• Publications
  • Influence
Approximation of Grammar-Based Compression via Recompression
  • A. Jez
  • Mathematics, Computer Science
  • CPM
  • 24 January 2013
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 generatingExpand
Conjunctive Grammars Can Generate Non-regular Unary Languages
  • A. Jez
  • Mathematics, Computer Science
  • Developments in Language Theory
  • 1 June 2008
TLDR
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
Faster Fully Compressed Pattern Matching by Recompression
  • A. Jez
  • Computer Science, Mathematics
  • ACM Trans. Algorithms
  • 14 November 2011
TLDR
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
Recompression: a simple and powerful technique for word equations
  • A. Jez
  • Mathematics, Computer Science
  • STACS
  • 16 March 2012
TLDR
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
Hyper-minimisation Made Efficient
TLDR
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
Context Unification is in PSPACE
  • A. Jez
  • Mathematics, Computer Science
  • ICALP
  • 16 October 2013
TLDR
It is shown that context unification is in PSPACE, so as word equations, and NP is still the best known lower-bound. Expand
A really simple approximation of smallest grammar
  • A. Jez
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 18 March 2014
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 andExpand
One-Variable Word Equations in Linear Time
  • A. Jez
  • Mathematics, Computer Science
  • Algorithmica
  • 14 February 2013
TLDR
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
Balancing Straight-Line Programs
TLDR
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
Complexity of solutions of equations over sets of natural numbers
TLDR
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
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