Stamina: Stabilisation Monoids in Automata Theory

  • Nathanaël FijalkowEmail author
  • Hugo Gimbert
  • Edon Kelmendi
  • Denis Kuperberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)


We present Stamina, a tool solving three algorithmic problems in automata theory. First, compute the star height of a regular language, i.e. the minimal number of nested Kleene stars needed for expressing the language with a complement-free regular expression. Second, decide limitedness for regular cost functions. Third, decide whether a probabilistic leaktight automaton has value 1, i.e. whether a probabilistic leaktight automaton accepts words with probability arbitrarily close to 1.

All three problems reduce to the computation of the stabilisation monoid associated with an automaton, which is computationally challenging because the monoid is exponentially larger than the automaton. The compact data structures used in Stamina, together with optimisations and heuristics, allow us to handle automata with several hundreds of states. This radically improves upon the performances of ACME, a similar tool solving a subset of these problems.

The tool Stamina is open source and available from Github, details are given on the webpage


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nathanaël Fijalkow
    • 1
    Email author
  • Hugo Gimbert
    • 2
  • Edon Kelmendi
    • 3
  • Denis Kuperberg
    • 4
  1. 1.University of WarwickWarwickUK
  2. 2.LaBRIBordeauxFrance
  3. 3.TU MunichMunichGermany
  4. 4.CNRS, ÉNS LyonLyonFrance

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