New tools for state complexity
Pascal Caron, Edwin Hamel-De le court, Jean-Gabriel Luque, Bruno, Patrou
TL;DR
This paper introduces new theoretical tools called monsters and modifiers to analyze state complexity in automata, simplifying the calculation of complexities for language transformations like star of intersection and square root.
Contribution
It presents the concepts of monsters and modifiers as novel frameworks for understanding and computing state complexity in automata theory.
Findings
Simplified calculation of state complexity for star of intersection
Determined state complexity of the square root operation
Introduced theoretical tools for automata analysis
Abstract
A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language transformation algorithms in terms of modifier and monster. These new theoretical concepts allow one to find easily some state complexities. We illustrate this by retrieving the state complexity of the Star of Intersection and the one of the Square root operation.
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