On the determinization blowup for finite automata recognizing equal-length languages

Juhani Karhumäki, Alexander Okhotin

Research output


Motivated by the application to image compression (K. Čulìk II, J. Kari, “Image compression using weighted finite automata”, Computers & Graphics, 1993), the paper considers finite automata representing formal languages with all strings of the same length, and investigates relative succinctness of representation by deterministic and nondeterministic finite automata (DFA, NFA). It is shown that an n-state NFA recognizing a language of strings of length _ over a k-symbol alphabet can be transformed to a DFA with at most _ · k_ 2 log2 k n+3_+3 = 2O(√n) states. At the same time, for every k-symbol alphabet with k _ 2, and for every n _ 1, there exists an n-state NFA recognizing an equal-length language, which requires a DFA with at least k√ n k−1−2 = 2Ω(√n) states.

Original languageEnglish
Title of host publicationComputing with New Resources: Essays Dedicated to Jozef Gruska on the Occasion of His 80th Birthday
Number of pages12
Publication statusPublished - 1 Jan 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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