Text algorithms
Handbook of formal languages, vol. 1
Translating regular expressions into small εe-free nondeterministic finite automata
Journal of Computer and System Sciences
The commutation of finite sets: a challenging problem
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Conway's problem for three-word sets
Theoretical Computer Science
Computing epsilon-Free NFA from Regular Expressions in O(n log²(n)) Time
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
The Commutation with Codes and Ternary Sets of Words
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Satisfiability of word equations with constants is in PSPACE
Journal of the ACM (JACM)
Hi-index | 5.23 |
We investigate the complexity of basic decidable cases of the commutation problem for languages: testing the equality XY = YX for two languages X and Y. We show that it varies from co-NEXPTIME complete through PSPACE complete and co-NP complete to deterministic polynomial time, when Y is an explicitly given finite language and X is given by a CF grammar generating a finite language, a nondeterministic finite automaton (or a regular expression), an acyclic nondeterministic finite automaton or an explicitly given finite language, respectively. Interestingly in most cases the complexity status does not change if instead of explicitly given finite Y we consider general Y of the same type as X. For deterministic finite automata the problem remains open, due to the asymmetry of the catenation.