Related papers: On the Kolmogorov-Chaitin Complexity for short seq…
In this paper, we consider the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). The problem is as follows. For a positive integer $n$, a sequence of n strings $S=(s^1,\dots,s^n)$ is given. We should…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…
We formulate and investigate the simplest version of time-optimal quantum computation theory (t-QCT), where the computation time is defined by the physical one and the Hamiltonian contains only one- and two-qubit interactions. This version…
Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this…
We prove that ``almost generically'' for a one-relator group Delzant's $T$-invariant (which measures the smallest size of a finite presentation for a group) is comparable in magnitude with the length of the defining relator. The proof…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…
This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's universal prior M, the latter being an excellent…
Given a set of $k$ strings $I$, their longest common subsequence (LCS) is the string with the maximum length that is a subset of all the strings in $I$. A data-structure for this problem preprocesses $I$ into a data-structure such that the…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large…
In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…
In this paper, we investigate discrete topological complexity $TC(K)$ introduced for situations where the configuration space possesses a simplicial structure. %Simplicial complexes are well-known and commonly used in programming for…
Consider a d*n matrix A, with d<n. The problem of solving for x in y=Ax is underdetermined, and has infinitely many solutions (if there are any). Given y, the minimum Kolmogorov complexity solution (MKCS) of the input x is defined to be an…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's prior M, the latter being an excellent predictor in…