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arXiv · 2005.05907

Ideal Separation and General Theorems for Constrained Synchronization and their Application to Small Constraint Automata

Stefan Hoffmann
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Abstract

In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the computational complexity. Additionally, we state a theorem giving PSPACE-hardness that broadly generalizes previously used constructions and a result on how to combine languages by concatenation to get polynomial time solvable constrained synchronization problems. We use these results to give a classification of the complexity landscape for small constraint automata of up to three states.

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Stefan Hoffmann. 2020-05-12. Ideal Separation and General Theorems for Constrained Synchronization and their Application to Small Constraint Automata. https://arxiv.org/abs/2005.05907

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