Text algorithms
Handbook of formal languages, vol. 1
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
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
On the Centralizer of a Finite Set
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Translating Regular Expressions into Small epsilon-Free Nondeterministic Finite Automata
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Satisfiability of Word Equations with Constants is in PSPACE
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The Commutation of Finite Sets: a Challenging Problem
The Commutation of Finite Sets: a Challenging Problem
Decision Questions Concerning Semilinearity Morphisms and
Decision Questions Concerning Semilinearity Morphisms and
Complexity measures for regular expressions
Journal of Computer and System Sciences
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We investigate the complexity of basic decidable cases of the commutation problem for languages: testing the equality XY = YX for two languages X, Y, given different types of representations of X, Y. We concentrate on (the most interesting) case when Y is an explicitly given finite language. This is motivated by a renewed interest and recent progress, see [12,1], in an old open problem posed by Conway [2]. We show that the complexity of the commutation problem varies from co-NEXPTIME-complete, through P-SPACE complete and co-NP complete, to deterministic polynomial time. Classical types of description are considered: nondeterministic automata with and without cycles, regular expressions and grammars. 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 that of X. For the case of commutation of two finite sets we provide polynomial time algorithms whose time complexity beats that of a naive algorithm. For deterministic automata the situation is more complicated since the complexity of concatenation of deterministic automaton language X with a finite set Y is asymmetric: while the minimal dfa's for XY would be polynomial in terms of dfa's for X and Y , that for YX can be exponential.