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On nonpermutational transformation semigroups with an application to syntactic complexity [article]

Szabolcs Ivan, Judit Nagy-Gyorgy
2014 arXiv   pre-print
As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.  ...  We give an upper bound of n((n-1)!-(n-3)!) for the possible largest size of a subsemigroup of the full transformational semigroup over n elements consisting only of nonpermutational transformations.  ...  syntactic semigroup [12]: There is an ongoing line of research for syntactic complexity of regular languages. 31 In general, a regular language with state complexity n can have a syntactic 32 complexity  ... 
arXiv:1402.7289v1 fatcat:kb6jyj656zguzn5tl5clplmham

On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity

Szabolcs Iván, Judit Nagy-György
2016 Acta Cybernetica  
As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.  ...  We give an upper bound of n((n−1)!−(n−3)!) for the possible largest size of a subsemigroup of the full transformational semigroup over n elements consisting only of nonpermutational transformations.  ...  On the other hand, viewing a sink C as a (reduced) automaton C = (C, Σ, δ| C , p, F ∩C) with p being an arbitrary state of C we get that the transition semigroup of C consists of nonpermutational transformations  ... 
doi:10.14232/actacyb.22.3.2016.9 fatcat:xrfbkivuuzgqjan7miaelavjn4