Related papers: On Time-Bounded Incompressibility of Compressible …
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…
This paper explores the computational complexity of various natural one-variable fragments of first-order modal logics with the addition of counting quantifiers, over both constant and varying domains. The addition of counting quantifiers…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
We reveal a connection between the incompressibility method and the Lovasz local lemma in the context of Ramsey theory. We obtain bounds by repeatedly encoding objects of interest and thereby compressing strings. The method is demonstrated…
Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. In this paper, we identify all fragments…
We develop conjectures and theorems expressing the idea that the prime sequence exhibits computational irreducibility in the transition from one prime to its successor. Informally, given a prime pp p, no general algorithm can compute the…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
Answering a question raised by V. V. Tkachuk, we present several examples of $\sigma$-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In…
Random access to highly compressed strings -- represented by straight-line programs or Lempel-Ziv parses, for example -- is a well-studied topic. Random access to such strings in strongly sublogarithmic time is impossible in the worst case,…
We prove a strong Symmetry of Information relation for random strings (in the sense of Kolmogorov complexity) and establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a…
The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable…
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…
We study the satisfiability of string constraints where context-free membership constraints may be imposed on variables. Additionally a variable may be constrained to be a subword of a word obtained by shuffling variables and their…
Much research in stringology focuses on structures that can, in a way, ``grasp'' repeats (substrings that occur multiple times) as, for example, the so-called runs, a.k.a. maximal repetitions, compactly describe all tandem repeats. In this…
In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate…
We consider subsequences with gap constraints, i.e., length-k subsequences p that can be embedded into a string w such that the induced gaps (i.e., the factors of w between the positions to which p is mapped to) satisfy given gap…
Tensors are often compressed by expressing them in low rank tensor formats. In this paper, we develop three methodologies that bound the compressibility of a tensor: (1) Algebraic structure, (2) Smoothness, and (3) Displacement structure.…
Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the…