Araújo, JoãoBentz, WolframCameron, Peter J.2015-03-232015-03-232013Araújo, João; Bentz, Wolfram; Cameron, Peter - Groups synchronizing a transformation of non-uniform kernel. "Theoretical Computer Science" [Em linha]. ISSN 0304-3975. Vol. 498 (2013), p. 1-150304-3975http://hdl.handle.net/10400.2/3794Suppose that a deterministic finite automata A = (Q ,Σ) is such that all but one letters from the alphabet Σ act as permutations of the state set Q and the exceptional letter acts as a transformation with non-uniform kernel. Which properties of the permutation group G generated by the letters acting as permutations ensure that A becomes a synchronizing automaton under every possible choice of the exceptional letter (provided the exceptional letter acts as a transformation of non-uniform kernel)? Such permutation groups are called almost synchronizing. It is easy to see that an almost synchronizing group must be primitive; our conjecture is that every primitive group is almost synchronizing. Clearly every synchronizing group is almost synchronizing. In this paper we provide two different methods to find non-synchronizing, but almost synchronizing groups. The infinite families of examples provided by the two different methods have few overlaps. The paper closes with a number of open problems on group theory and combinatorics.engAlgebraic theory of languages and automataComplexity classesComputational methodsFinite automorphism groups of algebraicGeometric, or combinatorial structuresPrimitive groupsPseudo-coresSemigroups in automata theorySemigroups of transformationsShronizing automataGroups synchronizing a transformation of non-uniform kerneljournal articledoi:10.1016/j.tcs.2013.06.016