We present a simple linear-time algorithm constructing a context-free grammar of size \(\mathcal{O}(g \log (N/g))\) for the input string of size N, where g the size of the optimal grammar generating… Expand

A negative answer is given, contrary to the conjectured positive one, by constructing a conjunctive grammar for the language \(\{ a^{4^{n}} : n \in \mathbb{N} \}\).Expand

In this article, a fully compressed pattern matching problem is studied using a recently developed technique of local recompression: the SLPs are refactored so that substrings of the pattern and text are encoded in both SLPs in the same way.Expand

An application of a local recompression technique, previously developed by the author in the context of compressed membership problems and compressed pattern matching, to word equations, which yields new self-contained proofs of many known results for word equations.Expand

The previously known $\mathcal O (|\Sigma|n^2)$ solution is improved by giving an expected time algorithm for this problem, where |?| is the size of the (potentially partial) transition function.Expand

In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size 4 g log 3 / 2 ? ( N / g ) for the input string, where N is the size of the input string and… Expand

A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case and the running time is lowered to $$\mathcal {O}(n)$$O (n) in the RAM model.Expand

It is shown that a context-free grammar of size m that produces a single string w of length n can be transformed in linear time into a context -free grammar for w of size O(m), whose unique derivation tree has depth O(log n), solving an open problem in the area of grammar-based compression.Expand

The general membership problem for these equations is proved to be EXPTIME-complete and it is established that least solutions of all such systems are in EXPTime.Expand