An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
On the disjunctive set problem
Theoretical Computer Science - Special issue: papers dedicated to the memory of Marcel-Paul Schützenberger
Descriptional complexity of deterministic finite automata with multiple initial states
Journal of Automata, Languages and Combinatorics
Automata, Languages, and Machines
Automata, Languages, and Machines
On the state complexity of k-entry deterministic finite automata
Journal of Automata, Languages and Combinatorics - Special issue: selected papers of the second internaional workshop on Descriptional Complexity of Automata, Grammars and Related Structures (London, Ontario, Canada, July 27-29, 2000)
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Multiple-entry finite automata
Journal of Computer and System Sciences
Automata with extremal minimality conditions
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Slowly synchronizing automata and digraphs
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Some remarks on automata minimality
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Never minimal automata and the rainbow bipartite subgraph problem
DLT'11 Proceedings of the 15th international conference on Developments in language theory
A graph theoretic approach to automata minimality
Theoretical Computer Science
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In this paper we investigate the minimality problem of DFAs by varying the set of final states. In other words, we are interested on how the choice of the final states can affect the minimality of the automata. The state-pair graph is a useful tool to investigate such a problem. The choice of a set of final states for the automaton A defines a coloring of the closed components of the state-pair graph and the minimality of A corresponds to a property of these colored components. A particular attention is devoted to the analysis of some extremal cases such as, for example, the automata that are minimal for any choice of the subset of final states F from the state set Q of the automaton (uniformly minimal automata), the automata that are minimal for any proper subset F of Q (almost uniformly minimal automata) and the automata that are never minimal, under any assignment of final states (never-minimal automata). More generally, we seek to characterize those families of automata and show that some of them are related to well-known objects in a different context (e.g. multiple-entry automata and Fischer covers of irreducible sofic shifts in Symbolic Dynamics). Next, we study the complexity of the related decision problems and show, in some cases, how to derive a polynomial algorithm. Finally, we pay particular attention to the relationship between the problem to decide if an automaton is never-minimal and the ''syntactic monoid problem''.