
Constrained Synchronization and Subset Synchronization Problems for Weakly Acyclic Automata
We investigate the constrained synchronization problem for weakly acycli...
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Computational Complexity of Synchronization under Regular Commutative Constraints
Here we study the computational complexity of the constrained synchroniz...
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Constraint Synchronization with Two or Three State Partial Constraint Automata
Here, we study the question if synchronizing words exist that belong to ...
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On synchronization of partial automata
A goal of this paper is to introduce the new construction of an automato...
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ComplexityTheoretic Aspects of Expanding Cellular Automata
The expanding cellular automata (XCA) variant of cellular automata is in...
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Distributed graph problems through an automatatheoretic lens
We study the following algorithm synthesis question: given the descripti...
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Synchronization under Dynamic Constraints
Imagine an assembly line where a box with a lid and liquid in it enters in some unknown orientation. The box should leave the line with the open lid facing upwards with the liquid still in it. To save costs there are no complex sensors or image recognition software available on the assembly line, so a reset sequence needs to be computed. But how can the dependencies of the deforming impact of a transformation of the box, such as 'do not tilt the box over when the lid is open' or 'open the lid again each time it gets closed' be modeled? We present three attempts to model constraints of these kinds on the order in which the states of an automaton are transitioned by a synchronizing word. The first two concepts relate the last visits of states and form constraints on which states still need to be reached, whereas the third concept concerns the first visits of states and forms constraints on which states might still be reached. We examine the computational complexity of different variants of the problem, whether an automaton can be synchronized with a word that respects the constraints defined in the respective concept, and obtain nearly a full classification. While most of the problems are PSPACEcomplete we also observe NPcomplete variants and variants solvable in polynomial time. We will also observe a drop of the complexity if we track the orders of states on several paths simultaneously instead of tracking the set of active states. Further, we give upper bounds on the length of a synchronizing word depending on the size of the input relation and show that the Cerny conjecture holds for partial weakly acyclic automata.
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