Word equations in non-deterministic linear space

Satisfiability of word equations problem is: Given two sequences consisting letters and variables decide whether there is a substitution for the that turns this equation into true equality. The exact computational complexity remains unknown, with best lower upper bounds being, respectively, NP PSPACE . Recently, novel technique recompression was applied to problem, simplifying known proofs lowering space (non-deterministic) O ( n log ⁡ ) In paper we show satisfiability in non-deterministic linear space, thus language satisfiable context-sensitive. We use recompression-based algorithm additionally employ Huffman coding letters. proof, however, uses analysis how fragments depend on each other as well new strategy choices algorithm.