Related papers: On the Smallest Size of Internal Collage Systems
In grammar-based compression a string is represented by a context-free grammar, also called a straight-line program (SLP), that generates only that string. We refine a recent balancing result stating that one can transform an SLP of size…
It was recently proved that any Straight-Line Program (SLP) generating a given string can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We generalize this proof to a general class of grammars we…
It was recently proved that any SLP generating a given string $w$ can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We show that this result also holds for RLSLPs, which are SLPs extended with…
The convolution between a text string $S$ of length $N$ and a pattern string $P$ of length $m$ can be computed in $O(N \log m)$ time by FFT. It is known that various types of approximate string matching problems are reducible to…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
We give algorithms that, given a straight-line program (SLP) with $g$ rules that generates (only) a text $T [1..n]$, builds within $O(g)$ space the Lempel-Ziv (LZ) parse of $T$ (of $z$ phrases) in time $O(n\log^2 n)$ or in time…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure $\delta$ based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness (which are…
We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string.…
We consider building, given a straight-line program (SLP) consisting of $g$ productions deriving a two-dimensional string $T$ of size $N\times N$, a structure capable of providing random access to any character of $T$. For one-dimensional…
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 solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
The CTL learning problem consists in finding for a given sample of positive and negative Kripke structures a distinguishing CTL formula that is verified by the former but not by the latter. Further constraints may bound the size and shape…
Tsetlin machine (TM) is a logic-based machine learning approach with the crucial advantages of being transparent and hardware-friendly. While TMs match or surpass deep learning accuracy for an increasing number of applications, large clause…
Explicit chain-of-thought (CoT) reasoning substantially improves the reasoning ability of large language models (LLMs), but incurs high inference cost due to lengthy autoregressive traces. Existing latent reasoning methods offer a promising…
The minimum circuit size problem (MCSP) is a string compression problem with a parameter $s$ in which, given the truth table of a Boolean function over inputs of length $n$, one must answer whether it can be computed by a Boolean circuit of…
We present novel variants of fully online LCA (FOLCA), a fully online grammar compression that builds a straight line program (SLP) and directly encodes it into a succinct representation in an online manner. FOLCA enables a direct encoding…
We propose a new approach for universal lossless text compression, based on grammar compression. In the literature, a target string $T$ has been compressed as a context-free grammar $G$ in Chomsky normal form satisfying $L(G) = \{T\}$. Such…
A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and…