of the head movement) can differ from that prescribed by the transition…
We define a subclass of quantum Turing machine (QTM) named SR-QTM, which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With the help of QSTD, we…
In this paper, we extend the techniques used in our previous work to show that there exists a probabilistic Turing machine running within time $O(n^k)$ for all $k\in\mathbb{N}_1$ accepting a language $L_d$ that is different from any…
The Busy Beaver Challenge (or bbchallenge) aims at collaboratively solving the following conjecture: "$S(5) = 47{,}176{,}870$" [Rad\'o, 1962], [Marxen and Buntrock, 1990], [Aaronson, 2020]. This conjecture says that if a 5-state Turing…